Quantum Field Theory
0800-KTPOL
I.
1. Review of the canonical formalism applied to classical field theory (
from n-point mechanics to field theory, Lagrangian and the
Hamiltonian formalism, Euler-Lagrange equation, Poisson bracket,
Noether's theorem, four-vector algebra )
[Requirement: the canonical formalism ]
2. Poincaré group and a Lorentz subgroup
- Lorentz Transformations and the Lorentz Group
- Lorentz transformation as orthogonal transformations in four dimensions
- infinitesimal Lorentz transformations
- generators of group transformations
[Requirement: knowing how to use the four-vector algebra]
1. Free scalar (real and complex Klein-Gordon field) and spinor
(Dirac) field
- canonical field quantization
- causality and commutation relations
- creation and annihilation operators
- continuous symmetries and conservation laws (Noether's Theorem)
- single-particle and multiparticle states in the quantum field theory
- derivation of the Faynman propagator
[Requirement: plane wave solutions of the Klein-Gordon equation,
free particle solutions of Dirac equation, Dirac matrices, invariance
and covariance properties of the Dirac equation]
2. Quantization of the photon field
- canonical quantization in the Coulomb gauge
- canonical quantization in the Lorentz gauge
- the Gupta-Bleuler method
- the Feynman propagator for photons
[Required recall: classical electromagnetic field theory ]
II.
1. Perturbation theory
- asymptotic states and S-matix
- LSZ reduction theorem
[Required recall: knowledge of the S-matrix theory]
2. Quantum fields with interactions - introduction
- interacting lagrangians - examples
- time ordered products and contractions, Wick's theorem
3. Gauge invariant interacting theory
- local and global gauge symmetries
- minimal subtraction schemes
- construction of a gauge-invariant QED Lagrangian
4. Quantum electrodynamical processes
- fundamental QED interaction diagrams
- Feynman rules of quantumelectrodynamic in momentum space
- The scattering matrix in higher orders
- Coulomb scattering of electrons
- two particle systems: nonrelativistic limit and the
Dirac-Coulomb-Breit-Pauli equation
6. Renormalization - how this works for the scalar field
with psi^4 interaction
- relation between the theoretical parameters and the observables
(bare field, physical mass and coupling constant, counterterms, dressing the propagator)
7. Renormalization in QED - general structure
- mass renormalization and electron propagator
- charge renormalization and photon propagator
|
Term 2021/22L:
I.
1. Review of the canonical formalism applied to classical field theory (
from n-point mechanics to field theory, Lagrangian and the
Hamiltonian formalism, Euler-Lagrange equation, Poisson bracket,
Noether's theorem, four-vector algebra )
[Requirement: the canonical formalism ]
2. Poincaré group and a Lorentz subgroup
- Lorentz Transformations and the Lorentz Group
- Lorentz transformation as orthogonal transformations in four dimensions
- infinitesimal Lorentz transformations
- generators of group transformations
[Requirement: knowing how to use the four-vector algebra]
1. Free scalar (real and complex Klein-Gordon field) and spinor
(Dirac) field
- canonical field quantization
- causality and commutation relations
- creation and annihilation operators
- continuous symmetries and conservation laws (Noether's Theorem)
- single-particle and multiparticle states in the quantum field theory
- derivation of the Faynman propagator
[Requirement: plane wave solutions of the Klein-Gordon equation,
free particle solutions of Dirac equation, Dirac matrices, invariance
and covariance properties of the Dirac equation]
2. Quantization of the photon field
- canonical quantization in the Coulomb gauge
- canonical quantization in the Lorentz gauge
- the Gupta-Bleuler method
- the Feynman propagator for photons
[Required recall: classical electromagnetic field theory ]
II.
