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Books on the topic 'Spontaneous chiral symmetry breaking'

Author: Grafiati

Published: 4 May 2024

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1

Malomed, Boris A., ed. Spontaneous Symmetry Breaking, Self-Trapping, and Josephson Oscillations. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-21207-9.

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2

Malomed, Boris A. Spontaneous Symmetry Breaking, Self-Trapping, and Josephson Oscillations. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013.

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3

Doi, Takahiro. Lattice QCD Study for the Relation Between Confinement and Chiral Symmetry Breaking. Singapore: Springer Singapore, 2017. http://dx.doi.org/10.1007/978-981-10-6596-5.

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4

Marino, Marcos. Quantum chromodynamics. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.32.

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This article focuses on chiral random matrix theories with the global symmetries of quantum chromodynamics (QCD). In particular, it explains how random matrix theory (RMT) can be applied to the spectra of the Dirac operator both at zero chemical potential, when the Dirac operator is Hermitian, and at non-zero chemical potential, when the Dirac operator is non-Hermitian. Before discussing the spectra of these Dirac operators at non-zero chemical potential, the article considers spontaneous symmetry breaking in RMT and the QCD partition function. It then examines the global symmetries of QCD, taking into account the Dirac operator for a finite chiral basis, as well as the global symmetry breaking pattern and the Goldstone manifold in chiral random matrix theory (chRMT). It also describes the generating function for the Dirac spectrum and applications of chRMT to QCD to gauge degrees of freedom.

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5

Vigdor, Steven E. Water, Water, Here and There. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198814825.003.0004.

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Chapter 4 deals with the stability of the proton, hence of hydrogen, and how to reconcile that stability with the baryon number nonconservation (or baryon conservation) needed to establish a matter–antimatter imbalance in the infant universe. Sakharov’s three conditions for establishing a matter–antimatter imbalance are presented. Grand unified theories and experimental searches for proton decay are described. The concept of spontaneous symmetry breaking is introduced in describing the electroweak phase transition in the infant universe. That transition is treated as the potential site for introducing the imbalance between quarks and antiquarks, via either baryogenesis or leptogenesis models. The up–down quark mass difference is presented as essential for providing the stability of hydrogen and of the deuteron, which serves as a crucial stepping stone in stellar hydrogen-burning reactions that generate the energy and elements needed for life. Constraints on quark masses from lattice QCD calculations and violations of chiral symmetry are discussed.

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6

Malomed, Boris A. Spontaneous Symmetry Breaking, Self-Trapping, and Josephson Oscillations. Springer, 2016.

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7

Malomed, Boris A. Spontaneous Symmetry Breaking, Self-Trapping, and Josephson Oscillations. Springer, 2013.

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8

Kachelriess, Michael. Symmetries and symmetry breaking. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198802877.003.0013.

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The spontaneous breaking of symmetries (SSB) is discussed for global symmetries and Goldstones theorem is derived. The renormalisation of theories with SSB is studied using the effective potential. Then SSB is applied to the Abelian Higgs model, both on the classical and quantum level.

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9

Gaudenzi, Rocco. Historical Roots of Spontaneous Symmetry Breaking: Steps Towards an Analogy. Springer International Publishing AG, 2022.

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10

Doi, Takahiro. Lattice QCD Study for the Relation Between Confinement and Chiral Symmetry Breaking. Springer, 2017.

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11

Doi, Takahiro. Lattice QCD Study for the Relation Between Confinement and Chiral Symmetry Breaking. Springer, 2017.

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12

Doi, Takahiro. Lattice QCD Study for the Relation Between Confinement and Chiral Symmetry Breaking. Springer Singapore Pte. Limited, 2018.

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13

Lectures of David Olive on Gauge Theories and Lie Algebras: With Some Applications to Spontaneous Symmetry Breaking and Integrable Dynamical Systems - with Foreword by Lars Brink. World Scientific Publishing Co Pte Ltd, 2019.

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14

Iliopoulos, John. Spontaneously Broken Symmetries. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198805175.003.0005.

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In this chapter we present the solution to the problem of mass. It is based on the phenomenon of spontaneous symmetry breaking (SSB). We first give the example of buckling, a typical example of spontaneous symmetry breaking in classical physics. We extract the main features of the phenomenon, namely the instability of the symmetric state and the degeneracy of the ground state. The associated concepts of the critical point and the order parameter are deduced. A more technical exposition is given in a separate section. Then we move to a quantum physics example, that of the Heisenberg ferromagnet. We formulate Goldstone’s theorem which associates a massless particle, the Goldstone boson, to the phenomenon of spontaneous symmetry breaking. In the last section we present the mechanism of Brout–Englert–Higgs (BEH). We show that spontaneous symmetry breaking in the presence of gauge interactions makes it possible for particles to become massive. The remnant of the mechanism is the appearance of a physical particle, the BEH boson, which we identify with the particle discovered at CERN.

