. "Quantum Physics And Technology"@en . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . "Quantum field theory I"@en . . "5" . "LEARNING OUTCOMES\nThe student knows basics of relativistic quantum field theory and can apply the methodology to leading order scattering processes.\n\nCONTENT\nClassical field theory and quantization of free real and complex scalar fields.\n\nQuantization of free Dirac field.\n\nInteracting theories and development of perturbation theory. \n\nExamples in quantum electrodynamics.\n\nIntroduction to renormalisation." . . "Presential"@en . "FALSE" . . "Quantum field theory II"@en . . "5" . "LEARNING OUTCOMES\nThe student knows path integral formulation of quantum mechanics and field theory. The student can apply path integral methods to quantise abelian gauge theory. The student knows the need of renormalisation in quantum field theory.\n\nCONTENT\nPath integral formulation of quantum field theory.\n\nGrassmann variables and path integral for fermion fields.\n\nGenerating functionals\n\nGauge theory and its quantization\n\nRenormalisation of scalar field theory." . . "Presential"@en . "FALSE" . . "Quantum field theory III"@en . . "5" . "CONTENT\nSystematics of renormalization\n\nRenormalization group\n\nQuantization of Yang-Mills theory, BRST invariance\n\nRenormaliation of Yang-Mills theory, asymptotic freedom." . . "Presential"@en . "FALSE" . . "Quantum field theory Iv"@en . . "5" . "CONTENT\nSpontaneous symmetry breaking \n\nEffective potential in quantum field theory\n\nHiggs mechanism\n\nRenormalization of the electroweak theory\n\nAnomalies." . . "Presential"@en . "FALSE" . . "Path integral quantization of gauge field theories"@en . . "5" . "CONTENT\nBrief introduction to path integral as solution of diffusion equation. Path integrals in quantum mechanics. Quantization of systems with constraints. Path integrals in quantum field theory; generating functional; Schwinger action principle. Grassmann variables and path integrals for fermionic fields. Path integral quantization in QED. Path integral quantization of non-Abelian gauge field theories; Faddeev-Popov ghosts. Symmetries in functional formalism; Ward-Takahashi identities." . . "Presential"@en . "FALSE" . . "Quantum cryptography"@en . . "6" . "Description:\n Foundations of quantum cryptography.\nLearning outcomes:\nThe student understands the basics of quantum cryptography and is able to apply this knowledge in the context of cyber security research." . . "Presential"@en . "FALSE" . . "Introduction to quantum algorithms"@en . . "6" . "Description:\nQuantum mechanics for non-physicists; quantum circuit model of universal fault-tolerant quantum computing; basic quantum algorithms.\nLearning outcomes:\nAfter completing the course, the student will be familiar with quantum mechanics to the level that is essential for designing and analyzing quantum algorithms; with the quantum circuit model of universal fault-tolerant quantum computation; with the basic quantum algorithms." . . "Presential"@en . "FALSE" . . "Engineering of complex quantum systems"@en . . "5" . "no data" . . "Presential"@en . "FALSE" . . "advanced field theory"@en . . "6" . "no data" . . "Presential"@en . "FALSE" . . "electrodynamics and field theory"@en . . "6" . "1. Quantities describing electromagnetic field and its sources.\n1.1. Vector description.\n1.2. Tensor description.\n1.3. Differential forms.\n2. Maxwell field equations.\n2.1. Full form of the equations.\n2.2. Material equations.\n2.3. Differential form of field equations.\n2.4. Field discontinuities.\n3. Maxwell's methods of solving equations.\n3.1. Behavioural laws.\n3.2. The problem of unambiguity.\n3.3. Potential Theory.\n4. Relativistic formulation of electrodynamics.\n4.1. Einstein's principle of relativity.\n4.2. Minkowski's spacetime.\n4.3. Maxwell's equations in covariant form.\n4.4. Lorentz transformation for electromagnetic field.\n4.5. Variational principle.\n5. Theory of radiation.\n5.1. Electromagnetic field in media.\n5.2. Radiation. The Lienard-Wührtt field.\n5.3. Stationary and static fields.\n5.4. Hamiltonian form of Maxwell's equations." . . "Presential"@en . "TRUE" . . "quantum optics 1"@en . . "5" . "Lecture (30 hrs)\n1. General information about the subject – a review (basic phenomena and processes, photons).