1. Perturbation theory
- asymptotic states and S-matix
- LSZ reduction theorem
[Required recall: knowledge of the S-matrix theory]
2. Quantum fields with interactions - introduction
- interacting lagrangians - examples
- time ordered products and contractions, Wick's theorem
3. Gauge invariant interacting theory
- local and global gauge symmetries
- minimal subtraction schemes
- construction of a gauge-invariant QED Lagrangian
4. Quantum electrodynamical processes
- fundamental QED interaction diagrams
- Feynman rules of quantumelectrodynamic in momentum space
- The scattering matrix in higher orders
- Coulomb scattering of electrons
- two particle systems: nonrelativistic limit and the
Dirac-Coulomb-Breit-Pauli equation
6. Renormalization - how this works for the scalar field
with psi^4 interaction
- relation between the theoretical parameters and the observables
(bare field, physical mass and coupling constant, counterterms, dressing the propagator)
7. Renormalization in QED - general structure
- mass renormalization and electron propagator
- charge renormalization and photon propagator |
Total student workload
Lecturing - 30 hours
Conducting the discussions - 30 hours
Time dedicated to the individual work with the student (80h.):
- lecture preparation - 20 hours
- preparation of the discussions - 10 hours
- reading of the literature materials used in the lecture - 20 hours
- preparation of the exam - 20 hours
- preparation of the tests - 10 hours
Total of 140 hours ( 5 ECTS)
Learning outcomes - knowledge
K_W01 - the student has extended knowledge of quantum physics. That includes the Langrange and Hamilton formalisms, theorems used to describe quantum fields (scalar, vector, and spinor fields), and the formalism of interacting field theory, in particular, the quantum electrodynamics
K_W02 - the student has in-depth knowledge of advanced quantum theory of interacting fields, knows the basic methods of renormalization
K_W03 - the student knows the basic concepts and definitions needed for the theoretical description of quantum fields; understands the importance of symmetry in the description of quantum systems
K_W04 - the student has knowledge of the description of the interaction of a fermion field with an electromagnetic field and the theory of renormalization
K_W05 - the student has knowledge of the current development of quantum electrodynamics
The above-mentioned subjects implement the following directional effects:
K_W01, K_W03, K_W04, and K_W05 for physics s2
Learning outcomes - skills
K_U01 - The graduate is able to use scientific methods in problem - solving,
K_U04 - The graduate is able to find relevant information in specialist literature, both in databases and other sources and is able to reconstruct
the reasoning
K_U05 - The graduate is able to adapt knowledge and methodology of physics as well as theoretical and experimental methods to related branches of science.
Learning outcomes - social competencies
K_K01 - the student appreciates the role of natural sciences and understands the need for further scientific research; effects
K_K01 and K_K03 for physics s2.
Teaching methods
Didactic method giving:
Informative interactive lecturing (conventional)
Teaching method - discussions
Expository teaching methods
- informative (conventional) lecture
Exploratory teaching methods
- practical
- classic problem-solving
Prerequisites
Lagrangian and the Hamiltonian formalism, Euler–Lagrange equation, Noether's theorem, four-vector algebra, free particle solution of the Dirac equation and Klein-Gordon equation, Dirac matrices, Lorentz transformation, relativistic particle in the electromagnetic field
Course coordinators
Assessment criteria
A grade for the discussion section will be assigned based on the
class participation, obligatory homework assignments, and an examination.
A passing grade for the class will be assigned based on the written examination graded according to the grade scale used at the University.
Bibliography
M.E. Peskin, D.V. Schroeder "Quantum Field Theory"
F. Mandl, G. Shaw - "Quantum Field Theory"
J.D. Bjorken , S.D. Drell, "Relatywistyczna teoria kwantów"
N. N. Bogoljubov, D. W. Shirkov, "Introduction to the Theory of Quantized Fields"
L. H. Ryder, "Quantum Field Theory"
C.Itzykson, J.B. Zuber, "Quantum Field Theory"
A.Bechler, "Kwantowa teoria oddziaływań elektromagnetycznych"
W. Greiner, J. Reinhard, "Field Quantization"
W.Greiner, J.Reinhard "Quantum Electrodynamics"
V. Radovanović "Kwantowa teoria pola w zadaniach"
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Term 2021/22L:
M.E. Peskin, D.V. Schroeder "Quantum Field Theory"
F. Mandl, G. Shaw - "Quantum Field Theory"
J.D. Bjorken , S.D. Drell, "Relatywistyczna teoria kwantów"
N. N. Bogoljubov, D. W. Shirkov, "Introduction to the Theory of Quantized Fields"
L. H. Ryder, "Quantum Field Theory"
C.Itzykson, J.B. Zuber, "Quantum Field Theory"
A.Bechler, "Kwantowa teoria oddziaływań elektromagnetycznych"
W. Greiner, J. Reinhard, "Field Quantization"
W.Greiner, J.Reinhard "Quantum Electrodynamics" |
Additional information
Additional information (registration calendar, class conductors,
localization and schedules of classes), might be available in the USOSweb system: