UFTF007 Quantum Field Theory I

Faculty of Philosophy and Science in Opava
Winter 2021
Extent and Intensity
4/2/0. 8 credit(s). Type of Completion: zk (examination).
Teacher(s)
prof. Ing. Peter Lichard, DrSc. (lecturer)
RNDr. Filip Blaschke, Ph.D. (seminar tutor)
RNDr. Josef Juráň, Ph.D. (seminar tutor)
Guaranteed by
prof. Ing. Peter Lichard, DrSc.
Centrum interdisciplinárních studií – Faculty of Philosophy and Science in Opava
Prerequisites
TF001, TF003
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
To acquaint students with the quantum theory of free scalar, electromagnetic and spinor fields. The basic idea of the Lagrangian and Hamiltonian theory of classical fields is first laid out in analogy with the theory of systems with a finite number of degrees of freedom. The transition to a quantum description is based on an analogous transition from classical to quantum mechanics.
Syllabus
  • Motivation for quantum field theory. The final volume normalization of the free states. General Lorentz transformation. Lorentz group and its subgroups.
    Scalar field. Klein-Gordon equation. Real scalar field. Hamilton's variational principle, Euler-Lagrange equations. Hamiltonian formalism. Energy-momentum tensor. Noether's theorem. Generalization to multi-component fields. Complex scalar field. Quantization of the scalar field, creation and annihilation operators, Fock space. Operators of energy, momentum and charge of the scalar field. Transition to the Heisenberg picture. Commutators and contractions of the field operators.
    Spinor field. Dirac equation . Classical and quantum theory of the spinor field. Anticommutators. Fock space for fermions. Heisenberg picture.
    Electromagnetic field. The equation for the four-potential, gauge transformations . Classical field theory. Quantization in the Coulomb calibration. Covariant quantization. Heisenberg picture.
    Massive vector field. Proca equation. Classical and quantum theory of the massive vector field.
    Continuous spectrum. Normalization of single-particle states, field operators, creation and annihilation operators, commutators and anticommutators.
Literature
    recommended literature
  • Maggiore M. A Modern Introduction to Quantum Field Theory. Oxford University Press, 2005. ISBN 0198520743. info
  • 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
  • Sterman G. An Introduction to Quantum Field Theory. Cambridge University Press, 1993. ISBN 0521311322. info
  • Guidry M. Gauge Field Theories. John Wiley & Sons, 1991. ISBN 047135385X. info
Teaching methods
Students' self-study
Lectures, tutorial sessions, regularly assigned and evaluated home tasks.
Assessment methods
Credit
Active participation on tutorial sessions and the timely completion of home tasks is required. Detailed criteria will be announced by the tutorial lecturer. The exam consists of the main written part and a supplemental oral part.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
Teacher's information
The attending of lectures is recommended, that of tutorial sessions is compulsory. If a student was absent for serious reasons, the teacher may prescribe him/her an alternative way of fulfilling the duties.
The course is also listed under the following terms Winter 2013, Winter 2014, Winter 2015, Winter 2016, Winter 2017, Winter 2018, Winter 2019, Winter 2020, Winter 2022, Winter 2023.
  • Enrolment Statistics (Winter 2021, recent)
  • Permalink: https://is.slu.cz/course/fpf/winter2021/UFTF007