\n Orders of magnitude and units of physical quantities characterizing atoms, optical fields and interaction between them. Estimating \nthe number of photons in a laser beam of given power and frequency. \n Examples of quantum behaviour: photon detection after its passing through a Mach-Zehnder interferometer, nondemolition \nmeasurement.\n Photon statistics: counting photons, statistics of the number of photons in a coherent beam, Poisson distribution and \"Poissonian, \nsuper-Poissonian and sub-Poissonian light\".\n2. Quantum theory of radiation\n Maxwell's equations (ME) for electric and magnetic fields, electromagnetic potentials, gauge\n ME in Fourier space (r,t) -> (kn, t), longitudinal and transverse components of electric and magnetic fields (\"electrostatics\" and \n\"radiation\")\n Polarization and radiation modes\n Dynamics of transverse fields, expression through normal variables \n Vector and scalar electromagnetic potentials in Fourier space, longitudinal and transverse components of the vector potential, \ngauge, evolution equations\n Coulomb gauge\n Energy of radiation field, expression through longitudinal and transverse components of the electric field and vector potential in \nthe Fourier space, analogy to a set of uncoupled harmonic oscillators\n Quantization rules, creation and ahhinilation operators, Hamiltonian and momentum operator, number operator, eigenstates and \neigenvalues of the Hamiltonian and momentum operator, radiation modes, photons.\n3. Quantum states of radiation\n Vacuum state and its basic properties.\n Single-mode states, Fock (number) and coherent (quasiclassical, Glauber) states, their basic properties and interpretation. \nMultimode states. \n Single- and multimode single-photon states.\n Beam splitter and its classical and quantum model. Input and output states. Single-photon experiments, Hong – Ou – Mandel (HOM) \neffect. \n Quadrature operators for radiation fields (definition, commutation rules, Heisenberg relations).\n Squeezed states of radiation (definitnion, properties, generation scheme in a parametric process).\n4. Interaction of electromagnetic fields with atomic systems\n Time-dependent perturbation theory, transition amplitude and probability, transitions among discrete states and from discrete to \ncontinuous spectrum.\n Interaction of atomic systems with classical electromagnetic fields (interaction Hamiltonian, electric – dipole and magnetic –\ndipole interaction, absorption and stimulated emission).\n \"Exactly solvable\" models:Rabi model, Weisskopf-Wigner model..\n Remarks on more complicated cases: more levels, more fields.\nExercises (30 hrs)\n5. Harmonic oscillator. A review of the subject (a, a+ and n = a+a operators, their basic properties and algebra, eigenstates and eigenvalues of \nharmonic oscillator Hamiltonian). Coherent states of harmonic oscillator and their properties: definition, decomposition in the Fock basis, \nPoissonian statistics of excitation numbers, graphical representation, temporal evolution, Heisenberg relations, quasiorthogonality and \ncompleteness, displacement operator for generation operator of coherent states from vacuum state. \n6. A few operator relations. Functions of operators, commutation relations involving functions of operators, derivative of an operator, \nGlauber and Baker-Hausdorff formulas, displacement and squeezing operators.\n7. Spin ½ dynamics in a magnetic field as a prototype two-level system. Magnetic resonance, classical and quantum description, Bloch, \nSchroedinger and von Neumann equations, evolution of expectation value of magnetization. \n8. Optical Bloch equations" . . "Presential"@en . "TRUE" . . "quantum optics laboratory"@en . . "5" . "no data" . . "Presential"@en . "FALSE" . . "quantum information"@en . . "3" . "1. Basic theory of convex sets 2. Basic theory of classical channels and measurements 3. Quatnum mechanics as a on-commutative generalisation of probility calculus. 