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15

Mann, Peter. Classical Electromagnetism. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0027.

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In this chapter, Noether’s theorem as a classical field theory is presented and the properties of variations are again discussed for fields (i.e. field variations, space variations, time variations, spacetime variations), resulting in the Noether condition. Quasisymmetries and spontaneous symmetry breaking are discussed, as well as local symmetry and global symmetry. Following these definitions, Noether’s first theorem and Noether’s second theorem are developed. The classical Schrödinger field is investigated and the key equations of classical mechanics are summarised into a single Lagrangian. Symmetry properties of the field action and equations of motion are then compared. The chapter discusses the energy–momentum tensor, the Klein–Utiyama theorem, the Liouville equation and the Hamilton–Jacobi equation. It also discusses material science, special orthogonal groups and complex scalar fields.

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16

Mann, Peter. Symmetries & Lagrangian-Hamilton-Jacobi Theory. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0011.

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This chapter discusses conservation laws in Lagrangian mechanics and shows that certain conservation laws are just particular examples of a more fundamental theory called ‘Noether’s theorem’, after Amalie ‘Emmy’ Noether, who first discovered it in 1918. The chapter starts off by discussing Noether’s theorem and symmetry transformations in Lagrangian mechanics in detail. It then moves on to gauge theory and surface terms in the action before isotropic symmetries. continuous symmetry, conserved quantities, conjugate momentum, cyclic coordinates, Hessian condition and discrete symmetries are discussed. The chapter also covers Lie algebra, spontaneous symmetry breaking, reduction theorems, non-dynamical symmetries and Ostrogradsky momentum. The final section of the chapter details Carathéodory–Hamilton–Jacobi theory in the Lagrangian setting, to derive the Hamilton–Jacobi equation on the tangent bundle!

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17

Baulieu, Laurent, John Iliopoulos, and Roland Sénéor. Beyond the Standard Model. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198788393.003.0026.

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The motivation for supersymmetry. The algebra, the superspace, and the representations. Field theory models and the non-renormalisation theorems. Spontaneous and explicit breaking of super-symmetry. The generalisation of the Montonen–Olive duality conjecture in supersymmetric theories. The remarkable properties of extended supersymmetric theories. A brief discussion of twisted supersymmetry in connection with topological field theories. Attempts to build a supersymmetric extention of the standard model and its experimental consequences. The property of gauge supersymmetry to include general relativity and the supergravity models.

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18

Baulieu, Laurent, John Iliopoulos, and Roland Sénéor. Supersymmetry, or the Defence of Scalars. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198788393.003.0027.

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The only fields of the Standard Model whose masses are not protected by a symmetry are the scalar fields. Supersymmetry is a symmetry between fermions and bosons which provides precisely such a protection mechanism. This chapter presents a comprehensive study of supersymmetric field theories. In particular, it is shown that they do not suffer from the phenomenon of gauge hierarchy. They have remarkable renormalisation properties and offer the most attractive framework to build a unified theory. The breaking of supersymmetry, both explicit and spontaneous, is studied in detail. The generalisation of electric-magnetic duality in supersymmetric theories yields non-perturbative results and the concept of twist makes possible the study of topological field theories. The supersymmetric extension of the Standard Model is shown to predict the existence of new elementary particles, whose phenomenological properties are analysed.

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19

Bertel, E., and A. Menzel. Nanostructured surfaces: Dimensionally constrained electrons and correlation. Edited by A. V. Narlikar and Y. Y. Fu. Oxford University Press, 2017. http://dx.doi.org/10.1093/oxfordhb/9780199533046.013.11.

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This article examines dimensionally constrained electrons and electronic correlation in nanostructured surfaces. Correlation effects play an important role in spatial confinement of electrons by nanostructures. The effect of correlation will become increasingly dominant as the dimensionality of the electron wavefunction is reduced. This article focuses on quasi-one-dimensional (quasi-1D) confinement, i.e. more or less strongly coupled one-dimensional nanostructures, with occasional reference to 2D and 0D systems. It first explains how correlated systems exhibit a variety of electronically driven phase transitions, and especially the phases occurring in the generic phase diagram of correlated materials. It then describes electron–electron and electron–phonon interactions in low-dimensional systems and the phase diagram of real quasi-1D systems. Two case studies are considered: metal chains on silicon surfaces and quasi-1D structures on metallic surfaces. The article shows that spontaneous symmetry breaking occurs for many quasi-1D systems on both semiconductor and metal surfaces at low temperature.

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20

Iliopoulos, John, and Theodore N. Tomaras. Elementary Particle Physics. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780192844200.001.0001.

