Description and contextualization of the subject

La teoría cuántica de campos es, en principio, el estudio del comportamiento cuántico de sistemas descritos por campos. Esta herramienta es imprescindible para estudiar física cuántica relativista (no hay más que pensar en el sistema relativista clásico por excelencia: el campo electromagnético). Sin embargo, su aplicabilidad se extiende a todas las áreas de aplicación de la física cuántica, pero de manera especial cuando el número de grados de libertad es infinito. Ello se debe a que en esas áreas las magnitudes accesibles a la medida son, de manera específica a cada área, conectadas a unas funciones de correlación concretas. A la hora de estudiar funciones de correlación, las técnicas de teoría cuántica de campos presentan ventajas frente a otras.

En este curso, se introduce el campo escalar relativista. Debido a su alta simetría, permite estudiar en detalle y con relativa sencillez matemática la cuantización, conexión con observables, y necesidad de renormalización y de técnicas no perturbativas. En paralelo, en otras asignaturas, el alumnado será expuesto a las funciones de correlación en el contexto de electrones y fonones de materia condensada, como otro ejemplo de teoría cuántica de campos.

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.

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.

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. Classical Field Theory.

Classical mechanics, Lagrangian, conjugate momentum, Hamiltonian. Classical Field Theory, lagrangian density, momenta, hamiltonian density. Euler-Lagrange. Noether¿s theorem. Lorentz invariance.

2. Canonical Quantization

Canonical quantization in classical mechanics . The harmonic oscillator. Canonical quantization of a relativistic scalar field. Propagators. Relativistic invariance and causality. Canonical quantization of the Dirac field.

3. Interactions

S matrix. LSZ. Perturbations. Wick theorem. Feynman diagrams.

4. Introduction to Renormalization

Loops and infinities. Physical renormalization. The systematics of renormalization: superficial degree of divergence. Computational tools: regularization, dimensional regularization, Wick rotation. Counterterm renormalization. Renormalization group: ß function and Callan-Symanzik equations.

Bibliography

Basic bibliography

1. Peskin, Michael E. and Daniel V. Schroeder, An Introduction to Quantum Field Theory. Advanced book classics. Addison-Wesley Publishing Company, 1995.

2. Maggiore, Michele, A Modern Introduction to Quantum Field Theory. Oxford University Press, 2005.

3. Schwartz, Matthew D, Quantum Field Theory and the Standard Model. Cambridge University Press, 2014.

In-depth bibliography

For conceptual aspects we highly recommend Álvarez-Gaumé, Luis and Miguel Á Vázquez-Mozo, An Invitation to Quantum Field Theory. Lecture Notes in Physics, vol. 839. Springer Nature, 2012.

An older descriptive text is Zee, Anthony, Quantum Field Theory in a Nutshell. Princeton University Press, 2010.

A very useful set of lecture notes is provided by David Tong, DAMTP, U Cambridge.

To make contact with field theory from a condensed matter physics point of view, see Altland, Alexander and Ben D. Simons, Condensed Matter Field Theory. Cambridge University Press, 2010.