en.unionpedia.org

Spontaneous symmetry breaking, the Glossary

Index Spontaneous symmetry breaking

Spontaneous symmetry breaking is a spontaneous process of symmetry breaking, by which a physical system in a symmetric state spontaneously ends up in an asymmetric state.[1]

Table of Contents

  1. 97 relations: Autocatalysis, Baryon, Catastrophe theory, Chiral symmetry breaking, Chirality (physics), Convection cell, Cosmic inflation, Cosmic string, CP violation, Curie temperature, Diameter, Domain wall, Effective action, Electric potential, Electromagnetism, Electroweak interaction, Elitzur's theorem, Equations of motion, Equidistant, Equilibrium point (mathematics), Euclidean group, Explicit symmetry breaking, Fermi ball, Fermionic condensate, Ferromagnetism, Fluid, Force carrier, Fractional quantum Hall effect, Friedmann–Lemaître–Robertson–Walker metric, Gauge gravitation theory, Gauge theory, Goldstone boson, Grand Unified Theory, Gravitational potential, Higgs boson, Higgs field (classical), Higgs mechanism, Homotopy group, Invariant (physics), Irreversible process, Jeffrey Goldstone, Kyoto University, Lagrangian (field theory), Lie group, Liquid crystal, Magnetic catalysis, Magnetization, Makoto Kobayashi, Maximum and minimum, Mermin–Wagner theorem, ... Expand index (47 more) »

  2. Quantum phases
  3. Standard Model

Autocatalysis

In chemistry, a chemical reaction is said to be autocatalytic if one of the reaction products is also a catalyst for the same reaction.

See Spontaneous symmetry breaking and Autocatalysis

Baryon

In particle physics, a baryon is a type of composite subatomic particle, including the proton and the neutron, that contains an odd number of valence quarks, conventionally three.

See Spontaneous symmetry breaking and Baryon

Catastrophe theory

In mathematics, catastrophe theory is a branch of bifurcation theory in the study of dynamical systems; it is also a particular special case of more general singularity theory in geometry.

See Spontaneous symmetry breaking and Catastrophe theory

Chiral symmetry breaking

In particle physics, chiral symmetry breaking generally refers to the dynamical spontaneous breaking of a chiral symmetry associated with massless fermions. Spontaneous symmetry breaking and chiral symmetry breaking are quantum chromodynamics and quantum field theory.

See Spontaneous symmetry breaking and Chiral symmetry breaking

Chirality (physics)

A chiral phenomenon is one that is not identical to its mirror image (see the article on mathematical chirality). Spontaneous symmetry breaking and chirality (physics) are quantum chromodynamics, quantum field theory and symmetry.

See Spontaneous symmetry breaking and Chirality (physics)

Convection cell

In fluid dynamics, a convection cell is the phenomenon that occurs when density differences exist within a body of liquid or gas.

See Spontaneous symmetry breaking and Convection cell

Cosmic inflation

In physical cosmology, cosmic inflation, cosmological inflation, or just inflation, is a theory of exponential expansion of space in the early universe.

See Spontaneous symmetry breaking and Cosmic inflation

Cosmic string

Cosmic strings are hypothetical 1-dimensional topological defects which may have formed during a symmetry-breaking phase transition in the early universe when the topology of the vacuum manifold associated to this symmetry breaking was not simply connected.

See Spontaneous symmetry breaking and Cosmic string

CP violation

In particle physics, CP violation is a violation of CP-symmetry (or charge conjugation parity symmetry): the combination of C-symmetry (charge conjugation symmetry) and P-symmetry (parity symmetry). Spontaneous symmetry breaking and cP violation are quantum field theory.

See Spontaneous symmetry breaking and CP violation

Curie temperature

In physics and materials science, the Curie temperature (TC), or Curie point, is the temperature above which certain materials lose their permanent magnetic properties, which can (in most cases) be replaced by induced magnetism.

See Spontaneous symmetry breaking and Curie temperature

Diameter

In geometry, a diameter of a circle is any straight line segment that passes through the centre of the circle and whose endpoints lie on the circle.

See Spontaneous symmetry breaking and Diameter

Domain wall

A domain wall is a type of topological soliton that occurs whenever a discrete symmetry is spontaneously broken.

