. "Quantum Physics And Technology"@en . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . "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" . . "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 . . . . . . . . . . . . . . . . . . . . .