4. Postulates of quantum mechanics in comparison to classical theory 4. Basics of theory of spin 5. Qubit states and dynamics in Bloch ball 6. Uncertainty principle in Bloch ball 7. Quantum channels and POVMs 8. Composite system and dilation theorems 9. Distinguishability of quantum states 10. Processing states of photon polarisation 11. No-cloning theorem and BB84 protocol 10. CHSH inequality, non-kolmogorovness of quantum theory and no-signaling condition 11. Quantum teleportation 12. Measures and criteria of entanglement 13. Quantum Shor algorithm 14. NMR realisation of quantum computer 15. Quantum tomography, estimation theory, MUBs and POVMs 16. Dynamics of open quantum systems, decoherence, quantum error-correcting codes" . . "Presential"@en . "FALSE" . . "quantum optics 2"@en . . "5" . "Lecture:\n1) Introduction: Single photon physics.\n2) Quantum information encoding in a single photon polarization state.\n3) Quantum communication protocols exploiting polarization states. Practical implementation: quantum key distribution. \n4) Single photon spatial mode and the methods of quantum states encoding. \n5) Multilevel quantum states -- generation and detection. Majorana representation.\n6) Practical implementations of quantum information processing based on spatial mode encoding. \n7) Parametric down conversion process -- quantum description and experimental methods.\n8) Single photon detection \n9) Phase space and Wigner function\nTutorials – calculations on selected problems, such as:\n1) simple examples on “quantum world” sizes,\n2) Bell states, Pauli matrices, transformations on Bloch sphere,\n3) coding information in single-photons' polarization states,\n4) quantum key distribution schemes, practical implementations,\n5) Helmholtz equation, gaussian beam, propagation in fibers, \n6) Jones matrices, optical networks,\n7) single photon spatial mode encoding,\n8) higher-dimensional entangled states generation methods,\n9) nonlinear processes, parametric down conversion, phase matching conditions,\n10) “cat” states and Wigner function" . . "Presential"@en . "FALSE" . . "Quantum field theory"@en . . "no data" . "no data" . . "Presential"@en . "FALSE" . . "Advanced effective field theories"@en . . "5" . "no data" . . "Presential"@en . "TRUE" . . "Effects, superconducting electronics and superconducting quantum circuits"@en . . "5" . "no data" . . "Presential"@en . "TRUE" . . "Quantum electrodynamics"@en . . "6" . "Lagrangian formalism and Noether theorem. Quantization of scalar, Dirac and\nelectromagnetic fields. Klein-Gordon and Dirac equations. Feynman rules. S matrix and cross\nsections. Ward-Takahasi identities, LSZ reduction formulas, optical theorem." . . "Presential"@en . "FALSE" . . "Quantum black holes and holography"@en . . "6" . "1 The classical laws of black hole physics.\r\n2 Quantum field theory on black hole space-times and Hawking radiation\r\n3 The membrane paradigm\r\n4 Introduction to string theory\r\n5 Holography and the AdS/CFT conjecture.\r\n6 Black hole entropy\r\n7 Tensor network states and holography.\r\n8 Research topics: e.g. firewall problem, thermalisation and black holes, MERA and holography.\nFinal competences: \n1 Working knowledge of the present state of the research at the intersection of quantum\r\n1 mechanics and general relativity.\r\n2 With an emphasis on the physical principles and mathematical techniques, preparing for\r\n1 independent research." . . "Presential"@en . "FALSE" . . "Quantum computing"@en . . "6" . "• Quantum entanglement\r\n• Quantum computing\r\n• Quantum Tensor Networks\r\nFinal competences:\nBasic knowledge about quantum computing and quantum entanglement" . . "Presential"@en . "FALSE" . . "Quantum electrodynamics"@en . . "6" . "Quantum theory of the free e.m.field: Maxwell equations, global and local gauge symmetries,\r\nquantization of the e.m.field, state vectors of the e.m.field, coherent states. Interaction between\r\nradiation and matter, dipole radiation, photon scattering off electrons, Thompson cross-section,\r\nnatural linewidth. Second quantization: occupation number representation for bosons and\r\nfermions, relation to first quantization, field operators. Interacting quantum fields: FeynmannGoldstone diagrams. Application for nonrelativistic bremsstrahlung: Coulomb interaction,\r\nbremsstrahlung cross-section. Divergences and renormalization in QED: quantumfluctuations,\r\nCasimir effect. Renormalization of the electron mass: nonrelativistic approach, Lamb shift,\r\nmethod of Bethe. Electromagnetic coupling using the Dirac equation: minimal coupling,\r\ncovariant e.m. coupling. Foldy- Wouthuysen transformation: free particle, e.m.field, applicaton\r\nto the H-atom. Compton effect, Klein-Nishinaformula, charge conjugation in Dirac theory,\r\nparticle-antiparticle transformation, hole theory.