See Spontaneous symmetry breaking and Domain wall

Effective action

In quantum field theory, the quantum effective action is a modified expression for the classical action taking into account quantum corrections while ensuring that the principle of least action applies, meaning that extremizing the effective action yields the equations of motion for the vacuum expectation values of the quantum fields. Spontaneous symmetry breaking and effective action are quantum field theory.

See Spontaneous symmetry breaking and Effective action

Electric potential

Electric potential (also called the electric field potential, potential drop, the electrostatic potential) is defined as the amount of work/energy needed per unit of electric charge to move the charge from a reference point to a specific point in an electric field.

See Spontaneous symmetry breaking and Electric potential

Electromagnetism

In physics, electromagnetism is an interaction that occurs between particles with electric charge via electromagnetic fields.

See Spontaneous symmetry breaking and Electromagnetism

Electroweak interaction

In particle physics, the electroweak interaction or electroweak force is the unified description of two of the four known fundamental interactions of nature: electromagnetism (electromagnetic interaction) and the weak interaction.

See Spontaneous symmetry breaking and Electroweak interaction

Elitzur's theorem

In quantum field theory and statistical field theory, Elitzur's theorem states that in gauge theories, the only operators that can have non-vanishing expectation values are ones that are invariant under local gauge transformations. Spontaneous symmetry breaking and Elitzur's theorem are symmetry.

See Spontaneous symmetry breaking and Elitzur's theorem

Equations of motion

In physics, equations of motion are equations that describe the behavior of a physical system in terms of its motion as a function of time.

See Spontaneous symmetry breaking and Equations of motion

Equidistant

A point is said to be equidistant from a set of objects if the distances between that point and each object in the set are equal.

See Spontaneous symmetry breaking and Equidistant

Equilibrium point (mathematics)

In mathematics, specifically in differential equations, an equilibrium point is a constant solution to a differential equation.

See Spontaneous symmetry breaking and Equilibrium point (mathematics)

Euclidean group

In mathematics, a Euclidean group is the group of (Euclidean) isometries of a Euclidean space \mathbb^n; that is, the transformations of that space that preserve the Euclidean distance between any two points (also called Euclidean transformations).

See Spontaneous symmetry breaking and Euclidean group

Explicit symmetry breaking

In theoretical physics, explicit symmetry breaking is the breaking of a symmetry of a theory by terms in its defining equations of motion (most typically, to the Lagrangian or the Hamiltonian) that do not respect the symmetry. Spontaneous symmetry breaking and explicit symmetry breaking are symmetry.

See Spontaneous symmetry breaking and Explicit symmetry breaking

Fermi ball

In cosmology, Fermi balls are hypothetical objects that may have been created in the early history of the universe by spontaneous symmetry breaking.

See Spontaneous symmetry breaking and Fermi ball

Fermionic condensate

A fermionic condensate (or Fermi–Dirac condensate) is a superfluid phase formed by fermionic particles at low temperatures. Spontaneous symmetry breaking and fermionic condensate are quantum field theory and quantum phases.

See Spontaneous symmetry breaking and Fermionic condensate

Ferromagnetism

Ferromagnetism is a property of certain materials (such as iron) that results in a significant, observable magnetic permeability, and in many cases, a significant magnetic coercivity, allowing the material to form a permanent magnet. Spontaneous symmetry breaking and Ferromagnetism are quantum phases.

See Spontaneous symmetry breaking and Ferromagnetism

Fluid

In physics, a fluid is a liquid, gas, or other material that may continuously move and deform (flow) under an applied shear stress, or external force.

See Spontaneous symmetry breaking and Fluid

Force carrier

In quantum field theory, a force carrier (also known as a messenger particle, intermediate particle, or exchange particle) is a type of particle that gives rise to forces between other particles.

See Spontaneous symmetry breaking and Force carrier

Fractional quantum Hall effect

The fractional quantum Hall effect (FQHE) is a physical phenomenon in which the Hall conductance of 2-dimensional (2D) electrons shows precisely quantized plateaus at fractional values of e^2/h, where e is the electron charge and h is the Planck constant. Spontaneous symmetry breaking and fractional quantum Hall effect are quantum phases.

See Spontaneous symmetry breaking and Fractional quantum Hall effect

Friedmann–Lemaître–Robertson–Walker metric

The Friedmann–Lemaître–Robertson–Walker metric (FLRW) is a metric based on an exact solution of the Einstein field equations of general relativity.

