TFNSP0005 Quantum Field Theory I

Institute of physics in Opava
summer 2022
Extent and Intensity
4/2/0. 8 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Filip Blaschke, Ph.D. (lecturer)
doc. RNDr. Filip Blaschke, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Filip Blaschke, Ph.D.
Institute of physics in Opava
Timetable
Mon 13:05–14:40 309, Wed 14:45–16:20 B4
  • Timetable of Seminar Groups:
TFNSP0005/01: Thu 9:45–11:20 B1, F. Blaschke
Prerequisites (in Czech)
(FAKULTA(FU) && TYP_STUDIA(N))
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
These lectures introduce students to the basics of Quantum Field Theory. Basic knowledge of Quantum mechanics is expected.
Learning outcomes
At the end of this course the student will gain a basic orientation in:
- path integral in non-relativistic quantum mechanics and in Quantum Field Theory.
- the structure and representations of the Lorentz Group.
- the basic field equations for the lowest representations of the Lorentz Group, that is Klein-Gordon, Weyl, Dirac, and Maxwell equations.
- canonical quantization of scalar, fermion, and vector fields.
- the properties of the propagators for scalar, fermion, and vector field.
Syllabus
The main topics are:
• Historical motivation for quantum field theory.
• Path integral for a free particle in non-relativistic and relativistic cases. The need for the introduction of the quantum field.
• Hilbert space for one and infinitely many free particles. The machinery of creation and annihilation operators. The Fock space representations. Fields as local observables and their properties.
• A basic introduction to the Lie Groups. SU(2) group and its representations. Relation between SU(2) and SO(3). Scalars, spinors, and vectors.
• General structure of the Lorentz Group. SO(3,1) and SU(2)xSU(2) correspondence. Representations of connected Lorentz Group.
• Introduction to classical Field theory. Euler-Lagrange equations. Energy-Momentum tensor. Symmetries, conserved currents, and Noether theorem.
• Real and complex scalar field theory and Klein-Gordon equation. General solution. Canonical quantization and scalar propagator.
• Spinor field. Weyl equation, chirality. Pauli matrix technology and dotted un-dotted notation.
• Properties of the Dirac equation. Gamma matrix technology. The spin and magnetic moment of the electron.
• General solution of the Dirac equation. Canonical quantization of the Dirac equation and spin-statistic theorem. Propagator for a fermionic field.
• Proca equation and Maxwell equations. Helicity and degrees of freedom for a spin one particle.
• Kalibration invariance. Gauge fixing. Gupta-Bleuler formalism.
• General solutions to Proca and Maxwell equations. Polarization vectors. Canonical quantization of Proca and Maxwell fields. Propagator for massless and massive spin one particle.
• Principle of minimal interaction. Lagrangian for quantum electrodynamics. Feynman rules. Feynman diagrams.
Literature
    recommended literature
  • Zee A. Quantum Field Theory in a Nutshell, Princeton University Press, 2010
  • Formánek J. Úvod do relativistické kvantové mechaniky a kvantové teorie pole 1. Nakladatelství Karolinum, 2004. ISBN 80-246-0060-9. info
  • Formánek J. Úvod do relativistické kvantové mechaniky a kvantové teorie pole 2a, 2b. Karolinum, 2000. ISBN 978-80-246-0063-5. info
  • Srednicki M. Quantum Field Theory. Cambridge University Press, 2007. ISBN 0521864496. info
  • Tong D. Quantum Field Theory (lecture notes), University of Cambridge, 2007
  • Padmanabhan T. Quantum Field Theory, Springer, 2016
  • Mojžiš M. Quantum Field Theory I (lecture notes), 2005
Teaching methods
Lectures, presentations. Exercises.
Assessment methods
Oral examination, test.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is also listed under the following terms summer 2021, summer 2023, summer 2024, summer 2025.
  • Enrolment Statistics (summer 2022, recent)
  • Permalink: https://is.slu.cz/course/fu/summer2022/TFNSP0005