Broken Symmetries

1962/08/01 by Jeffrey Goldstone, Abdus Salam, Steven Weinberg · 1,657 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Conjecture #Goldstone #Goldstone boson #Homogeneous space #Invariant (physics) #Invariant mass #Lagrangian #Mathematical physics #Mathematics #Particle physics theoretical and experimental studies #Physics #Pure mathematics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Symmetry (geometry) #Symmetry breaking #Theoretical physics #Transformation (genetics)

paper · doi:10.1103/physrev.127.965

published in Physical Review 127(3), 965-970 (American Institute of Physics)

openalex publication_date 1962/08/01 · openalex created_date 2022/05/12 · openalex updated_date 2026/07/31

Abstract

Some proofs are presented of Goldstone's conjecture, that if there is continuous symmetry transformation under which the Lagrangian is invariant, then either the vacuum state is also invariant under the transformation, or there must exist spinless particles of zero mass.

Cited by

• Modern theory of nuclear forces
• Effective Lagrangians and Field Algebras with Chiral Symmetry
• Keldysh field theory for driven open quantum systems
• The Stueckelberg Field
• Black Hole Thermodynamics
• Spontaneously Broken Spacetime Symmetries and Goldstone's Theorem
• Ultra-Light Dark Matter
• Gedanken Worlds without Higgs: QCD-Induced Electroweak Symmetry Breaking
• The future of the Higgs boson
• General Theory of Broken Local Symmetries
• Symmetry breaking and scalar bosons
• Kaon condensation and Goldstone's theorem
• Introduction to Effective Field Theory
• Chiral effective field theory and nuclear forces
• Fermion Interactions and Universal Behavior in Strongly Interacting Theories
• Cosmological phase transitions: From perturbative particle physics to gravitational waves
• More Is Different
• Plasmons, Gauge Invariance, and Mass
• Goldstone-Mode Phonon Dynamics in the PyrochloreCd2Re2O7
• Radiative Corrections as the Origin of Spontaneous Symmetry Breaking
• Complete EFT operator bases for dark matter and weakly-interacting light particle
• Unified Description of Nambu-Goldstone Bosons without Lorentz Invariance
• There are no Goldstone bosons in two dimensions
• Localization and symmetries
• Gauge dependence of effective gravitational field
• Goldstone bosons in presence of charge density
• Quantum field theory in a magnetic field: From quantum chromodynamics to graphene and Dirac semimetals
• Identity of the imaginary-time and real-time thermal propagators for scalar bound states in a one-generation Nambu–Jona-Lasinio model
• Effective action and density functional theory
• Goldstone theorem, Hugenholtz–Pines theorem, and Ward–Takahashi relation in finite volume Bose–Einstein condensed gases
• Finite-Size Studies on the SO(5) Symmetry of the Hubbard Model
• Anomalous chiral perturbation theory meson Lagrangian to orderp6reexamined
• Induced symmetry breaking and a new phase of hadronic matter at high density
• Conceptual Developments of 20th Century Field Theories
• Magnetism and thermodynamics of spin-(12,1)decorated Heisenberg chain with spin-1 pendants
• “Induced” supersymmetry breaking with a vanishing vacuum energy?
• Higgs mechanism with type-II Nambu-Goldstone bosons at finite chemical potential
• Effective potential for composite operators and for an auxiliary scalar field in a Nambu–Jona-Lasinio model
• Extension of the Anderson-Higgs mechanism
• Ultracold gases far from equilibrium
• Quantum dynamics in the thermodynamic limit
• U(1)symmetry breaking and violated axial symmetry inTlCuCl3and other insulating spin systems
• Lorentz violation with an antisymmetric tensor
• Isospin breaking in Kℓ4 decay of the neutral kaon
• SPONTANEOUS SUPERSYMMETRIC GENERATION OF AN INDETERMINATE MASS SCALE AND A POSSIBLE LIGHT STERILE NEUTRINO
• Effective Lagrangian for Nonrelativistic Systems
• Matter-gravity couplings and Lorentz violation
• Double-counting ambiguities in the linear model
• Low energy theorems of quantum gravity from effective field theory
• THE HISTORY OF THE GURALNIK, HAGEN AND KIBBLE DEVELOPMENT OF THE THEORY OF SPONTANEOUS SYMMETRY BREAKING AND GAUGE PARTICLES
• A Model of Leptons
• Broken Symmetries and the Masses of Gauge Bosons
• Broken Symmetry and the Mass of Gauge Vector Mesons
• Global Conservation Laws and Massless Particles
• Magnetic Catalysis: A Review
• The 1979 Nobel Prize in Physics
• Bogoliubov excitations of disordered Bose-Einstein condensates
• How generic scale invariance influences quantum and classical phase transitions
• Electrodynamics with Lorentz-violating operators of arbitrary dimension
• Dynamical symmetry breaking in models with strong Yukawa interactions
• Symmetry improvement of 3PI effective actions forO(N)scalar field theory
• Fermions with Lorentz-violating operators of arbitrary dimension
• Anomalous multi-order Raman scattering in LaMnO3: a signature of quantum lattice effects in a Jahn–Teller crystal
