Theoretical Particle Physics (TPP)

Each module has to be completed with 8 credit points.

2nd (summer) semester modules

Module 1. The Standard Model of Elementary Particle Physics
ID: SMTP
Compulsoriness: Elective, with an alternative of SFT, VTT, and EQFT
ECTS credits: 8
Workload: 240 hours
Duration of Module: 1 semester
Semester: Summer (2nd)
Qualification goals: The students learn the properties and foundations of the Standard Model of Elementary Particle Physics.
General Note: Scope of written homework: 20 - 25 pages.
Assessment Measures: The form of the examination of the module is announced at the beginning of the semester in which the examination will be conducted. One of two options is possible:
• written homework (12 weeks), unrestrictedly repeatable;
• oral module examination (30 minutes), unrestrictedly repeatable.

Components of the Module

SMTP-a. "The Standard Model of Elementary Particle Physics - a"
Compulsoriness: Compulsory
Form of Study: Lectures
Weekly Hours: 4
Overall Workload: 180 hours
Contents: Foundations and properties of the Standard Model.

SMTP-b. "The Standard Model of Elementary Particle Physics - b"
Compulsoriness: Compulsory
Form of Study: Lectures and exercises
Weekly Hours: 2
Overall Workload: 60 hours
Description: Contents of the lecture are practiced in dedicated exercises.

Module 2. Statistical Field Theory
ID: SFT
Compulsoriness: Elective, with an alternative of SMTP, VTT, and EQFT
ECTS credits: 8
Workload: 240 hours
Duration of Module: 1 semester
Semester: Summer (2nd)
Qualification goals: The students know advanced phenomena in solid state physics which can not be explained by one particle properties. They are able to describe and compute the interaction of phonons with electrons within the framework of perturbation 
theory.
General Note: Scope of written homework: 20 - 25 pages.
Assessment Measures: The form of the examination of the module is announced at the beginning of the semester in which the examination will be conducted. One of two options is possible:
• written homework (12 weeks), unrestrictedly repeatable;
• oral module examination (30 minutes), unrestrictedly repeatable.

Components of the Module

SFT-a. "Statistical Field Theory - a"
Compulsoriness: Compulsory
Form of Study: Lectures
Weekly Hours: 4
Overall Workload: 180 hours
Contents: Critical Phenomena. Renormalisation Group. Conformal Invariance and Field Theory. Finite-Size Scaling. Two-Dimensional Ising Model. Nonlinear Sigma Model. Thermodynamics of Exactly Solvable Vertex Models. Stochastic Systems. Random Walk and Brownian Motion.

SFT-b. "Statistical Field Theory - b"
Compulsoriness: Compulsory
Form of Study: Exercises
Weekly Hours: 2
Overall Workload: 60 hours
Description: Contents of the lecture are practiced in dedicated exercises.

Module 3. Many Particle Theory
ID: VTT
Compulsoriness: Elective, with an alternative of SMTP, SFT, and EQFT
ECTS credits: 8
Workload: 240 hours
Duration of Module: 1 semester
Semester: Summer (2nd)
Qualification goals: The students know advanced phenomena in solid state physics which can not be explained by one particle properties. They are able to describe and compute the interaction of phonons with electrons within the framework of perturbation theory.
General Note: Scope of written homework: 20 - 25 pages.
Assessment Measures: The form of the examination of the module is announced at the beginning of the semester in which the examination will be conducted. One of two options is possible:
• written homework (12 weeks), unrestrictedly repeatable;
• oral module examination (30 minutes), unrestrictedly repeatable.

Components of the Module

VTT-a. "Many Particle Theory - a"
Compulsoriness: Compulsory
Form of Study: Lectures 
Weekly Hours: 4
Overall Workload: 180 hours
Contents: Occupation number representation. Microscopic electronic models of solid state physics. Green functions and perturbation theory. Feynman diagrams. Physical applications of perturbation theory. Linear response theory

VTT-b. "Many Particle Theory - b"
Compulsoriness: Compulsory
Form of Study: Exercises
Weekly Hours: 2
Overall Workload: 60 hours
Description: Contents of the lecture are practiced in dedicated exercises.

