Quantum field theory
Competences to be gained during study
— Capacity to effectively identify, formulate and solve problems, and to critically interpret and assess the results obtained.
— Knowledge forming the basis of original thinking in the development or application of ideas, typically in a research context.
— 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.
— 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.
— 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.
— Skills to enable lifelong self-directed and independent learning.
— Capacity to communicate, give presentations and write scientific articles in English on fields related to the topics covered in the master’s degree.
— Capacity to critically analyze rigour in theory developments.
— Capacity to acquire the necessary methodological techniques to develop research tasks in the field of study.
— Capacity to analyze and interpret a physical system in terms of the relevant scales of energy.
— Capacity to identify relevant observable magnitudes in a specific physical system.
— 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).
— Capacity to critically analyze the results of calculations, experiments or observations, and to calculate possible errors.
Learning objectives
Referring to knowledge
— Learn to renormalise at one-loop scalar theories and QED.
— Understand the consequences of exact and approximate symmetries.
Teaching blocks
1. Classical field theory
* 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
2. Quantisation of free field theory
* 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
3. Interactive field theory
* 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
4. Path integral quantisation
* 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
5. Renormalisation
* 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
Teaching methods and general organization
Lectures. Expository classes. Problem-solving sessions.
Official assessment of learning outcomes
Assessment is based on problem-solving activities carried out throughout the course.
Repeat assessment consists of an examination in June.
Reading and study resources
Check availability in Cercabib
Book
Peskin, Michael E. ; Schroeder, Daniel V. An Introduction to quantum field theory. Reading (Mass.) : Addison Wesley, 1998 Enllaç
https://cercabib.ub.edu/discovery/search?vid=34CSUC_UB:VU1&search_scope=MyInst_and_CI&query=any,contains,b1330066* Enllaç
Banks, Tom. Modern quantum field theory : a concise introduction. Cambridge : Cambridge University Press, 2008 Enllaç
Ramond, Pierre. Field theory : a modern primer. 2a ed. Reading : Addison-Wesley, cop. 1989. Enllaç
Srednicki, Mark. Quantum field theory, Cambridge : Cambridge University Press, 2007 Enllaç
Weinberg, Steven. The Quantum theory of fields v. 1. Cambridge [etc.] : Cambridge University Press, 1995-1996 Enllaç
Zee, A. Quantum field theory in a nutshell. 2nd ed. Princeton : Princeton University Press, cop. 2010 Enllaç Ed. 2003
More information at: http://grad.ub.edu/grad3/plae/AccesInformePDInfes?curs=2023&assig=568427&ens=M0D0B&recurs=pladocent&n2=1&idioma=ENG
Presential
FALSE
Quantum field theory
Funded by the European Union. Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or HaDEA. Neither the European Union nor the granting authority can be held responsible for them. The statements made herein do not necessarily have the consent or agreement of the ASTRAIOS Consortium. These represent the opinion and findings of the author(s).
