Quantum Theory of Fields

OBJECTIVES:

Provide the student with the basic knowledge for the study of quantum theories of relativistic fields and gauge theories in relation to particle physics.

Learning outcomes:
After completing the course, the student:
• Will know the basics of quantum field theories and gauge theories in relation to particle physics.
• Will be able to perform simple calculations of dispersion amplitudes in quantum electrodynamics using Feynman diagrams.

- Relativistic wave equations: The Klein-Gordon equation and the Dirac equation.

- Quantization of free fields: Quantization of the scalar field, the Dirac field and the electromagnetic field.

- Perturbation theory and Feynman diagrams: Calculation of cross sections and decay rates.

- Introduction to gauge theories: quantum electrodynamics (QED). Calculation of elementary processes in QED at first order (tree-level approximation).

Basic bibliography:
Bibliografía básica:
- M. E. Peskin y D. V. Schroeder, An Introduction to Quantum Field Theory, Addison-Wesley (1995).
- D. Tong, Quantum Field Theory, Cambridge University (2006). http://www.damtp.cam.ac.uk/user/tong/qft.html.
- C. Itzykson y J. B. Zuber, Quantum Field Theory, McGraw-Hill (1980).
- M. Srednicki, Quantum Field Theory, Cambridge University Press (2007).

Complementary:
- S. Weinberg, The Quantum Theory of Fields (Vol. I: Foundations), Cambridge University Press (1995).
- M. Stone, The physics of quantum fields, Springer-Verlag (2000).
- J. D. Bjorken and S.D. Drell, Relativistic Quantum Mechanics, McGraw-Hill (1964); Relativistic Quantum Fields, McGraw-Hill (1965).

Online resources:
• Virtual Classroom: Notes prepared by teacher poles.
• Virtual Classroom: Problem bulletins, problem solutions, exams from previous courses.

Basic and general

CB1 - That the students have demonstrated to possess and understand knowledge in a study area that starts from the general secondary education, and is usually found at a level that, although supported by advanced textbooks, also includes some aspects that involve knowledge from the forefront of their field of study.

CB2 - That students know how to apply their knowledge to their work or vocation in a professional way and possess the competencies that are usually demonstrated through the elaboration and defense of arguments and the resolution of problems within their area of study.

CB3 - That students have the ability to collect and interpret relevant data (usually within their area of study) to make judgments that include reflection on relevant issues of a social, scientific or ethical nature.

CG1 - Possess and understand the most important concepts, methods and results of the different branches of Physics, with a historical perspective of their development.

CG2 - Have the ability to gather and interpret relevant data, information and results, obtain conclusions and issue reasoned reports on scientific, technological or other problems that require the use of knowledge of Physics.

CG3 - Apply both the theoretical-practical knowledge acquired and the capacity for analysis and abstraction in the definition and approach of problems and in the search for solutions in both academic and professional contexts.

Transversal and specific

CT1 - Acquire analysis and synthesis capacity.

CT2 - Have organization and planning capacity.

CT5 - Develop critical reasoning.

CE1 - Have a good understanding of the most important physical theories, locating in their logical and mathematical structure, their experimental support and the physical phenomenon that can be described through them.

CE2 - Be able to clearly manage orders of magnitude and make adequate estimates in order to develop a clear perception of situations that, although physically different, show some analogy, allowing the use of known solutions to new problems.

CE5 - Be able to carry out the essentials of a process or situation and establish a working model for it, as well as perform the required approximations in order to reduce the problem to a manageable level. Demonstrate critical thinking to build physical models.

CE6 - Understand and master the use of the most commonly used mathematical and numerical methods in Physics

CE8 - Be able to manage, search and use bibliography, as well as any relevant source of information and apply it to research work and technical development of projects.

A course will be activated on the Moodle platform of the Virtual Campus, to which information of interest to the student and diverse teaching material will be uploaded.

The general methodological indications established in the USC's Memory of the bachelor’s degree in Physics will be followed. The teaching will be face-to-face and will be scheduled in theoretical classes (24 hours), small group practices (18 hours) and tutoring in very small groups (3 hours). In the theoretical and practical classes, the basic contents of the subject will be presented, and some exercises will be solved. The most advanced contents and problems will be proposed to the student for their personal work with the support of the tutoring hours. The tutorials may be face-to-face or telematic. If they are telematic, they will need an appointment, which will also be recommended for face-to-face tutoring.

The course does not include taking a final exam for the first evaluation opportunity. Instead, the evaluation system will combine a continuous evaluation, which will consist of carrying out exercises and weekly problems that the student will deliver, and an additional control of a longer duration to evaluate the global competences that will account for up to 75% of the final grade. For the second evaluation opportunity there will be a conventional final exam on the official dates set by the center.

Continuous assessment is valid only for the first opportunity and will not be retained for subsequent courses.

In cases of fraudulent performance of exercises or tests, the provisions of the "Regulations for the evaluation of student academic performance and review of grades" will apply:

24 hours of face-to-face or telematic lectures.
18 hours of interactive classroom or telematic classes.
3 hours of face-to-face or telematic tutoring.

It is difficult to determine the study time necessary to assimilate the subject, since it depends a lot on the dedication and ability of each student. As a general indication, the USC's Memory of the bachelor’s degree in Physics estimates the student's personal work in 47 hours, not counting face-to-face or telematic teaching, writing exercises, conclusions and other work in 18 hours, and the preparation of oral presentations, debates or similar in 2.5 hours. Total 67.5 hours

Attendance and active participation in theoretical and practical classes. Taking advantage of tutoring.