Module 4. Introduction to Quantum Field Theory
ID: EQFT
Compulsoriness: Elective, with an alternative of SMTP, SFT, and VTT
ECTS credits: 8
Workload: 240 hours
Duration of Module: 1 semester
Semester: Summer (2nd)
Qualification goals: The students shall be enabled to carry out modern research in the field of theoretical particle physics andits computer assisted applications.
General Note: Scope of written homework: 20 - 25 pages.
Assessment Measures: The form of the examination of the module is announced at the beginning of the semester in which the examination will be conducted. One of two options is possible:
• written homework (12 weeks), unrestrictedly repeatable;
• oral module examination (45 minutes), unrestrictedly repeatable.

Components of the Module

EQFT-a. "Introduction to Quantum Field Theory"
Compulsoriness: Compulsory
Form of Study: Lectures
Weekly Hours: 2
Overall Workload: 150 hours
Contents:  Relativistic quantum mechanics. Nöther theorem. Field quantization in momentum space. Propagator of the free scalar field. Wick theorem. Interaction, normal ordering, time ordering. Feynman diagrams. Cross sections and decay rates. Regularization and renormalization. Representations of the Poincare group. Grassmann variables. Path integrals. Quantization of gauge theories. Quantum electrodynamics.

EQFT-b. "Exercises Introduction to Quantum Field Theory"
Compulsoriness: Compulsory
Form of Study: Exercises
Weekly Hours: 2
Overall Workload: 90 hours
Description: Contents of the lecture are practiced in dedicated exercises.

3rd (winter) semester module

Module 5. Cosmology and General Relativity
ID: COS
Compulsoriness: Elective, with an alternative of FQM
ECTS credits: 8
Workload: 240 hours
Duration of Module: 1 semester
Semester: Winter (3rd)
Qualification goals: Mastering of the basic principles of general relativity as the theoretical foundation of cosmology. The students understand the Big Bang model and its important pillars (Hubble-expansion, microwave backgroung radiation, synthesis of light elements) and they recognize the necessity for the existence of dark matter and dark energy. The students shall be enabled to learn independently new special topics of the Elementary- or Astro-particle physics related to cosmology and to make a presentation about them. They master modern presentation media.
Assessment Measures: Assessment of folder, contents, time and form of each single achievement will be announced at the beginning of the semester.

Components of the Module

COS-a. "Introduction to Cosmology and General Relativity"
Compulsoriness: Compulsory
Form of Study: Lectures and exercises
Weekly Hours: 4
Overall Workload: 180 hours
Contents: General co-ordinate transformations, metrics of space-time, Robertson-Walker metrics, Einstein and Friedmann Equations, cosmic dynamics and world models, Hubble Law, critical density of Universe, cosmological constant, age measurements, cosmic microwave background radiation, primordial nucleo-synthesis, dark matter.

STP-a. "Main Seminar on Particle Physics"
Compulsoriness: Compulsory
Form of Study: Seminar
Weekly Hours: 2
Overall Workload: 60 hours
Description: Seminar on topics of theoretical and experimental particle physics.

Module 6. Advanced Quantum Mechanics
ID: FQM
Compulsoriness: Elective, with an alternative of COS
ECTS credits: 8
Workload: 240 hours
Duration of Module: 1 semester
Semester: Winter (3rd)
Qualification goals: The students learn advanced methods and techniques of quantum mechanics, inparticular the relativistic formulation and the field quantization. They are able to derive and solve the formulation of advanced quantum mechanical problems. They will gain an overview of various computational methods and approximations as well as the fundamental importance of relativistic phenomena in physics. They will also learn the foundations of theoretical particle physics.
Assessment Measures: The form of the examination of the module is announced at the beginning of the semester in which the examination will be conducted. One of two options is possible:
• written module examination (120 minutes), unrestrictedly repeatable;
• oral module examination (30 minutes), unrestrictedly repeatable.

Components of the Module

FQM-a. "Advanced Quantum Mechanics"
Compulsoriness: Compulsory
Form of Study: Lectures and exercises
Weekly Hours: 6
Overall Workload: 240 hours
Contents: Invariance of the equations of motion and conserved quantities. Time reversal. Time dependent perturbation theory. Variational methods. Hartree Fock equation. Structure of molecules. Scattering theory: cross section, Born series, single and multiple scattering. S- and T-matrix. Relativistic quantum mechanics: Klein-Gordon and Dirac equation. Field quantization. Quantum theory of radiation. Foundations of particle physics.