\nFinal competences: \n1 Calculate autonomously electromagnetic processes in different branches of modern physics.\r\n2 Have a coherent overview of electromagnetic processes in astrophysics, elementary particle physics, nuclear physics, atomic and molecular physics.\r\n3 Evaluate and apply the contents of the specialized literature on these topics.\r\n4 Give a clear presentation on a chosen subject matter related to QED.\r\n5 Analyze and solve complex problems in QED." . . "Presential"@en . "FALSE" . . "Quantum field theory"@en . . "6" . "The combination of quantum mechanics with the laws of special relativity requires the introduction of a new framework: relativistic quantum field theory. This course introduces the concepts and techniques of quantum field theory using a realistic theory: quantum electrodynamics (QED). This is the theory which provides a microscopic description of electrically charged particles interacting through the electro-magnetic force.\r\n\r\nAfter introducing the free Maxwell and Dirac fields, interactions are introduced in a systematic way. The full theory is then treated using time dependent perturbation theory - translated in the form of Feynman diagrams and rules.\r\n\r\nSubsequently we use this to analyze several standard processes in QED: pair production, scattering in an external field, Compton scattering, ...\r\n\r\nNext radiative corrections are studied thereby introducing the concepts of regularization and renormalization. The course ends with a brief introduction to the generalization of QED to the other fundamental interactions.\nGENERAL COMPETENCIES\r\nRelativistic quantum fiel theory is a new conceptual layer in physics relevant when studying natural phenomena at small scales where the laws of quantum mechanics and special relativity apply simultaneously.\r\n\r\nThe course aims at a good understanding of the foundational principles of quantum field theory while simultaneously the student will enlarge his technical and analytical skills such as to be able to analyze complex realistic problems.\r\n\r\nAs quantum field theory is one of the basic topics in theoretical physics, the course provides the foundation for numerous other courses." . . "Presential"@en . "TRUE" . . "Strongly correlated quantum systems"@en . . "6" . "1 Introduction: second quantisation, interacting electrons, the Hubbard model and itsdescendants\n2 Quantum Ising model in transverse magnetic field: exact solution via Jordan Wigner, Fourier and Bogoliubov transform. Quantum phase transitions and criticality. Order an disorder. Duality. Excitations and domain walls. Entanglement entropy: area laws and logarithmic divergence.\n3 Half-integer spin chains: Heisenberg antiferromagnets, Lieb-Schultz-Mattis theorem, order and disorder, Goldstone-bosons, Mermin-Wagner theorem, exact solution via coordinate Bethe ansatz.\n4 Integer spin chains: Haldane’s conjecture, Affleck-Kennedy-Tasaki-Lieb model, introduction to MPS (Matrix Product States) and tensor networks. Gapless edge modes and symmetry protected topological order.\n5 Topological classification of free fermion systems: periodic table of topological insulators and superconductors, Su-Schriefer-Heeger model and Kitaev’s quantum wire: topological.\ndegeneracy and majorana edge modes.\r\n6 Spin models in higher dimensions, spin liquids, gauge theories and Kitaev's toric code\r\n1 model, topological order and anyons\r\nThere will also be a group project, which can be chosen as either a literature review (e.g.