Lorentz Symmetry Breaking―Classical and Quantum Aspects: Classical and Quantum Aspects (SpringerBriefs in Physics)

✍ Scribed by Tiago Mariz, Jose Roberto Nascimento, Albert Petrov

• Publisher: Springer
• Year: 2022
• Tongue: English
• Leaves: 122
• Edition: 1
• Category: Library

✦ Synopsis

This book presents a review of various issues related to Lorentz symmetry breaking. Explicitly, we consider (i) motivations for introducing Lorentz symmetry breaking, (ii) classical aspects of Lorentz-breaking field theory models including typical forms of Lorentz-breaking additive terms, wave propagation in Lorentz-breaking theories, and mechanisms for breaking the Lorentz symmetry; (iii) quantum corrections in Lorentz-breaking theories, especially the possibilities for perturbation generating the most interesting Lorentz-breaking terms; (iv) correspondence between non-commutative field theories and Lorentz symmetry breaking; (v) supersymmetric Lorentz-breaking theories; and (vi) Lorentz symmetry breaking in a curved space-time. We close the book with the review of experimental studies of Lorentz symmetry breaking.

The importance and relevance of these topics are explained, first, by studies of limits of applicability of the Lorentz symmetry, second, by searches of the possible extensions of the standard model, including the Lorentz-breaking ones, and need to study their properties, third, by the relation between Lorentz symmetry breaking with string theory, fourth, by the problem of formulating a consistent quantum gravity theory, so that various modified gravity models are to be examined.

✦ Table of Contents

1 Introduction
2 Classical aspects
2.1 Review of LV extensions
2.2 Wave propagation in LV theories
2.3 Duality issues in LV theories
2.4 Spontaneous breaking of Lorentz symmetry
2.5 Conclusions
3 Perturbative generation
3.1 Problem of ambiguities
3.2 LV contributions in the scalar sector
3.3 Mixed LV scalar-vector contribution
3.4 The Carroll-Field-Jackiw term
3.4.1 General situation and zero temperature case
3.4.2 Finite temperature case
3.4.3 Non-Abelian generalization
3.5 CPT-even term for the gauge field
3.6 Higher-derivative LV terms
3.7 Divergent contributions in gauge and spinor sectors of LV QED
3.8 Discussion and conclusions
4 Lorentz symmetry breaking and noncommutativity
4.1 Formulations for noncommutativity
4.2 LV impacts of the Moyal product
4.3 Seiberg-Witten map
4.4 Noncommutative fields
4.5 Conclusions
5 Lorentz symmetry breaking and supersymmetry
5.1 Deformation of the supersymmetry algebra
5.2 Lorentz symmetry breaking through introducing extra superfields
5.3 Straightforward breaking
5.4 Conclusions
6 Lorentz and CPT symmetry breaking in gravity
6.1 Motivations for 4D gravitational CS term
6.2 Perturbative generation of the gravitational CS term
6.3 Problem of spontaneous Lorentz symmetry breaking in gravity
6.4 Possible LV terms in gravity
6.5 Conclusions
7 Experimental studies
7.1 Non-gravitational studies
7.2 Gravitational effects