Narrow Results

We incorporate the parameters of the gauge group G into the gauge theory of interactions through a nonlinear partial-trace σ-model Lagrangian on G/H. The minimal coupling of the new (Goldstone-like) scalar bosons provides mass terms to those intermediate vector bosons associated with the quotient G/H, without spoiling gauge invariance, while the H-vector potentials remain massless. The main virtue of a partial trace on G/H, rather than on the entire G, is that we can find an infinite-dimensional symmetry, with nontrivial Noether invariants, which ensures quantum integrability in a non-canonical quantization scheme. The present formalism is explicitly applied to the case G = SU(2)× U(1), as a Higgsless alternative to the Standard Model of electroweak interactions, although it can also be used in low-energy phenomenological models for strong interactions.

In this paper, spinor and vector decomposition of SU(2) gauge potential are presented and their equivalence is constructed using a simple proposal. We also obtain the action of Skyrme–Faddeev model from the SU(2) massive gauge field theory which is proposed according to the gauge invariant principle. Then, the knot structure in Skyrme–Faddeev model is discussed in terms of the so-called ϕ-mapping topological current theory. The topological charge of the knot is characterized by the Hopf indices and the Brouwer degrees of ϕ-mapping, naturally. At last, we briefly discussed the topological invariant–Hopf invariant which describes the topology of these knots. It is shown that Hopf invariant is the total number of all the linking numbers and self-linking numbers of these knots.

Monopole-instanton in topologically massive gauge theories in 2+1 dimensions with a Chern–Simons mass term have been studied by Pisarski some years ago. He investigated the SU(2) Yang–Mills–Higgs model with an additional Chern–Simons mass term in the action. Pisarski argued that there is a monopole-instanton solution that is regular everywhere, but found that it does not possess finite action. There were no exact or numerical solutions being presented by Pisarski. Hence it is our purpose to further investigate this solution in more detail. We obtained numerical regular solutions that smoothly interpolates between the behavior at small and large distances for different values of Chern–Simons term strength and for several fixed values of Higgs field strength. The monopole-instanton's action is real but infinite. The action vanishes for large Chern–Simons term only when the Higgs field expectation value vanishes.

The compensating Utiyama's method including space-time symmetries is revisited as well as the gauge gravitational theories associated with translation, Poincaré and Weyl groups. Then we propose an extension of the gauge symmetry, allowing for the incorporation of the gauge group parameters into the theory as dynamical fields by considering the jet-gauge group as fundamental symmetry. As a consequence, a natural mass-generating mechanism for the gauge potentials arises without damaging gauge invariance. We also present, as a simple example, some sort of generalized Stueckelberg model for the Weyl group, thus accounting for massive dilatonic gauge field. Finally, the standard diffeomorphism symmetry of gravitation is extended by resorting to the jet-diffeomorphism group, formalism which helps to fix the Hilbert-Einstein Lagrangian in the teleparallelism version.