\r\nquantum hall effect, Levin-Wen string net models, topological insulators, entanglement\r\nrenormalization for critical systems, entanglement entropy in conformal field theory, …) or\r\n(density matrix renormalization group algorithm, tensor renormalization group, …)." . . "Presential"@en . "FALSE" . . "Quantum theory of condensed matter"@en . . "6" . "Specific Competition\nCE6 - Understand the structure of matter being able to solve problems related to the interaction between matter and radiation in different energy ranges\nCE11 - Know how to use current astrophysical instrumentation (both in terrestrial and space observatories) especially that which uses the most innovative technology and know the fundamentals of the technology used\nGeneral Competencies\nCG1 - Know the advanced mathematical and numerical techniques that allow the application of Physics and Astrophysics to the solution of complex problems using simple models\nBasic skills\nCB6 - Possess and understand knowledge that provides a basis or opportunity to be original in the development and/or application of ideas, often in a research context\nCB7 - That students know how to apply the knowledge acquired and their ability to solve problems in new or little-known environments within broader contexts\nCB8 - That students are able to integrate knowledge and face the complexity of formulating judgments based on information that, being incomplete or limited, includes reflections on the social and ethical responsibilities linked to the application of their knowledge and judgments\nCB10 - That students possess the learning skills that allow them to continue studying in a way that will be largely self-directed or autonomous\nExclusive to the Structure of Matter Specialty\nCX13 - Understand in depth the basic theories that explain the structure of matter and collisions as well as the state of matter in extreme conditions\nCX14 - Understand the interrelation between atoms, molecules and radiation and diagnostic tools for the state of matter from the spectrum\nCX16 - Understand the mechanisms of electromagnetic wave propagation and the dynamics of charged particles\n6. Subject contents\nTheoretical and practical contents of the subject\n- Professor: Fernando Delgado Acosta\n- Topics:\nSymmetry in crystals. Theory of crystalline solids.\nBorn-Oppenheimer approximation. Ionic and electronic Hamiltonian.\nVibrations in the network. Experimental techniques to investigate the vibration spectrum.\nElectrons in a lattice: Non-interacting electrons in a periodic lattice.\nElectrons in a periodic lattice and the Bragg-Laue condition.\nApproximation of localized electrons: \" tight-binding \" models.\nBloch's theorem: effective mass, speed of electrons. \nBand theory: band filling, material classification.\ninteracting electrons\nSecond quantization: fermionic and bosonic field operators.\nMedium field approaches. Hartree, Hartree-Fock. Exchange and correlation. Density functional theory.\nLinear response theory. Dielectric function and magnetic susceptibility.\nTransport.\nSemiclassical transport: Boltzman equation. Conductivity and heat conduction.\nElectromagnetic waves in high magnetic fields.\nQuantum transport. Ballistic transport. Landauer formula and quantization of conductance. Tunneling and Coulomb blockage regime .\nOptical properties\nReview of fundamental relationships for optical phenomena.\nContribution of free charges. Plasmons. Interband transitions.\nLight absorption in solids. Impurities. Luminescence and photoconductivity.\n\nPractices preferably applied to materials of geophysical or astrophysical interest, although initially simple systems will be used as a model to obtain results in a reasonable time. Emphasis will be placed on the choice of the case study, its current state and the establishment of viable objectives according to the knowledge and means available." . . "Presential"@en . "FALSE" . . "Quantum field theory"@en . . "6.0" . "https://sigarra.up.pt/fcup/en/ucurr_geral.ficha_uc_view?pv_ocorrencia_id=509349" . . "Presential"@en . "FALSE" . . "Introduction to quantum computing for ai and data science"@en . . "6.0" . "In this course we lay down the foundations and basic concepts of quantum computing. We will use the mathematical formalism borrowed from quantum mechanics to describe quantum systems and their interactions. We introduce the concept of a quantum bit and discuss different physical realizations of it. We then introduce the basic building blocks of quantum computing: quantum measurements and quantum circuits, single and multi-qubit gates, the difference between correlated (entangled) and uncorrelated states and their representation, quantum communication, and basic quantum protocols and quantum algorithms. Finally, we discuss the different types of noise involved in real quantum computers (coherent and incoherent errors, state preparation, projection and measurement) and their effect on performance, and outline current efforts for mitigating the issues.