See Spontaneous symmetry breaking and Friedmann–Lemaître–Robertson–Walker metric

Gauge gravitation theory

In quantum field theory, gauge gravitation theory is the effort to extend Yang–Mills theory, which provides a universal description of the fundamental interactions, to describe gravity.

See Spontaneous symmetry breaking and Gauge gravitation theory

Gauge theory

In physics, a gauge theory is a type of field theory in which the Lagrangian, and hence the dynamics of the system itself, do not change under local transformations according to certain smooth families of operations (Lie groups).

See Spontaneous symmetry breaking and Gauge theory

Goldstone boson

In particle and condensed matter physics, Goldstone bosons or Nambu–Goldstone bosons (NGBs) are bosons that appear necessarily in models exhibiting spontaneous breakdown of continuous symmetries. Spontaneous symmetry breaking and Goldstone boson are quantum field theory.

See Spontaneous symmetry breaking and Goldstone boson

Grand Unified Theory

Grand Unified Theory (GUT) is any model in particle physics that merges the electromagnetic, weak, and strong forces (the three gauge interactions of the Standard Model) into a single force at high energies.

See Spontaneous symmetry breaking and Grand Unified Theory

Gravitational potential

In classical mechanics, the gravitational potential is a scalar field associating with each point in space the work (energy transferred) per unit mass that would be needed to move an object to that point from a fixed reference point.

See Spontaneous symmetry breaking and Gravitational potential

Higgs boson

The Higgs boson, sometimes called the Higgs particle, is an elementary particle in the Standard Model of particle physics produced by the quantum excitation of the Higgs field, one of the fields in particle physics theory. Spontaneous symmetry breaking and Higgs boson are quantum field theory and Standard Model.

See Spontaneous symmetry breaking and Higgs boson

Higgs field (classical)

Spontaneous symmetry breaking, a vacuum Higgs field, and its associated fundamental particle the Higgs boson are quantum phenomena. Spontaneous symmetry breaking and Higgs field (classical) are symmetry and theoretical physics.

See Spontaneous symmetry breaking and Higgs field (classical)

Higgs mechanism

In the Standard Model of particle physics, the Higgs mechanism is essential to explain the generation mechanism of the property "mass" for gauge bosons. Spontaneous symmetry breaking and Higgs mechanism are quantum field theory, Standard Model and symmetry.

See Spontaneous symmetry breaking and Higgs mechanism

Homotopy group

In mathematics, homotopy groups are used in algebraic topology to classify topological spaces.

See Spontaneous symmetry breaking and Homotopy group

Invariant (physics)

In theoretical physics, an invariant is an observable of a physical system which remains unchanged under some transformation.

See Spontaneous symmetry breaking and Invariant (physics)

Irreversible process

In science, a process that is not reversible is called irreversible.

See Spontaneous symmetry breaking and Irreversible process

Jeffrey Goldstone

Jeffrey Goldstone (born 3 September 1933) is a British theoretical physicist and an emeritus physics faculty member at the MIT Center for Theoretical Physics.

See Spontaneous symmetry breaking and Jeffrey Goldstone

Kyoto University

, or, is a national research university located in Kyoto, Japan.

See Spontaneous symmetry breaking and Kyoto University

Lagrangian (field theory)

Lagrangian field theory is a formalism in classical field theory. Spontaneous symmetry breaking and Lagrangian (field theory) are quantum field theory.

See Spontaneous symmetry breaking and Lagrangian (field theory)

Lie group

In mathematics, a Lie group (pronounced) is a group that is also a differentiable manifold, such that group multiplication and taking inverses are both differentiable. Spontaneous symmetry breaking and Lie group are symmetry.

See Spontaneous symmetry breaking and Lie group

Liquid crystal

Liquid crystal (LC) is a state of matter whose properties are between those of conventional liquids and those of solid crystals.

See Spontaneous symmetry breaking and Liquid crystal

Magnetic catalysis

Magnetic catalysis is a physics phenomenon, which is defined as an enhancement of dynamical symmetry breaking by an external magnetic field in quantum field theory, used for the description of quantum (quasi-)particles in particle physics, nuclear physics and condensed matter physics. Spontaneous symmetry breaking and magnetic catalysis are quantum field theory.

See Spontaneous symmetry breaking and Magnetic catalysis

Magnetization

In classical electromagnetism, magnetization is the vector field that expresses the density of permanent or induced magnetic dipole moments in a magnetic material.

