Effective Field Theory for Spontaneously Broken Symmetry

ISBN-13: 9783031483776 / Angielski

Tomás Brauner

Spis treści

·         PART I: PROLOGUE

o   Introduction

§  What is effective field theory?

§  Broken symmetry zoo

§  Structure of this book

o   Our first model

§  Spontaneous symmetry breaking

§  Nambu–Goldstone boson and its interactions

§  Low-energy effective field theory

o   Generalizations of the model

§  Non-Abelian symmetry

§  Nonzero density

§  Moral lessons

·         PART II: FOUNDATIONS

o   Spontaneous symmetry breaking

§  Symmetries in classical and quantum physics

§  Order parameter and the vacuum manifold

§  Some mathematical subtleties

o   Nambu–Goldstone bosons

§  Intuitive picture

§  Goldstone theorem

§  Classification

o   Effective field theory

§  Scale separation

§  Power counting

§  Parameter matching

·         PART III: SPONTANEOUSLY BROKEN INTERNAL SYMMETRY

o   Nonlinear realization of symmetry

§  Group action on manifolds

§  Classification of nonlinear realizations

§  Standard realization of symmetry

§  Geometry of the coset space

o   Low-energy effective field theory

§  Structure of the effective Lagrangian

§  Explicit solution at leading order of the derivative expansion

§  Equation of motion and spectrum of Nambu–Goldstone bosons

§  Simplified method for construction of effective Lagrangians

o   Some examples and applications

§  Spin waves in ferro- and antiferromagnets

§  Chiral perturbation theory of mesons

§  Effective field theory of fully broken SU(2)

o   Scattering of Nambu–Goldstone bosons

§  Single soft limit of scattering amplitudes

§  Exceptions to the Adler zero property

§  Soft limit bootstrap of effective theories

§  Exceptional effective theories with enhanced soft limit

·         PART IV: SPONTANEOUSLY BROKEN SPACETIME SYMMETRY

o   Differences between internal and spacetime symmetry

§  Redundant symmetries

§  Relations between Noether currents

§  Spectrum of Nambu–Goldstone bosons

o   Nonlinear realization of spacetime symmetry

§  Inverse Higgs constraints

§  Coset construction without broken translations

§  Coset construction with broken translations

o   Broken spacetime symmetry in quantum matter

§  Global versus local action of symmetry

§  Effective actions from the Stückelberg trick

§  Comparison with coset construction

§  Some applications

o   Broken spacetime symmetry in classical matter

§  Emergent symmetry of classical matter

§  Nonlinear realization of emergent symmetry

§  Effective field theory of fluids and solids

·         PART V: EPILOGUE

o   Topics not covered in this book

§  Topological aspects of spontaneous symmetry breaking

§  No-go theorems for spontaneous symmetry breaking

§  Gauge invariance and the Higgs mechanism

§  Generalized symmetries and their breaking

o   Some open questions

·         APPENDIX

o   Basics of differential geometry

§  Tangent and cotangent space, differential forms

§  Lie transport and Lie derivative

§  Exterior derivative and exterior calculus

§  Affine connection and covariant derivative

§  Riemann metric and the Hodge star

§  Integration on manifolds

§  Homology and cohomology

O autorze

Tomáš Brauner earned his PhD in theoretical physics, astronomy, and astrophysics from Charles University in Prague in 2006. Following postdoctoral positions in Frankfurt, Bielefeld, Helsinki, and Vienna, he joined the University of Stavanger as an associate professor of physics in 2015 and was promoted to full professor in 2016. His research interests encompass various aspects of quantum field theory and its applications to particle, nuclear, and condensed-matter physics, with a particular emphasis on the role of symmetries and their spontaneous breaking.

Blurb

This book is about spontaneous symmetry breaking, which is a classic area of theoretical physics that lies at the core of many fascinating phenomena such as ferromagnetism, superfluidity, superconductivity, or the Higgs mechanism. The book brings an up-to-date overview of spontaneous symmetry breaking and of modern effective field theory description thereof. The topics covered include the classification of Nambu–Goldstone bosons, nonlinear realization of internal and spacetime symmetries and the construction of the corresponding effective actions, and selected applications. With in-depth exposition of conceptual foundations and numerous illustrative examples, the book is accessible to anybody having taken a basic course on quantum field theory. It serves as a self-contained text for graduate students and junior researchers in diverse areas of physics, but also as a useful reference for experts.