\n\n!! This course is a prerequisite for the planned elective courses Quantum Algorithms, Quantum AI, and Quantum Information and Security, which will be offered in Semester 1 of the upcoming academic year 2024-2025. These four courses, together with a dedicated research project on quantum computing forms the specialization in Quantum Computing for AI and Data Science.\n\nPrerequisites\nNone.\n\nDesired prior knowledge: probability theory, linear algebra, design and analysis of algorithms\n\n!! This course is a prerequisite for the planned elective courses Quantum Algorithms, Quantum AI, and Quantum Information and Security, which will be offered in Semester 1 of the upcoming academic year 2024-2025. These four courses, together with a dedicated research project on quantum computing forms the specialization in Quantum Computing for AI and Data Science.\n\nMore information at: https://curriculum.maastrichtuniversity.nl/meta/477741/introduction-quantum-computing-ai-and-data-science" . . "Presential"@en . "FALSE" . . "Gauge theory: the standard model"@en . . "6.0" . "Learning objectives\n\nReferring to knowledge\n\nBegin to develop an understanding of the technicalities and common characteristics of gauge theories, such as quantum electrodynamics (QED), quantum chromodynamics (QCD) and electroweak theory.\n\nUnderstand and be able to easily use the characteristic techniques of field theories with gauge symmetry: Feynman diagram, dimensional regularisation, renormalisation groups.\nLearn the fundamental principles of the standard model in elemental interactions: structure, symmetries, radiative corrections and renosmalisation.\nLearn other key aspects of field theories in fundamental interactions.\n\n \n\n \n\nTeaching blocks\n\n \n\nIntroduction: Gauge symmetry and spin-one particles\n* Global symmetries of a theory with N Dirac fermions: covariant derivatives, massless vector fields and the Gauge principle\n\n\nQuantum representations of the Lorentz group and one-particle states. Massless and massive spin-1 particles\n\n\nWard Identity in Compton scattering: One photon case (QED), and N photon case (YM)\n\nNon-Abelian Gauge Theory\n* \n\nConnected Lie group of transformations: Structure constants and Lie Algebra. N-dimensional representations: Adjoint representation, Fundamental representation, and the case of SU(N). Complex, real and pseudo-real representations. Expressing a field in the adjoint representation of SU(N) as a linear combination of the generators in the fundamental representation.\n\n \n\nLocal SU(N) symmetry. Non abelian covariant derivative, Non-abelian Gauge fields, Feynman rules for YM coupled to fermions, and Gauge boson self-interactions. Theta term.\n\n \n\nExtension to more general symmetry groups. U(1) subalgebras, Compact simple subalgebras, and the Cartan catalog. The covariant derivative in the Standard Model.\n\n \nSpontaneous Symmetry Breaking (SSB) and Anomalies\n* \n\nSSB and the Linear Sigma Model: Goldstone’s theorem. Broken and unbroken generators. Flavor symmetry and Pions as Goldstone bosons.\n\n \n\nSSB in gauge theories: the Higgs Mechanism: The U(1) case, photon mass terms, transversity of the vaccuum polarization and the unitarity gauge.The Non-Abelian case: broken generators and gauge-boson mass matrix.\n\n \n\nQuantization of gauge theories with SSB: The U(1) case, Faddeev Popov, R_xi gauges and Ghosts. Fermion-antifermion scattering: Gauge-independence, the role of Goldstones, and the Unitarity gauge. Extension to the non-abelian case.\n\n \n\nAnomalous Symmetries\nQuantisation of gauge theories\n* \n\nPath integral quantization: Generating functional, correlation functions, Green’s functions and propagators.\n\nQuantization of U(1) gauge theory and the Faddeev-Popov method.\n\n \n\nFaddeev-Popov for Non-Abelian YM: Functional determinants, fermionic path integrals, functional determinants for fermions, and the Faddeev-Popov determinant in the non-abelian case, Gauge fixing and Ghosts. Feynman rules for YM theory.\n\n \n\nWard identity and unitarity in Non-Abelian YM theory: Optical theorem. The case of fermion-antifermion annihilation in YM theory: how Ghosts restore unitarity by cancelling unphysical gauge-boson polaizations.