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Quantum QFT: groups, effective action, fiber bundles, anomalies, EFT

  1. Aug 7, 2017 #1
    Hi, I am looking for textbooks in QFT. I studied QFT using Peskin And Schroeder + two year master's degree QFT programme.
    I want to know about the next items:
    1) Lorentz group and Lie group (precise adjectives, group representation and connection between fields and spins from the standpoint of Lorentz group)
    2) Effective action, effective potential, external sources.
    3) Geometric sense of gauge fields (Vertical and horizontal bundles, connection with tensors)
    4) Anomalies
    - clear division between axial anomaly in QCD (Theta Vacuum: axion -> 2 gluons) and axial anomaly in QCD of current (Chern–Simons term: pion->two photons, photon->three pions, ...)
    - consideration anomalies in different approaches (perturbative, functional, topological (index theorem))
    - difference between Consistent, Covariant, Multiplicative Anomalies
    5) topologically aspects of quantum theory (instantons, sfalerons, Theta Vacuum)
    6) effective theory field (sigma models, Nambu–Jona-Lasinio model)
    7) introduction temperate in theory.

    I would appreciate for good books.
     
  2. jcsd
  3. Aug 8, 2017 #2

    vanhees71

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    2016 Award

    S. Weinberg, The Quantum Theory of Fields, 3 Vols, Cambridge University Press

    I don't underst and 7). Do you mean finite-temperature QFT? Then I'd recommend

    M. LeBellac, Thermal Field Theory, Cambridge University Press, Cambridge, New York, Melbourne, 1996.
    J. I. Kapusta and C. Gale, Finite-Temperature Field Theory; Principles and Applications, Cambridge University Press, 2 ed., 2006.
    M. Laine and A. Vuorinen, Basics of Thermal Field Theory, vol. 925 of Lecture Notes in Physics, 2016.
     
  4. Aug 8, 2017 #3
    Yes. Thank you for advice. Is there something other than Weinberg?

    And I would like to know are there any QFT books written from a mathematical view?
     
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