• Chiral effective field theory for nuclear matter with long- and short-range multi-nucleon interactions
• Spontaneous symmetry breaking in light front field theory
• New branches of massive gravity
• New Vacuum of Bethe Ansatz Solutions in Thirring Model
• The pion: an enigma within the Standard Model
• The abelian Higgs Kibble model, unitarity of the S-operator
• Jarzynski Equality for Driven Quantum Field Theories
• Gapless Hartree-Fock resummation scheme for theO(N)model
• The Higgs field and the resolution of the Cosmological Constant Paradox in the Weyl-geometrical Universe
• Lorentz and diffeomorphism violations in linearized gravity
• Spontaneous symmetry probing
• Emergence of the Unconventional Type-II Nambu-Goldstone Modes with Topological Origin in Bose Superfluids
• Statistics and Properties of Low-Frequency Vibrational Modes in Structural Glasses
• NMSSMCALC: A program package for the calculation of loop-corrected Higgs boson masses and decay widths in the (complex) NMSSM
• The making of the Standard Model
• Dark Matter Superfluidity
• Monopole and instanton effects in QCD
• Elasticity of polydomain liquid crystal elastomers
• The supersymmetric origin of chaos and its hidden topological order
• Dissipation at the two-loop level: Undressing the chiral condensate
• Global SU(3)C×SU(2)L×U(1)Y linear sigma model: Axial-vector Ward-Takahashi identities and decoupling of certain heavy BSM particles due to the Goldstone theorem
• Symmetries and Dualities in the Theory of Elasticity
• Gauge-independent Brout–Englert–Higgs mechanism and Yang–Mills theory with a gauge-invariant gluon mass term
• A robust generalization of the Legendre transform for QFT
• Chiral Perturbation Theory
• Monitoring and manipulating Higgs and Goldstone modes in a supersolid quantum gas
• Spin-orbit-coupled Bose gases at finite temperatures
• Constraining the effective action by a method of external sources
• Observational Constraints on Local Lorentz Invariance
• CFT data in the Gross-Neveu model
• Non-equivalence between Heisenberg XXZ spin chain and Thirring model
• Nonlinearly realized local scale invariance: gravity and matter
• Predicción del compromiso del personal a partir del análisis del clima organizacional
• Phase diagram and dynamics of the SU(N) symmetric Kondo lattice model
• BCS–BEC CROSSOVER IN RELATIVISTIC FERMI SYSTEMS
• Properties of the top quark
• A Renormalization-Group Study of Interacting Bose–Einstein Condensates: II. Anomalous Dimension η for \(d \lesssim 4\) at Finite Temperatures
• A general framework to diagonalize vector–scalar and axial-vector–pseudoscalar transitions in the effective meson Lagrangian
• Broken symmetries, massless particles and gauge fields
• Spontaneous Symmetry Breakdown without Massless Bosons
• Symmetry Breaking in Non-Abelian Gauge Theories
• Does Spontaneous Breakdown of Symmetry Imply Zero-Mass Particles?
• Spontaneously broken boosts and the Goldstone continuum
• Higgs boson [wikipedia]
• Brane Effective Actions, Kappa-Symmetry and Applications. [europepmc]
• Scale invariance in natural and artificial collective systems: a review. [europepmc]
• Cooper Pairing in A Doped 2D Antiferromagnet with Spin-Orbit Coupling. [europepmc]
• Non-Equilibrium Quantum Electrodynamics in Open Systems as a Realizable Representation of Quantum Field Theory of the Brain. [europepmc]
• Toward a Unified View of Cognitive and Biochemical Activity: Meditation and Linguistic Self-Reconstructing May Lead to Inflammation and Oxidative Stress Improvement. [europepmc]
• Sounds Stimulation on In Vitro HL1 Cells: A Pilot Study and a Theoretical Physical Model. [europepmc]
• On Collective Molecular Dynamics in Biological Systems: A Review of Our Experimental Observations and Theoretical Modeling. [europepmc]
• Thermodynamic Insights into Symmetry Breaking: Exploring Energy Dissipation across Diverse Scales. [europepmc]
• Dirac equation for photons in a fibre: Origin of polarisation. [europepmc]
• Monte Carlo Based Techniques for Quantum Magnets with Long-Range Interactions. [europepmc]
• SU( N ) symmetry of coherent photons controlled by rotated waveplates. [europepmc]
• Magnons from time-dependent density-functional perturbation theory and nonempirical Hubbard functionals. [europepmc]
• Phase diagram and spectroscopic signatures of a supersolid in the quantum ising magnet K 2 Co(SeO 3 ) 2 . [europepmc]
• Observation of phase correlations in ferrofluids. [europepmc]
• Conscious simultaneity with continuous motion: a measure-theoretic resolution of the hard problem. [europepmc]
• Beyond the standard Higgs after the 125 GeV Higgs discovery [europepmc]
• Non-Equilibrium Quantum Brain Dynamics: Super-Radiance and Equilibration in 2 + 1 Dimensions [europepmc]

Related

• Goldstone theorem revisited
• Spontaneously Broken Spacetime Symmetries and Goldstone's Theorem
• New Symmetries of Massless QED
• Soft theorems and spontaneous symmetry breaking
• Symmetries, Symmetry Breaking, Gauge Symmetries