Gauge symmetry fields

It was demonstrated by Higgs [50] that the appearance of massless bosons can be avoided by combining the spontaneous breakdown of symmetry under a compact Lie group with local gauge symmetry. The potential V() which is invariant under the local transformation of the charged field... 

The SUC(2) gauge symmetry does not break spontaneously and confines. Calling H a mass dimension four composite field describing the scalar glueball we can construct the following Lagrangian [44] ... 

The development just given illustrates the fact that the topology of the vacuum determines the nature of the gauge transformation, field tensor, and field equations, as inferred in Section (I). The covariant derivative plays a central role in each case for example, the homogeneous field equation of 0(3) electrodynamics is a Jacobi identity made up of covariant derivatives in an internal 0(3) symmetry gauge group. The equivalent of the Jacobi identity in general relativity is the Bianchi identity. 

This is a broken gauge theory at low energy, which can be expressed as in Eq. (686) as a gauge theory accompanied by a broken gauge symmetry. Assume a simple Lagrangian that couples the left-handed fields , to the right-handed boson and the right-handed fields v ir to the left-handed boson ... 

From the foregoing, it becomes clear that fields and potentials are freely intermingled in the symmetry-broken Lagrangians of the Higgs mechanism. To close this section, we address the question of whether potentials are physical (Faraday and Maxwell) or mathematical (Heaviside) using the non-Abelian Stokes theorem for any gauge symmetry ... 

For these reasons there are reasons to consider this model, or a similar variant, as a reasonable model for the unification of gauge fields outside of gravitation. The extension of the gauge symmetries for electromagnetism at high energy, even if the field is 17(1) on the physical vacuum, leads to a standard model with a nice symmetry between chiral fields, and this symmetry is further contained in GUT. 

We depart from former treatments in other ways. Commencing with a correct observation that the Aharonov-Bohm effect depends on the topology of the experimental situation and that the situation is not simply connected, a former treatment then erroneously seeks an explanation of the effect in the connectedness of the U(l) gauge symmetry of conventional electromagnetism, but for which (1) the potentials are ambiguously defined, (the U(l) A field is gauge invariant) and (2) in U(l) symmetry V x A = 0 outside the solenoid. 

Noether s theorem for gauge symmetry For a local infinitesimal gauge transformation about a solution of the field equations,... 

According to the Goldstone theorem [79] the three real fields Pi x) would introduce three massless Goldstone bosons to the theory. These can, however, be gauged away if one takes advantage of the local SU 2)i, gauge symmetry given by... 

We conjecture that the mass difference between leptons and baryons is due to a different internal wave structure, related to the SU 2) and SU 3) gauge symmetries of quantum field theories. Antispin is responsible for the appearance of antimatter. The annihilation of matter and antimatter occurs... 

Nevertheless, the introduction of the potentials (p and A reduces the number of fields, and they are to be considered as the dynamical variables of the theory. Owing to the gauge symmetry given by Eqs. (2.130) and (2.131), it is obvious that Maxwell s theory of electromagnetism features redundant degrees of freedom which will seriously hamper its quantization in chapter 7. The potentials cp and A themselves are denoted gauge potentials. 

The Maxwell-Heaviside theory seen as a U(l) symmetry gauge field theory has no explanation for the photoelectric effect, which is the emission of electrons from metals on ultraviolet irradiation [39]. Above a threshold frequency, the emission is instantaneous and independent of radiation intensity. Below the threshold, there is no emission, however intense the radiation. In U(l), electrodynamics energy is proportional to intensity and there is, consequently, no possible explanation for the photoelectric effect, which is conventionally regarded as an archetypical quantum effect. In classical 0(3) electrodynamics, the effect is simply... 

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