See Spontaneous symmetry breaking and Magnetization

Makoto Kobayashi

is a Japanese physicist known for his work on CP-violation who was awarded one-fourth of the 2008 Nobel Prize in Physics "for the discovery of the origin of the broken symmetry which predicts the existence of at least three families of quarks in nature.".

See Spontaneous symmetry breaking and Makoto Kobayashi

Maximum and minimum

In mathematical analysis, the maximum and minimum of a function are, respectively, the largest and smallest value taken by the function.

See Spontaneous symmetry breaking and Maximum and minimum

Mermin–Wagner theorem

In quantum field theory and statistical mechanics, the Hohenberg–Mermin–Wagner theorem or Mermin–Wagner theorem (also known as Mermin–Wagner–Berezinskii theorem or Coleman theorem) states that continuous symmetries cannot be spontaneously broken at finite temperature in systems with sufficiently short-range interactions in dimensions. Spontaneous symmetry breaking and Mermin–Wagner theorem are quantum field theory.

See Spontaneous symmetry breaking and Mermin–Wagner theorem

Monopole (mathematics)

In mathematics, a monopole is a connection over a principal bundle G with a section of the associated adjoint bundle.

See Spontaneous symmetry breaking and Monopole (mathematics)

Nobel Prize in Physics

The Nobel Prize in Physics (Nobelpriset i fysik) is an annual award given by the Royal Swedish Academy of Sciences for those who have made the most outstanding contributions to mankind in the field of physics.

See Spontaneous symmetry breaking and Nobel Prize in Physics

Norton's dome

Norton's dome is a thought experiment that exhibits a non-deterministic system within the bounds of Newtonian mechanics.

See Spontaneous symmetry breaking and Norton's dome

Nucleon

In physics and chemistry, a nucleon is either a proton or a neutron, considered in its role as a component of an atomic nucleus.

See Spontaneous symmetry breaking and Nucleon

Order and disorder

In physics, the terms order and disorder designate the presence or absence of some symmetry or correlation in a many-particle system.

See Spontaneous symmetry breaking and Order and disorder

Particle physics

Particle physics or high-energy physics is the study of fundamental particles and forces that constitute matter and radiation. Spontaneous symmetry breaking and particle physics are quantum field theory.

See Spontaneous symmetry breaking and Particle physics

Phase transition

In physics, chemistry, and other related fields like biology, a phase transition (or phase change) is the physical process of transition between one state of a medium and another.

See Spontaneous symmetry breaking and Phase transition

Photon

A photon is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force.

See Spontaneous symmetry breaking and Photon

Physical Review

Physical Review is a peer-reviewed scientific journal established in 1893 by Edward Nichols.

See Spontaneous symmetry breaking and Physical Review

Physical Review Letters

Physical Review Letters (PRL), established in 1958, is a peer-reviewed, scientific journal that is published 52 times per year by the American Physical Society.

See Spontaneous symmetry breaking and Physical Review Letters

Pion

In particle physics, a pion or pi meson, denoted with the Greek letter pi, is any of three subatomic particles:,, and.

See Spontaneous symmetry breaking and Pion

Quantum chromodynamics

In theoretical physics, quantum chromodynamics (QCD) is the study of the strong interaction between quarks mediated by gluons. Spontaneous symmetry breaking and quantum chromodynamics are quantum field theory and Standard Model.

See Spontaneous symmetry breaking and Quantum chromodynamics

Quantum field theory

In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics.

See Spontaneous symmetry breaking and Quantum field theory

Quantum mechanics

Quantum mechanics is a fundamental theory that describes the behavior of nature at and below the scale of atoms. Spontaneous symmetry breaking and Quantum mechanics are theoretical physics.

See Spontaneous symmetry breaking and Quantum mechanics

Quantum spin liquid

In condensed matter physics, a quantum spin liquid is a phase of matter that can be formed by interacting quantum spins in certain magnetic materials.

See Spontaneous symmetry breaking and Quantum spin liquid

Quantum vacuum state

In quantum field theory, the quantum vacuum state (also called the quantum vacuum or vacuum state) is the quantum state with the lowest possible energy. Spontaneous symmetry breaking and quantum vacuum state are quantum field theory.

See Spontaneous symmetry breaking and Quantum vacuum state

Quark

A quark is a type of elementary particle and a fundamental constituent of matter.