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Determining the nature of matter’s smallest constituents, and the interactions among them, is the subject of a branch of fundamental physics called “The Physics of Elementary Particles” – the subject of this book. During the last decades this field has gone through a phase transition. It culminated in the formulation of a new theoretical scheme, known as “The Standard Model”, which brought profound changes in our ways of thinking and understanding nature’s fundamental forces. Its agreement with experiment is impressive, to the extent that we should no longer talk about “The Standard Model” but instead “The Standard Theory”. This new vision is based on geometry; the interactions are required to satisfy a certain geometrical principle. In the physicists’ jargon this principle is called “gauge invariance”; in mathematics it is a concept of differential geometry. It is the purpose of this book to present and explain this modern viewpoint to a readership of well motivated undergraduate students. We propose to guide the reader to the more advanced concepts of gauge symmetry, quantum field theory and the phenomenon of spontaneous symmetry breaking through concrete physical examples. The presentation of the techniques required for particle physics is self-contained, and the mathematics is kept at the absolutely necessary level. The reader is invited to join the glorious parade of the theoretical advances and experimental discoveries of the last decades which established our current view. Our ambition is to make this fascinating subject accessible to undergraduate students and, hopefully, to motivate them to study it further.

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21

Baulieu, Laurent, John Iliopoulos, and Roland Sénéor. From Classical to Quantum Fields. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198788393.001.0001.

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Quantum field theory has become the universal language of most modern theoretical physics. This book is meant to provide an introduction to this subject with particular emphasis on the physics of the fundamental interactions and elementary particles. It is addressed to advanced undergraduate, or beginning graduate, students, who have majored in physics or mathematics. The ambition is to show how these two disciplines, through their mutual interactions over the past hundred years, have enriched themselves and have both shaped our understanding of the fundamental laws of nature. The subject of this book, the transition from a classical field theory to the corresponding Quantum Field Theory through the use of Feynman’s functional integral, perfectly exemplifies this connection. It is shown how some fundamental physical principles, such as relativistic invariance, locality of the interactions, causality and positivity of the energy, form the basic elements of a modern physical theory. The standard theory of the fundamental forces is a perfect example of this connection. Based on some abstract concepts, such as group theory, gauge symmetries, and differential geometry, it provides for a detailed model whose agreement with experiment has been spectacular. The book starts with a brief description of the field theory axioms and explains the principles of gauge invariance and spontaneous symmetry breaking. It develops the techniques of perturbation theory and renormalisation with some specific examples. The last Chapters contain a presentation of the standard model and its experimental successes, as well as the attempts to go beyond with a discussion of grand unified theories and supersymmetry.

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22

Kenyon, Ian R. Quantum 20/20. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198808350.001.0001.

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This text reviews fundametals and incorporates key themes of quantum physics. One theme contrasts boson condensation and fermion exclusivity. Bose–Einstein condensation is basic to superconductivity, superfluidity and gaseous BEC. Fermion exclusivity leads to compact stars and to atomic structure, and thence to the band structure of metals and semiconductors with applications in material science, modern optics and electronics. A second theme is that a wavefunction at a point, and in particular its phase is unique (ignoring a global phase change). If there are symmetries, conservation laws follow and quantum states which are eigenfunctions of the conserved quantities. By contrast with no particular symmetry topological effects occur such as the Bohm–Aharonov effect: also stable vortex formation in superfluids, superconductors and BEC, all these having quantized circulation of some sort. The quantum Hall effect and quantum spin Hall effect are ab initio topological. A third theme is entanglement: a feature that distinguishes the quantum world from the classical world. This property led Einstein, Podolsky and Rosen to the view that quantum mechanics is an incomplete physical theory. Bell proposed the way that any underlying local hidden variable theory could be, and was experimentally rejected. Powerful tools in quantum optics, including near-term secure communications, rely on entanglement. It was exploited in the the measurement of CP violation in the decay of beauty mesons. A fourth theme is the limitations on measurement precision set by quantum mechanics. These can be circumvented by quantum non-demolition techniques and by squeezing phase space so that the uncertainty is moved to a variable conjugate to that being measured. The boundaries of precision are explored in the measurement of g-2 for the electron, and in the detection of gravitational waves by LIGO; the latter achievement has opened a new window on the Universe. The fifth and last theme is quantum field theory. This is based on local conservation of charges. It reaches its most impressive form in the quantum gauge theories of the strong, electromagnetic and weak interactions, culminating in the discovery of the Higgs. Where particle physics has particles condensed matter has a galaxy of pseudoparticles that exist only in matter and are always in some sense special to particular states of matter. Emergent phenomena in matter are successfully modelled and analysed using quasiparticles and quantum theory. Lessons learned in that way on spontaneous symmetry breaking in superconductivity were the key to constructing a consistent quantum gauge theory of electroweak processes in particle physics.

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