Description and contextualization of the subject

El objetivo será ampliar lo visto en la asignatura obligatoria de Teoría Cuántica de Campos, donde se ha hecho una introducción general al tema. Se avanzará en la descripción de campos fermiónicos y vectoriales, además de campos de gauge no abelianos. Se introducirá y utilizará el formalismo de la Integral de Caminos para cuantizar teorías de campos gauge abelianos y no abelianos, como la Electrodinámica Cuántica, la Cromodinámica Cuántica y la teoría Electrodébil.

Learning outcomes of the subject

Knowledge or content:

RCO1. Demonstrate the ability to explain the fundamental principles of the quantum world, both at a basic and technical level.

RCO2. Have a basic knowledge of the relevant literature in quantum mechanics and be capable of effectively reading and understanding research articles.

RCO3. Be able to initiate the development of original ideas and applications within the context of quantum physics research.

RCO4. Possess the capacity for independent research, synthesis, and be able to present in a clear and structured way complex issues related to the various areas of quantum mechanics addressed in this Master¿s program.

RCO5. Under supervision, demonstrate the ability to write and defend original work that meets the quality standards required for publication in high-impact indexed journals.

RCO8. Know the basic literature and demonstrate the ability to solve standard problems in the field of Quantum Field Theory.

RCO9. Know the basic literature and demonstrate the ability to solve standard problems in the field of Quantum Statistical Physics.

RCO10. Know the basic literature and demonstrate the ability to solve standard problems in the field of Fields and Particle Physics.



Competencies:

RC1. Possess and understand knowledge that provides a basis or opportunity for developing and/or applying original ideas, often in a research context.

RC2. Apply acquired knowledge and problem-solving skills in new or unfamiliar environments within broader (or multidisciplinary) contexts related to their field of study.

RC3. Demonstrate the ability to integrate knowledge and address the complexity of formulating judgments based on incomplete or limited information, including reflection on social and ethical responsibilities linked to the application of their knowledge and judgments.

RC4. Communicate conclusions, as well as the underlying knowledge and rationale, clearly and unambiguously to both specialized and non-specialized audiences.

RC5. Possess learning skills that enable continued study in a largely self-directed or autonomous manner.



Abilities or skills:



RHE1. Demonstrate proficiency in using tools for bibliographic resource searches.

RHE2. Exhibit critical capacity to read research articles and incorporate their findings into one¿s own work.

RHE3. Write and present original work in one of the official languages and in English.

RHE4. Communicate scientific concepts and results clearly and effectively to both specialized and non-specialized audiences, through presentations and publications.

RHE5. Demonstrate the ability for autonomous learning and staying current with scientific and technological advances.





RHT1. Understand and apply the fundamental principles of quantum mechanics to analyze and solve problems in basic research in quantum science.

RHT2. Understand and apply the fundamental principles of quantum mechanics to analyze and solve problems in quantum technology.

RHT3. Effectively integrate into a fundamental or applied research project involving quantum aspects, and solve problems in multidisciplinary environments.

RHT4. Evaluate and select appropriate tools and techniques for research in fundamental physics.

Temary

1. Quantum Electrodynamics. Dirac equation, Lorentz symmetry, quantization of fermion field, Dirac propagator, quantization of vector field, gauges symmetries and gauge fields, basic QED processes, renormalization (1-loop).



2. Path Integral formalism. Path integral (PI) in quantum mechanics, PI for scalar fields and Feynman rules, generating functional, effective action, PI for fermions and Feynman rules, PI quantization of QED, Ward identity, axial anomaly.

3. Quantization of non-abelian Gauge Theories. Non-abelian gauge invariance, non-Abelian gauge fields, Yang-Mills Lagrangian and Feynman rules, Faddeev-Popov method, ghosts and unitarity, BRST symmetry and Ward (Slavnov-Taylor) identities.



4. Quantum Chromodynamics. Renormalization (1-loop), asymptotic freedom, confinement, DIS, DGLAP equations, jets.



5. Weak Interactions. GWS Lagrangian, spontaneous symmetry breaking and Englert¿Brout¿Higgs¿Guralnik¿Hagen¿Kibble effect, quantization and Feynman rules.

Bibliography

Basic bibliography

1. M.E. Peskin, D.V. Schröder: An Introduction to Quantum Field Theory; ABP, 1995

2. G. Sterman: An Introduction to Quantum Field Theory; Cambridge University Press, 1993

3. L.D. Faddeev, A.A. Slavnov: Gauge Fields. Introduction to Quantum Theory; The Bangamin /Cummings Publishing Company, 1980.

4. P. Ramond: Field Theory: A Modern Primer; Basic Books, 1990.

In-depth bibliography

1. S, Weinberg: The Quantum Theory of Fields: Volumes 1, 2, 3; Cambridge Univ. Press, 2005.

2. M.D. Schwartz: Quantum Field Theory and the Standard Model; Cambridge Univ. Press, 2013.

3. A.V. Smilga: Lectures on quantum chromodynamics; World Scientific, 2001.

Links

https://arxiv.org/list/hep-ph/new

https://arxiv.org/list/hep-th/new