See Spontaneous symmetry breaking and Quark

Reflection (mathematics)

In mathematics, a reflection (also spelled reflexion) is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as a set of fixed points; this set is called the axis (in dimension 2) or plane (in dimension 3) of reflection.

See Spontaneous symmetry breaking and Reflection (mathematics)

Rotational frequency

Rotational frequency, also known as rotational speed or rate of rotation (symbols ν, lowercase Greek nu, and also n), is the frequency of rotation of an object around an axis.

See Spontaneous symmetry breaking and Rotational frequency

Rotational symmetry

Rotational symmetry, also known as radial symmetry in geometry, is the property a shape has when it looks the same after some rotation by a partial turn. Spontaneous symmetry breaking and Rotational symmetry are symmetry.

See Spontaneous symmetry breaking and Rotational symmetry

Royal Swedish Academy of Sciences

The Royal Swedish Academy of Sciences (Kungliga Vetenskapsakademien) is one of the royal academies of Sweden.

See Spontaneous symmetry breaking and Royal Swedish Academy of Sciences

Scalar field theory

In theoretical physics, scalar field theory can refer to a relativistically invariant classical or quantum theory of scalar fields. Spontaneous symmetry breaking and scalar field theory are quantum field theory.

See Spontaneous symmetry breaking and Scalar field theory

Space group

In mathematics, physics and chemistry, a space group is the symmetry group of a repeating pattern in space, usually in three dimensions. Spontaneous symmetry breaking and space group are symmetry.

See Spontaneous symmetry breaking and Space group

Spontaneous absolute asymmetric synthesis

Spontaneous absolute asymmetric synthesis is a chemical phenomenon that stochastically generates chirality based on autocatalysis and small fluctuations in the ratio of enantiomers present in a racemic mixture.

See Spontaneous symmetry breaking and Spontaneous absolute asymmetric synthesis

Spontaneous magnetization

Spontaneous magnetization is the appearance of an ordered spin state (magnetization) at zero applied magnetic field in a ferromagnetic or ferrimagnetic material below a critical point called the Curie temperature or.

See Spontaneous symmetry breaking and Spontaneous magnetization

Spontaneous process

In thermodynamics, a spontaneous process is a process which occurs without any external input to the system.

See Spontaneous symmetry breaking and Spontaneous process

Standard Model

The Standard Model of particle physics is the theory describing three of the four known fundamental forces (electromagnetic, weak and strong interactions – excluding gravity) in the universe and classifying all known elementary particles.

See Spontaneous symmetry breaking and Standard Model

Strong interaction

In nuclear physics and particle physics, the strong interaction, also called the strong force or strong nuclear force, is a fundamental interaction that confines quarks into protons, neutrons, and other hadron particles. Spontaneous symmetry breaking and strong interaction are quantum chromodynamics.

See Spontaneous symmetry breaking and Strong interaction

Superconductivity

Superconductivity is a set of physical properties observed in certain materials where electrical resistance vanishes and magnetic fields are expelled from the material. Spontaneous symmetry breaking and Superconductivity are quantum phases.

See Spontaneous symmetry breaking and Superconductivity

Symmetry

Symmetry in everyday life refers to a sense of harmonious and beautiful proportion and balance. Spontaneous symmetry breaking and Symmetry are theoretical physics.

See Spontaneous symmetry breaking and Symmetry

Symmetry (physics)

The symmetry of a physical system is a physical or mathematical feature of the system (observed or intrinsic) that is preserved or remains unchanged under some transformation. Spontaneous symmetry breaking and symmetry (physics) are symmetry.

See Spontaneous symmetry breaking and Symmetry (physics)

Symmetry breaking

In physics, symmetry breaking is a phenomenon where a disordered but symmetric state collapses into an ordered, but less symmetric state. Spontaneous symmetry breaking and symmetry breaking are symmetry.

See Spontaneous symmetry breaking and Symmetry breaking

Symmetry group

In group theory, the symmetry group of a geometric object is the group of all transformations under which the object is invariant, endowed with the group operation of composition. Spontaneous symmetry breaking and symmetry group are symmetry.

See Spontaneous symmetry breaking and Symmetry group

Tachyon condensation

Tachyon condensation is a process in particle physics in which a system can lower its potential energy by spontaneously producing particles.

