# Advanced Quantum Field Theory

## Module PH2185

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

### Module version of SS 2019

There are historic module descriptions of this module. A module description is valid until replaced by a newer one.

Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.

available module versions | ||||
---|---|---|---|---|

SS 2020 | SS 2019 | SS 2018 | SS 2017 | SS 2014 |

### Basic Information

PH2185 is a semester module in English or German language at Master’s level which is offered in summer semester.

This Module is included in the following catalogues within the study programs in physics.

- Specific catalogue of special courses for nuclear, particle, and astrophysics
- Complementary catalogue of special courses for condensed matter physics
- Complementary catalogue of special courses for Biophysics
- Complementary catalogue of special courses for Applied and Engineering Physics
- Specialization Modules in Elite-Master Program Theoretical and Mathematical Physics (TMP)

If not stated otherwise for export to a non-physics program the student workload is given in the following table.

Total workload | Contact hours | Credits (ECTS) |
---|---|---|

300 h | 90 h | 10 CP |

Responsible coordinator of the module PH2185 in the version of SS 2019 was Andreas Weiler.

### Content, Learning Outcome and Preconditions

#### Content

- Renormalization group (fixed points etc.)
- Effective action and effective potential
- Spontaneous symmetry breaking, Goldstone bosons
- Non-linear symmetry realizations, effective Goldstone Lagrangians
- Non-trivial classical field configurations (solitons, instantons etc.) and their quantization
- Anomalies (chiral, gauge, discrete, etc.)
- Basics of supersymmetry (N=1 supersymmetry algebra, Wess-Zumino model etc.)
- Spin-two fields; weak field quantisation of gravitation.

#### Learning Outcome

The student will be prepared

- to understand the Higgs mechanism;
- to compute quantum corrections to classical potentials;
- to understand topologically non-trivial field configurations both at the classical and the quantum level;
- to understand anomalies and anomaly cancellation;
- to construct a supersymmetric action/theory.

#### Preconditions

No preconditions in addition to the requirements for the Master’s program in Physics.

### Courses, Learning and Teaching Methods and Literature

#### Courses and Schedule

Type | SWS | Title | Lecturer(s) | Dates |
---|---|---|---|---|

VO | 4 | Advanced Quantum Field Theory | Beneke, M. |
Wed, 08:00–10:00, PH 3344 Thu, 10:00–12:00, PH 3344 and singular or moved dates |

UE | 2 | Exercise to Advanced Quantum Field Theory |
Responsible/Coordination: Beneke, M. |
dates in groups |

#### Learning and Teaching Methods

The modul consists of a lecture and exercise classes.

The lecture is designed for the presentation of the subject, usuallyby blackboard presentation. The focus resides on theoretical foundations of the field, presentation of methods and simple, illustrative examples. Command of basic methods is deepened and practised through homework problems, which cover important aspects of the field. The homework problems should develop the analytic skills of the students and their ability to perform calculations. The homework problems are discussed in the ecercise classes by the students themselves under the supervision of a supervizor in order to develop the skills to solve and explain a physics problem coherently.

#### Media

Blackboard presentation, additional Powerpoint slides/presentations on demand.

#### Literature

- M.E. Peskin & D.V. Schroeder:
*An Introduction to Quantum Field Theory*, Westview Press, (1995) - S. Pokorski:
*Gauge Field Theories*, Cambridge University Press, (2000) - D. Bailin & A. Love:
*Introduction to Gauge Field Theory*, CRC Press, (2018) - S. Weinberg:
*The Quantum Theory of Fields,*I-III, Cambridge University Press, (2005) - M. Shifman:
*Advanced Topics in Quantum Field Theory*, Cambridge University Press, (2012) - M. Nakahara:
*Geometry, Topology and Physics*, CRC Press, (2003)

### Module Exam

#### Description of exams and course work

There will be a written exam of 180 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using calculation problems and comprehension questions.

For example an assignment in the exam might be:

- Calculate the propagator and the interaction vertices for a non-abelian gauge theory in a particular gauge fixing.
- Calculate the 1-loop corrections to a non-abelian gauge theory, regularize and renormalize.
- Extract the beta-function coefficients from the above calculation.
- Find the symmetry breaking pattern for a theory with spontaneous symmetry breaking, calculate the Goldstone boson interactions, find potentially anomalous symmetries.
- Derive the self-interactions of a spin 2 field using the decoupling of the Stueckelberg modes

Participation in the tutorials is strongly recommended since the exercises prepare for the problems of the exam and rehearse the specific competencies.

There will be a bonus (one intermediate stepping of "0,3" to the better grade) on passed module exams (4,3 is not upgraded to 4,0). The bonus is applicable to the exam period directly following the lecture period (not to the exam repetition) and subject to the condition that the student passes the mid-term of

- preparing at least 50 % of the exercises on the exercise sheets and
- presenting at least three exercises at the blackboard

#### Exam Repetition

The exam may be repeated at the end of the semester.