\nRadiative corrections in gauge theories\n* Divergent structure of gauge theories\n\nRenormalisation and counter-terms in QCD\nThe meaning of the renormalisation procedure\nCalculation of the beta function in QCD\nThe renormalisation group and fixed points\nThe R parameter and renormalisation ambiguities\nDecoupling of heavy quarks\n\nThe limits of perturbation theory\n* Confinement\n\nInfrared divergences: inclusive and exclusive processes\nThe operator product expansion\nPower corrections to R\n\nGauge structure of the electroweak theory\n* Summary of known results: the origin of the SU(2)xU(1) weak group\n\nUnitarity bounds and renormalization issues of Weak theories\n\nGauges and gauge fixing; Physical states\n\nMass generation and spontaneous symmetry breaking\n\nYukawa Interactions: Fermion masses and the CKM matrix.\n\nNeutrino Mass and the see-saw mechanism and the PMNS matrix.\n\nAnomaly Cancellation in Gauge Theories\n\nThe electroweak theory beyond tree level\n* Custodial Symmetry and Higgs Effective Theory. Electroweak Precision observables: Delta rho.\n\nFCNC transitions, the GIM mechanism, CP symmetry and CP violation in kaons and other neutral systems\n\nWeak effective theories: Wilson Coefficient, Matching, Anomalous dimensions and Renormalization group equations\n\n \n\n \n\nTeaching methods and general organization\n\n \n\nLecturers explain the different teaching blocks during face-to-face sessions.\n\nStudents solve weekly set exercises.\n\n \n\n \n\nOfficial assessment of learning outcomes\n\n \n\nIndependent study: questions, activities, attitude in class, formality and quality of submitted exercises: 10%\n\nSet exercises: 50%\n\nFinal examination: 40%\n\nRepeat assessment criteria: repeat assessment follows the same criteria as regular assessment and consists of a final exam.\n\n \n\nExamination-based assessment\n\nWritten final exam: 100%\n\nRepeat assessment criteria: repeat assessment follows the same criteria as regular assessment and consists of a final exam.\n\n \n\n \n\nReading and study resources\n\nCheck availability in Cercabib\n\nBook\n\nCheng, Ta-Pei ; Li, Ling-Fong. Gauge theory of elementary particle physics. Oxford : Clarendon Press ; New York : Oxford University Press, 2000 Enllaç\n\nEd. 1984 Enllaç\n\nGeorgi, Howard. Weak interactions and modern particle theory. Mineola, N.Y. : Dover Publications, 2009 Enllaç\n\n\nKaku, Michio. Quantum field theory : a modern introduction. New York [etc.] : Oxford University Press, 1993 Enllaç\n\n\nPeskin, Michael E. ; Schroeder, Daniel V. An introduction to quantum field theory. Reading (Mass.) [etc.] : Addison-Wesley, cop. 1995 Enllaç\n\n\nRamond, Pierre. Field theory : a modern primer. Redwood City, Calif. [etc.] : Addison-Wesley Pub Co, cop. 1989 Enllaç\n\n\nTaylor, John Clayton. Gauge theories of weak interactions. Cambridge : Cambridge University Press, 1976\n\nMore information at: http://grad.ub.edu/grad3/plae/AccesInformePDInfes?curs=2023&assig=568436&ens=M0D0B&recurs=pladocent&n2=1&idioma=ENG" . . "Presential"@en . "FALSE" . . "Quantum field theory"@en . . "6.0" . "Competences to be gained during study\n\n— Capacity to effectively identify, formulate and solve problems, and to critically interpret and assess the results obtained.\n\n— Knowledge forming the basis of original thinking in the development or application of ideas, typically in a research context.\n\n— Capacity to apply the acquired knowledge to problem-solving in new or relatively unknown environments within broader (or multidisciplinary) contexts related to the field of study.\n\n— Capacity to integrate knowledge and tackle the complexity of formulating judgments based on incomplete or limited information, taking due consideration of the social and ethical responsibilities involved in applying knowledge and making judgments.\n\n— Capacity to communicate conclusions, judgments and the grounds on which they have been reached to specialist and non-specialist audiences in a clear and unambiguous manner.\n\n— Skills to enable lifelong self-directed and independent learning.\n\n— Capacity to communicate, give presentations and write scientific articles in English on fields related to the topics covered in the master’s degree.