See Spontaneous symmetry breaking and Tachyon condensation

Texture (cosmology)

In cosmology, a texture is a type of topological defect in the order parameter (typically a scalar field) of a field theory featuring spontaneous symmetry breaking.

See Spontaneous symmetry breaking and Texture (cosmology)

Topological defect

In mathematics and physics, solitons, topological solitons and topological defects are three closely related ideas, all of which signify structures in a physical system that are stable against perturbations.

See Spontaneous symmetry breaking and Topological defect

Toshihide Maskawa

was a Japanese theoretical physicist known for his work on CP-violation who was awarded one quarter of the 2008 Nobel Prize in Physics "for the discovery of the origin of the broken symmetry which predicts the existence of at least three families of quarks in nature.".

See Spontaneous symmetry breaking and Toshihide Maskawa

Two-balloon experiment

The two-balloon experiment is an experiment involving interconnected balloons.

See Spontaneous symmetry breaking and Two-balloon experiment

Unitary group

In mathematics, the unitary group of degree n, denoted U(n), is the group of unitary matrices, with the group operation of matrix multiplication.

See Spontaneous symmetry breaking and Unitary group

University of Chicago

The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private research university in Chicago, Illinois.

See Spontaneous symmetry breaking and University of Chicago

Vacuum expectation value

In quantum field theory the vacuum expectation value (also called condensate or simply VEV) of an operator is its average or expectation value in the vacuum. Spontaneous symmetry breaking and vacuum expectation value are quantum field theory and Standard Model.

See Spontaneous symmetry breaking and Vacuum expectation value

Vacuum solution (general relativity)

In general relativity, a vacuum solution is a Lorentzian manifold whose Einstein tensor vanishes identically.

See Spontaneous symmetry breaking and Vacuum solution (general relativity)

W and Z bosons

In particle physics, the W and Z bosons are vector bosons that are together known as the weak bosons or more generally as the intermediate vector bosons. Spontaneous symmetry breaking and w and Z bosons are Standard Model.

See Spontaneous symmetry breaking and W and Z bosons

Weak interaction

In nuclear physics and particle physics, the weak interaction, also called the weak force, is one of the four known fundamental interactions, with the others being electromagnetism, the strong interaction, and gravitation.

See Spontaneous symmetry breaking and Weak interaction

Yoichiro Nambu

was a Japanese-American physicist and professor at the University of Chicago.

See Spontaneous symmetry breaking and Yoichiro Nambu

Yukawa potential

In particle, atomic and condensed matter physics, a Yukawa potential (also called a screened Coulomb potential) is a potential named after the Japanese physicist Hideki Yukawa.

See Spontaneous symmetry breaking and Yukawa potential

1964 PRL symmetry breaking papers

The 1964 PRL symmetry breaking papers were written by three teams who proposed related but different approaches to explain how mass could arise in local gauge theories. Spontaneous symmetry breaking and 1964 PRL symmetry breaking papers are Standard Model.

See Spontaneous symmetry breaking and 1964 PRL symmetry breaking papers

See also

Quantum phases

Standard Model

References

[1] https://en.wikipedia.org/wiki/Spontaneous_symmetry_breaking

Also known as Champagne bottle potential, Dynamical symmetry breaking, Mexican hat diagram, Mexican hat potential, Sombrero potential, Spontaneous broken symmetry, Spontaneous chiral symmetry breaking, Spontaneously broken, Spontaneously broken symmetry, Symmetry breakdown.

, Monopole (mathematics), Nobel Prize in Physics, Norton's dome, Nucleon, Order and disorder, Particle physics, Phase transition, Photon, Physical Review, Physical Review Letters, Pion, Quantum chromodynamics, Quantum field theory, Quantum mechanics, Quantum spin liquid, Quantum vacuum state, Quark, Reflection (mathematics), Rotational frequency, Rotational symmetry, Royal Swedish Academy of Sciences, Scalar field theory, Space group, Spontaneous absolute asymmetric synthesis, Spontaneous magnetization, Spontaneous process, Standard Model, Strong interaction, Superconductivity, Symmetry, Symmetry (physics), Symmetry breaking, Symmetry group, Tachyon condensation, Texture (cosmology), Topological defect, Toshihide Maskawa, Two-balloon experiment, Unitary group, University of Chicago, Vacuum expectation value, Vacuum solution (general relativity), W and Z bosons, Weak interaction, Yoichiro Nambu, Yukawa potential, 1964 PRL symmetry breaking papers.