Fundamental Representation Of SU Research Articles

Deconfinement in the fundamental SU(2) Higgs model

The SU(2) Higgs model with a Higgs doublet in the fundamental representation of SU(2) is investigated at finite temperature by Monte Carlo methods. In addition to the phase-transition lines of the zero-temperature theory, rapid crossovers are found for the Polyakov line 〈 W〉 in the confinement sector of the theory. In the deconfined phase of this sector good agreement is found with an Ising-like behavior and a critical exponent for the magnetization of approximately 1 3 .

The phase structure of the SU(3) lattice gauge-Higgs model

The phase structure of SU(3) symmetric gauge-Higgs theory with a fluctuating radial mode is investigated. The Higgs fields are considered in the fundamental representation of SU(3). It is shown that the phase structures of SU(3) and SU(2) symmetric models coincide qualitatively.

Reduction of tensor products with definite permutation symmetry: Embeddings of irreducible representations of Lie groups into fundamental representations of SU(M) and branchings

We consider tensor products made out of a number of identical copies of the defining representations of Lie groups that are asymptotically free and complex. Decomposition of the tensor products into the terms with definite permutation symmetry is made by using the index sum rules and the congruence class. The results can also be used to find the branchings of SU(M) into a Lie group G, where M is equal to the dimension of the defining representation of G. Application of our results to preon dynamics is indicated in two examples.

A unification of boson expansion theories: (III). Applications

A general scheme of constructing boson expansions that was proposed in earlier work is applied to a number of examples. The Fukutome expansion is obtained by considering the spinor representation of the SO(2 N + 1) group. Its hermitian, Holstein-Primakoff-type version is also derived. The generalized Dyson expansions for even and odd fermion systems are given in terms of two spinor representations of the SO(2 N) group. For fixed fermion number systems the relevant boson expansions are obtained by considering the fundamental representations of SU( N) while for fixed seniority those of Sp( N) are concerned. The collective boson expansions corresponding to the Ginocchio model, the interacting boson model of Arima and Iachello and the Elliott model are given for the symmetric representations of SO(8) and SU( l + 1) and any representation of SU(3).

Matter-coupled Yang-Mills system in Minkowski space. II. Invariant solutions in the presence of Dirac spinor fields

For pt.I see ibid., vol.24, no.12, p.3179-83 (1981). Classical solutions to the Minkowskian field equations of a Yang-Mills system coupled to an isospinor of massless Dirac fields are found. The Dirac fields are taken in the fundamental representation of SU(2). In view of the conformal and Weyl invariance of the Lagrangian, the solutions are obtained by considering the system over the compactification /b M/ macr of Minkowski space. /b M/ macr is diffeomorphic to SU(2) otimes U(1)~/b S//sup 3/*/b S//sup 1/ and the action of the conformal group upon it is identified with that of SU(2,2) on SU(2) otimes U(1). The equations are simplified by using as Ansatze gauge and Dirac fields that are both invariant under the following (for combinations of the following) subtractions of SU(2,2): (i) left SU(2)/sub L/ translations, (ii) right SU(2)/sub R/ translations, (iii) left action of SU(2)/sub L/ otimes SU(2)/sub R /, and (iv) U(1) translations. All (real and complex) SU(2)/sub L / otimes U(1)-invariant solutions are obtained. The pullback of these solutions to Minkowski space leads to regular configurations with finite energy.