\n\n— Capacity to critically analyze rigour in theory developments.\n\n— Capacity to acquire the necessary methodological techniques to develop research tasks in the field of study.\n\n— Capacity to analyze and interpret a physical system in terms of the relevant scales of energy.\n\n— Capacity to identify relevant observable magnitudes in a specific physical system.\n\n— Capacity to understand and apply general gravitation theories and theories on the standard model of particle physics, and to learn their main experimental principles (specialization in Particle Physics and Gravitation).\n\n— Capacity to critically analyze the results of calculations, experiments or observations, and to calculate possible errors.\n\n \n\n \n\n \n\n \n\nLearning objectives\n\n \n\nReferring to knowledge\n\n— Learn to renormalise at one-loop scalar theories and QED.\n\n— Understand the consequences of exact and approximate symmetries.\n\n \n\n \n\nTeaching blocks\n\n \n\n1. Classical field theory\n* Motivations: from the quantum theory of relativistic particles to the quantum theory of fields; Classical field theory; Functional derivative; Lagrangian and Hamiltonian formulations; Noether’s theorem and conservation laws; Poincaré group generators\n\n2. Quantisation of free field theory\n* Harmonic oscillator and real scalar field; Canonical quantisation of real scalar fields; Klein Gordon equation; Microcausality; Propagators for the Klein-Gordon equation: retarded propagator and Feynman propagator; Particle creation by a classical source; Complex scalar field; Quantisation of the Dirac field; Quantisation of the electromagnetic field\n\n3. Interactive field theory\n* The Ø^4 interaction; Interaction picture; Time evolution operator; Correlation function; Wick’s theorem; Feynman diagrams; Feynman rules; Feynman rules for QED; Disconnected diagrams; Källén-Lehmann spectral representation; Collisions and S-matrix; LSZ reduction formula; Feynman diagrams, and KL and KLS formulas; 1PI diagrams and self-energy\n\n4. Path integral quantisation\n* Path integrals and quantum mechanics; Functional quantisation of the scalar field; Correlation function; Feynman rules for Ø^4 theory; Function generator; Interactions; Functional quantisation of spinor fields; Schwinger-Dyson equations; Conservation laws: Ward-Takahashi identity\n\n5. Renormalisation\n* Ultraviolet divergences and renormalised theories; Renormalised perturbation theory; Dimensional regularisation; Feynman parameters; One-loop renormalisation of Ø^4 theory; One-loop renormalisation of QED; Counterterms; Two-loop renormalisation of Ø^4 theory; Callan-Symanzik equation; Evolution of coupling constants\n\n \n\n \n\nTeaching methods and general organization\n\n \n\nLectures. Expository classes. Problem-solving sessions.\n\n \n\n \n\nOfficial assessment of learning outcomes\n\n \n\nAssessment is based on problem-solving activities carried out throughout the course.\n\n \n\nRepeat assessment consists of an examination in June.\n\n \n\n \n\nReading and study resources\n\nCheck availability in Cercabib\n\nBook\n\nPeskin, Michael E. ; Schroeder, Daniel V. An Introduction to quantum field theory. Reading (Mass.) : Addison Wesley, 1998 Enllaç\n\nhttps://cercabib.ub.edu/discovery/search?vid=34CSUC_UB:VU1&search_scope=MyInst_and_CI&query=any,contains,b1330066* Enllaç\n\nBanks, Tom. Modern quantum field theory : a concise introduction. Cambridge : Cambridge University Press, 2008 Enllaç\n\n\nRamond, Pierre. Field theory : a modern primer. 2a ed. Reading : Addison-Wesley, cop. 1989. Enllaç\n\n\nSrednicki, Mark. Quantum field theory, Cambridge : Cambridge University Press, 2007 Enllaç\n\n\nWeinberg, Steven. The Quantum theory of fields v. 1. Cambridge [etc.] : Cambridge University Press, 1995-1996 Enllaç\n\n\nZee, A. Quantum field theory in a nutshell. 2nd ed. Princeton : Princeton University Press, cop. 2010 Enllaç Ed. 2003\n\nMore information at: http://grad.ub.edu/grad3/plae/AccesInformePDInfes?curs=2023&assig=568427&ens=M0D0B&recurs=pladocent&n2=1&idioma=ENG" . . "Presential"@en . "FALSE" . . "Quantum physics"@en . . "6.0" . "http://grad.ub.edu/grad3/plae/AccesInformePDInfes?curs=2023&assig=569100&ens=M0D0G&recurs=pladocent&n2=1&idioma=ENG" . . "Presential"@en . "FALSE" .