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Applied Computational Physics$
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Joseph F. Boudreau and Eric. S. Swanson

Print publication date: 2017

Print ISBN-13: 9780198708636

Published to Oxford Scholarship Online: February 2018

DOI: 10.1093/oso/9780198708636.001.0001

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Quantum field theory

Quantum field theory

Chapter:
(p.844) 24 Quantum field theory
Source:
Applied Computational Physics
Author(s):

Joseph F. Boudreau

Eric S. Swanson

Publisher:
Oxford University Press
DOI:10.1093/oso/9780198708636.003.0024

Markov chain Monte Carlo techniques are developed to compute properties of a variety of quantum field theories. The method is introduced with a simple scalar field theory and used to evaluate the particle spectrum and phase diagram for parity symmetry breaking. The technique of micorcanonical updating is introduced to increase efficiency. The important topic of gauge theory is then introduced via the gauged Z2 model. Development of the gauge theory formalism continues with Abelian gauge theory in two dimensions. The interaction between static charges is computed and compared to the exact result. The string tension in nonableian SU(2) gauge theory is explored with the aid of the renormalization group, which gives an entrée to a discussion of the Higgs mechanism. Finally, the formalism for including fermions is briefly reviewed.

Keywords:   path integral, phi-4 theory, gauge theory, nonAbelian gauge theory, fermions, symmetry breaking

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