"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."
Discusses the phenomenon of spontaneous symmetry breaking, where a system at high energy possesses a symmetry that is broken at lower energies.
Symmetry and symmetry breaking: This topic covers the concept of symmetry in physics, the different types of symmetries and the ways they can be broken.
Quantum field theory (QFT): This topic covers the mathematical framework and physical principles of QFT, which is used to describe the behavior of elementary particles at a fundamental level.
Higgs mechanism: This topic covers the Higgs field and the way it interacts with particles to give them mass. It also involves the Higgs Boson, which was discovered in 2012.
Elementary particles: This topic covers the building blocks of matter, including quarks, leptons, and bosons.
Standard Model: This topic covers the current best model of elementary particle physics, which describes the interaction between elementary particles and the fundamental forces of nature.
Gauge invariance: This topic covers the concept of gauge symmetry, which is a type of symmetry that underlies the fundamental forces in nature.
Renormalization: This topic covers the concept of removing infinities from calculations in QFT, which is necessary to make them physically meaningful.
Vacuum expectation value (VEV): This topic covers the average value of a quantum field in its lowest energy state, which is also known as the vacuum.
Symmetry groups: This topic covers the mathematical structures that describe symmetries and their properties.
Phase transitions: This topic covers the way in which spontaneous symmetry breaking leads to the emergence of new properties of physical systems.
Higgs mechanism: In the Standard Model of particle physics, the Higgs field is responsible for giving masses to particles. The Higgs mechanism involves the spontaneous breaking of the electroweak symmetry, which describes the unification of the electromagnetic and weak interactions.
Chiral symmetry breaking: In quantum chromodynamics (QCD), the strong force which binds quarks together, chiral symmetry is spontaneously broken, leading to the formation of hadrons (such as protons and neutrons) from quarks.
BCS mechanism: The Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity involves the spontaneous breaking of the U(1) gauge symmetry, resulting in the formation of Cooper pairs.
Ising model: In the Ising model, which describes the behavior of magnetic materials, the spontaneous breaking of a Z(2) symmetry occurs, resulting in the formation of domains with aligned spins.
Kondo effect: In the Kondo effect, a magnetic impurity in a metal can lead to the spontaneous breaking of a U(1) symmetry, resulting in the formation of a screened spin.
Polyakov loop: In strongly-interacting gauge theories such as QCD, the Polyakov loop can undergo spontaneous breaking due to the confinement of quarks into hadrons.
Flux tube: In gauge theories with compact dimensions, such as lattice QCD or string theory, the formation of a flux tube can spontaneously break the translation symmetry of the system.
"It can describe systems where the equations of motion or the Lagrangian obey symmetries, but the lowest-energy vacuum solutions do not exhibit that same symmetry."
"When the system goes to one of those vacuum solutions, the symmetry is broken for perturbations around that vacuum even though the entire Lagrangian retains that symmetry."