Physikalisches Wahlfach: Quantenfeldtheorie II (PW-10)10 ECTS
(englische Bezeichnung: Elective Course in Physics: Quantum Field Theory II)
(Prüfungsordnungsmodul: Physikalische Wahlfächer)

Lehrveranstaltungen:

• • Quantenfeldtheorie II
    (Vorlesung, 4 SWS, Thomas Thiemann, Do, 8:00 - 10:00, 14:00 - 16:00, HE; Do; ab 16.10.2014; Die erste Vorlesung findet erst am Do, 16.10.2014 statt.)
  • Übung zur Quantenfeldtheorie II
    (Übung, Thomas Thiemann et al., Mi, 13:00 - 16:00, SR 02.729)

Inhalt:

• Canonical quantisation of classical field theories

Singular Lagrangians and gauge theories, Dirac algorithm, Higgs-Kibble-Stueckelberg mechanism, Grassmann-Calculus for Fermionic Fields, Noether theorem, Noether charges, Canonical CCR and CAR field algebras,

• Representations of CCR and CAR

States and representations, GNS construction. Invariant states and symmetries. Haag’s theorem, Bogol’ubov transformations and examples. Dynamics: From instantaneous fields to interacting fields. Wightman distributions and their axiomatic properties.

• Axiomatic Quantum Field Theory

Analytic properties of Wightman distributions, Jost sets, CPT theorem, Spin Statistics theorem, Cluster Decomposition theorem,

• Haag-Ruelle rigorous scattering theory

Moeller operators and Jost S-Matrix, Haag-Ruelle spectral conditions on Kaellen-Lehman measure of 2-point distribution, Asymptotic Creation operators for the interacting fields, Haag-Ruelle theorem and LSZ asymptotic conditions, LSZ reduction formula and time ordered Wightman distributions

• Formal scattering theory

Gell-Mann-Low formal scattering matrix, Normal ordering and Wick’s’ theorem, Gauge Invariance and Relativistic Covariance in QED: Gupta-Bleuler field, Computational techniques for QED, divergences in loop diagrammes, Feynman diagrammes and rules for QED

• Renormalisation and systematic perturbation theory

Removal of vacuum bubbles and tadpole diagrammes, Resummation, connected 1-PI diagrammes, effective action, Additive and multiplicative renormalisation, Renormalisation schemes: Pauli-Villars,BPHZ,Dimensional,Feynman,Schwinger,Epstein-Glaser, Renormalisation group, running couplings, asymptotic freedom, confinement

• Applications

Electroweak interaction, spontaneous symmetry breaking, Goldstone bosons, Quantum Chromodynamics, Selected tree graph processes of QED, Vacuum energy: Casimir effect, External field problems in QED: Classical current, classical Maxwell field (Schwinger effect), Outlook: Rigorous path integrals, constructive and Euclidian QFT

Lernziele und Kompetenzen:

Die Studierenden

• erläutern die wesentliche Inhalte der Vorlesung

• wenden die Methoden auf konkrete Beispiele an

Verwendbarkeit des Moduls / Einpassung in den Musterstudienplan:

1. Physik (Master of Science)
   (Po-Vers. 2010 | Masterprüfung | Masterprüfung - beschleunigtes Verfahren (Forschungsstudiengang) | Physikalische Wahlfächer)
2. Physik (Master of Science)
   (Po-Vers. 2010 | Masterprüfung | Masterprüfung | Physikalische Wahlfächer)

Studien-/Prüfungsleistungen:

Physikalisches Wahlfach: Quantenfeldtheorie II (Prüfungsnummer: 213403)

Prüfungsleistung, mündliche Prüfung, Dauer (in Minuten): 30, benotet

Anteil an der Berechnung der Modulnote: 100.0 %

Erstablegung: WS 2014/2015

1. Prüfer:

Thomas Thiemann