UFTF007 Quantum Field Theory I

Faculty of Philosophy and Science in Opava
Winter 2013
Extent and Intensity
4/2/0. 8 credit(s). Type of Completion: zk (examination).
Teacher(s)
prof. Ing. Peter Lichard, DrSc. (lecturer)
Guaranteed by
prof. Ing. Peter Lichard, DrSc.
Centrum interdisciplinárních studií – Faculty of Philosophy and Science in Opava
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 most important quantum theory of free fields: scalar, electromagnetic and spinor. The basic idea of ??Lagrangian and Hamiltonian theory of classical fields are 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 the analogous transition from classical to quantum mechanics.
Syllabus
  • Introduction. Motivation for quantum field theory. The formal introduction of a step-up and step-down operators. Normalization of the final volume . General Lorentz transformations . Lorentz group and its subgroups.
    Scalar field . Klein- Gordon equation . Real scalar field . Hamilton's variational principle , Euler - Lagrange equations . Hamilton formalism . Energy - momentum tensor . Noether Theorem . Generalization to multi-component field . Complex scalar field . Quantization of the scalar field creation and annihilation operators , Fock space . Hamilton's operator , operator charges and momentum of scalar field . Go to the Heisenberg picture. Switchboards and contractions of field operators .
    Spinor field . Dirac equation . Classical and quantum field theory spinor . Anti-comutators . Fock space for fermions. Heisenberg picture.
    Electromagnetic field. The equation for four-potential, gauge transformations . Classical field theory. Quantization in the Coulomb calibration. Covariant quantization. Heisenberg picture. Spin of photon.
    Vector field . Proca equation . Classical and quantum theory of vector fields . Spin vector particles .
    Continuous spectrum . Normalization of single-particle states , field operators , creation and annihilation operators.
Literature
    recommended literature
  • Srednicki M. Quantum Field Theory. Cambridge University Press, 2007. ISBN 0521864496. info
  • 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
  • Hořejší J. Fundamentals of Elektroweak Theory. Nakladatelství Karolinum, 2002. ISBN 8024606399. 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
  • Itzykson C., Zuber J.-B. Quantum Field Theory. McGraw-Hill Inc., 1980. ISBN 0486445682. info
Language of instruction
Czech
Further Comments
The course can also be completed outside the examination period.
Teacher's information
80% attendence in seminars. Elaboration of seminar papers from exercise and homeworks. 50% successful completion of a written and oral examination.
The course is also listed under the following terms Winter 2014, Winter 2015, Winter 2016, Winter 2017, Winter 2018, Winter 2019, Winter 2020, Winter 2021, Winter 2022, Winter 2023.
  • Enrolment Statistics (Winter 2013, recent)
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