. "Quantum Physics And Technology"@en . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . "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" . . "Master in Astrophysics, Particle Physics and Cosmology"@en . . "https://web.ub.edu/en/web/estudis/w/masteruniversitari-m0d0b" . "60"^^ . "Presential"@en . "The master's degree Astrophysics, Particle Physics and Cosmology of the University of Barcelona is intended for holders of bachelor's degrees and equivalent undergraduate degrees (particularly in physics), engineers and technical engineers who wish to pursue a specialization in one of the following branches of knowledge: astrophysics and space sciences; atomic, nuclear and particle physics; or gravitation and cosmology. The duration and specific content will depend on each applicant's previous studies.\nThe master's degree seeks to provide students with the training needed to conduct research in one of the fields listed above or in a related field, thanks to the interdisciplinary subjects also included in the program.\n\nThe course focuses on preparing students to begin a doctoral thesis upon completion of their degree, enabling them to pursue an academic career. However, it also provides highly valuable training for a career in the public or private sector, opening up a wide range of employment options.\n\nObjectives\nThe objectives of the master's degree are to provide students with advanced academic training in the fields of astrophysics, space sciences, atomic, nuclear and particle physics, gravitation and cosmology. More specifically, the objectives are:\n\n\n\nto study the content of a carefully selected set of subjects;\n\nto acquire the work methodology needed for conducting research and completing a doctoral thesis in the above fields through the completion of one or more research projects during the program;\n\nto acquire the skills needed to give scientific presentations;\n\nto acquire the competences, skills and abilities required to join a research group and complete doctoral studies or eventually join companies that pursue developments related to research in the mentioned fields.\n\nCompetences\nThe generic competences obtained by students will be instrumental (such as the capacity for analysis and synthesis, a working knowledge of English, knowledge of software tools and decision-making skills), interpersonal (such as critical reasoning, teamwork and creativity), and systemic (such as the capacity for independent learning and the capacity to adapt to new situations).\n\nThe specific competences obtained by students will be the capacity to understand a physical system in terms of the relevant scales of energy, the capacity to identify observable magnitudes and the capacity to test predictions from theoretical models with experimental and observational data.\n\nAnother potential specific competence is the capacity to develop and apply new technologies."@en . . . "1"@en . "FALSE" . . . "Master"@en . "Thesis" . "1660.20" . "Euro"@en . "4920" . "None" . "Obtaining the Master's Degree in Astrophysics, Particle Physics and Cosmology is the first step towards undertaking a doctoral thesis in one of the research lines in the general fields of Astronomy and Astrophysics (astrophysics and space sciences) or Particle Physics and Gravitation (atomic, nuclear and particle physics, gravitation and cosmology). Some of the more applied syllabus content may also open professional doors to work in companies in the aerospace, energy, financial and communications sectors, among others, as these require specialists in the fields of space science, data processing and analysis, process simulation and advanced computation, etc."@en . "2"^^ . "TRUE" . "Upstream"@en . . . . . . . . . . . . . . . . . . . . .