Quantum field theory

Enrollment into the program.

Positive result from two colloquia or written exam is necessary to enter the oral exam.

Probelms with relativistic quantum mechanics and the need for quantum field theory, causality

Classical field theory, Noether theorem, conserved current and charge, tensor of energy and momentum

Canonical quantization of relativistic free scalar field, Kline Gordon equation, propagator; nonrelativistic example of one-dimensional harmonic chain (phonons); complex scalar field

Transformations of vector and spinor fields under Lorentz transformations (boosts, rotations and their combinations), generators

Free Dirac field: Dirac equation, clasical field and canonical quantization, operator of charge, momentum and angular momentum, spin, antiparticles, propagators, difference between Dirac and Majorana fermions

Free electromagnetic field, clasical gauge theory, (naive) quantization

Various field theoreis with interactions between scalars, spinors and vectors, gauge transformations and interaction in electrodynamics, perturbation theory, interaction picture,  correlation functions, Wick's theorem, Feynman rules

Scattering and S-matrix and their relation to correlation functions (LSZ theorem), Feynman diagrams

Scattering at lowest order: examples for electrodynamics, scalar phi^4 theory and theory with interactions between scalars and fermions

Feynman path integral in scalar quantum field theory; application at zero temperature and at finite temperature; Matsubara frequencies, partition function for free bosons in both cases

Perturbative corrections at one-loop order for electrodynamics (electron and photon self-energy and vertex correction): dimensional regularization, Wick rotation, renormalization with the ordinary and counter term methods, field strength renormalization,  renormalization of n-point correlation functions, observable consequences in QED: anomalous magnetic moment, running of coupling (e) with energy, Lamb shift, LSZ theorem in more detail

Renormalization group equations; running couplings

Kosterlitz-Thouless transition, example of two-dimensional XY model, vortices 

- M. Peskin, D. Schroeder: An introduction to quantum field theory, Addison-Wesley publishing company, New York, 1995

- Claude Itzykson, Jean-Bernard Zuber: QuantumField Theory

McGraw-Hill, New York, 1987

 - A. Altland, B. Simons, Condensed Matter Field Theory, Cambridge University Press , 2010

Objectives:

Student gets familiar with the properties of free quantum fields, their quantization and interactions as well as symetry properties.

Competences:

Knowledge and understanding of basic principles of quantum field theory, quantisation approaches, principlesof gauge interactions .

Knowledge and understanding:

Knowledge of basic tyheoretical tools in elementary particle physics,  with additional applications applications to condensed matter systems.

Application:

The achieved knowledge enables student to solve theoretical problems within field elementary particle theory and examples of filed-theory applications in condesed matter systems.

Reflection:

Critical evalvation of theoretical approaches within relativistic and quantum physics.

Transferable skills:

Ability to construct theoretical models and analyze physical problems in theoretical high energy physics. Ability for application of field theory for non-relativistic problems in other fields of physics.

Lectures, exercises,  homework, consultations

grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)
2 midterm exams instead or final written exam
Oral exam

Sasa Prelovsek (ime v clankih)

(1) Approximate degeneracy of J = 1 spatial correlators in high temperature QCD

C. Rohrhofer, Y. Aoki, G. Cossu, H. Fukaya, L. Glozman, S. Hashimoto, C. Lang, S. Prelovsek Phys. Rev. D 96, 094501 (2017)

(2) Ds0∗ (2317) meson and DK Scattering from Lattice QCD  D. Mohler, C.B. Lang, L. Leskovec, S. Prelovsek, R.M. Woloshyn  Phys. Rev. Lett. 111 (2013) 222001

(3) Evidence for X(3872) from DD* scattering on the lattice S. Prelovsek , L. Leskovec Phys. Rev. Lett. 111 (2013) 192001

(4) Scattering phase shifts for two particles of different mass and non-zero total momentum in lattice QCD L. Leskovec, S. Prelovsek Phys.Rev. D85 (2012) 114507

(5) Coupled channel analysis of the rho meson decay in lattice QCD C.B. Lang, D. Mohler, S. Prelovsek, M. Vidmar Phys. Rev. D84 (2011) 054503