Therefore spontaneous symmetry breaking can have a pure quantum origin.

As for the real scalar field, spontaneous symmetry breaking is found if m is negative.

Spontaneous symmetry breaking is a promising mechanism, which could be used to give mass to the vector gauge particles.

The agent for this "spontaneous symmetry breaking" was a particle, still undiscovered, called the Higgs.

This type of spontaneous symmetry breaking is the essential component of the Higgs mechanism.

Spontaneous symmetry breaking is a quantum effect when the vacuum is not invariant under the transformation group.

To overcome this, spontaneous symmetry breaking is augmented by the Higgs mechanism to give these particles mass.

In this case, there is spontaneous symmetry breaking of the rotational symmetry of the Hamiltonian.

In this case the vacuum has less symmetry than the theory allows, and one says that spontaneous symmetry breaking has occurred.

These fields and/or particles are responsible for the Higgs mechanism, i.e. for the spontaneous symmetry breaking of a physical system.

Spontaneous symmetry breaking is a way that scientists start off with something completely symmetrical and end up (without creating an outside force) with something non-symmetrical.

In this framework, spontaneous symmetry breaking is characterized as a reduction of the structure group of a principal bundle to its closed subgroup .

By the very early sixties, people had begun to understand another source of massless particles: spontaneous symmetry breaking of a continuous symmetry.

Note that all the anomaly cancellation mechanisms result in a spontaneous symmetry breaking of the symmetry whose anomaly is being cancelled.

This is because if such a spontaneous symmetry breaking occurred, then the corresponding Goldstone bosons, being massless, would have an infrared divergent correlation function.

When a theory is symmetric with respect to a symmetry group, but requires that one element of the group be distinct, then spontaneous symmetry breaking has occurred.

This model exhibits a spontaneous symmetry breaking of the U(1) symmetry due to a chiral condensate due to a pool of instantons.

Soon 't Hooft's second paper was ready to be published, in which he showed that Yang-Mills theories with massive fields due to spontaneous symmetry breaking could be renormalized.

However, there will be a chiral condensate (but no confinement) leading to an effective mass term and a spontaneous symmetry breaking of the chiral symmetry, but not the charge symmetry.

An idealized example of spatial spontaneous symmetry breaking is the case in which we have two boxes of material separated by a permeable membrane so that material can diffuse between the two boxes.

In the standard model of particle physics, spontaneous symmetry breaking of the SU(2)xU(1) gauge-symmetry associated with the electro-weak force generates masses for several particles, and separates the electromagnetic and weak forces.

In QCD, this is interpreted as a consequence of spontaneous symmetry breaking of chiral symmetry in a sector of QCD with 3 flavours of light quarks.

However, at lower energies a phenomenon called spontaneous symmetry breaking is invoked to explain the fact that the photon has zero rest mass, whereas the W +, W -, and Z are all very massive.

In classical gauge theory, spontaneous symmetry breaking occurs if the structure group of a principal bundle is reducible to a closed subgroup , i.e., there exists a principal subbundle of with the structure group .

Spontaneous symmetry breaking is a mode of realization of symmetry breaking in a physical system, where the underlying laws are invariant under a symmetry transformation, but the system as a whole changes under such transformations, in contrast to explicit symmetry breaking.