Higgs fields and the determination of the Weinberg angle

SU(2) × U(1) gauge theories, in which the Higgs fields transform as doublets under SU(2) are interpreted as pure Yang-Mills theories in six dimensions, the components of the gauge potentials in the extra dimensions playing the role of the Higgs' fields. Two consistent theories are discovered: one in which SU(2) × U(1) is embedded in SU(3) and the vector bosons remain massless - and another where SU(2) × U(1) is embedded in the graded Lie algebra SU(2|1), the symmetry is spontaneously broken in a natural fashion and the theory is equivalent to that of Weinberg and Salam, with a specific value 30° for the Weinberg angle and a prediction of the Higgs' mass.     

Spontaneous symmetry breaking in O(10)

We consider the most general renormalizable O(10) invariant potential for a $\text{45 + 16 +}\text{16}$ representation of Higgs fields. We show that O(10) can be spontaneously broken down to SU(5), SU(4) × U(1) or SU(3) × SU(2) × U(1), this last case being, of course, the most appealing.     

Quantum entanglement in the system of a moving V-type three-level atom interacting with the SU（1,1）-related coherent fields

In a system with a moving V-type three-level atom interacting with the SU(1,1)-related coherent fields, we investigate the entanglement between the moving three-level atom and the SU(1,1)-related coherent fields by using the quantum-reduced entropy, and that between the SU(1,1)-related coherent fields by using the quantum relative entropy of entanglement. It is shown that the two kinds of entanglement are dependent on the atomic motion and exhibit the periodic evolution with a period of 2π/p. The maximal atom--field qutrit entanglement state can be prepared, and the entanglement preservation of the SU(1,1)-related coherent fields can be realized in the interacting process via the appropriate selection of system parameters and interaction time.     

Composite description for quarks and leptons from a geometrical picture of complementarity

We propose a geometrical formulation of complementarity between the Higgs phase and the confining phase of a non-abelian gauge theory, introducing local “vierbein” fields to provide for a one-to-one mapping between the states of the two phases. We investigate the gauge structure when a subgroup of the global symmetry is also gauged. The formalism is used to build up a composite model based on a SU(4) of subcolor complementary to a Pati-Salam SU(4), and allowing for dynamical symmetry breaking of SU(2)_L ? U(1).     

Wave fluctuations in the system with some Yang-Mills condensates

Self-consistent dynamics of non-homogeneous fluctuations and homogeneous and isotropic condensate of Yang–Mills fields was investigated in zero, linear and quasilinear approximations over the wave modes in the framework of N = 4 supersymmetric model in Hamilton gauge in quasiclassical theory. The models with SU(2), SU(3) and SU(4) gauge groups were considered. Particle production effect and effect of generation of longitudinal oscillations were obtained.     

Coulomb gauge vacua of SU(3) gauge theory

SU(3) gauge field theory is studied in the Coulomb gauge, and the topologically distinct, but gauge equivalent, vacuum configurations are analysed. Considering the gauge transformations of the form U ε U(2) ?SU(3)/U(2), we have obtained a new class of vacuum fields characterized by the topological quantum number η = ±1.     

Z2 × Z2 Discrete Symmetry in the Left-Right Symmetric Model SU(2)L × SU(2)R × U(l)B-L

From the point that the Higgs fields can be regarded as the gauge fields on a discrete group, we construct a gauge theory of the leftright symmetric model SU(2)_L × SU(2)_R × U(1)_B-L (LRSM) over Z₂ ⊙ Z₂ discrete symmetry.     

Deformations of the embedding of the SU(2) monopole solution in SU (3)

This paper is concerned with static Yang-Mills-Higgs fields, in the Prasad-Sommerfield limit of no Higgs self-interaction. One can obtain SU (3) multipole solutions from SU(2) solutions by embedding, in several different ways. In some of these cases, the embedding belongs to a family of SU(3) solutions that are not all embeddings; in other words, some embeddings can be deformed into non-embeddings. The simplest case, an embedding of the SU(2) spherically symmetric monopole, is studied with the aid of the twistor construction procedure. The family of axially symmetric SU(3) solutions to which it belongs is described.     

Transport theory for a two-flavor color superconductor

QCD with two light-quark flavors at high baryonic density is a color superconductor. The diquark condensate breaks the SU(3) gauge symmetry down to an SU(2) subgroup. We study thermal fluctuations of the superconductor for temperatures below the gap. These are described by a simple transport equation. In the collisionless limit and close to equilibrium, it gives rise to the "hard superconducting loop" effective theory for the SU(2) gauge fields. This theory describes Debye screening and Landau damping of the gauge fields in the presence of the diquark condensate. We explain how our effective theory follows to one-loop order from quantum field theory. Our approach provides a convenient starting point for the computation of transport coefficients of the two-flavor color superconductor.     

SU(l|m|n)阶化代数及其规范模型

本文将阶化李代数SU(m|n)扩充到SU(l|m|n),并讨论了它的局部规范理论。找到了规范不变的拉格郎日量,并将SU(2|1)弱电模型推广到统一强、弱、电相互作用模型。 关键词：     

The Unitarity of the W(3) Algebra from SU(3) Parafermion

We express the vacuum expectation value of the SU(3)k parafermion fields by that of two bosons and SU(3)_k current algebra. When k = 1,2,3, the SU(3)_k current algebra becomes an inner product of a unitary representation, and T(z), W⁽³⁾(z) are equivalent to "quasiself-adjoint" operators in this represen tation.     

A Schwarzschild-like model for baryons

We present a toy model of baryons using singular solutions of the SU(2) Yang-Mill-Higgs (YMH) field equations, which bears some similarity to the Schwarzschild solution of general relativity. The SU (2) solutions are used as a background field into which a scalar, SU (2) test particle is placed. This can be compared to placing an electrically charged particle in a Coulomb background field, except the SU (2) YMH solutions are singular on a spherical membrane thus trapping (confining) the test particle inside the sphere in a manner similar to certain bag models of baryons. An interesting consequence of this model is that the composite system is a fermion even though the original Lagrangian contains only bosonic fields.     

Gauged N = 8 supergravity in five dimensions

We construct gauged N = 8 supergravity theories in five dimensions. Instead of the twenty-seven vector fields of the ungauged theory, the gauged theories contain fifteen vector fields and twelve second-rank antisymmetric tensor fields satisfying self-dual field equations. The fifteen vector fields can be used to gauge any of the fifteen-dimensional semisimple subgroups of SL(6,R), specially SO(p, 6?p) for p = 0, 1, 2, 3. The gauged theories also have a physical global SU(1,1) symmetry which survives from the E₆₍₆₎ symmetry of the ungauged theory. This SU(1,1) for the SO(6) gauging is presumably related to that of the chiral N = 2 theory in ten dimensions. In our formalism we maintain a composite local USp(8) symmetry analogous to SU(8) in four dimensions.     

Quantum entanglement in the SU(1, 1)-related coherent fields interacting with a moving atom

The entanglement properties of the SU(1, 1)-related coherent fields interacting with a moving atom via the two-photon transition are investigated. We discuss the quantum entanglement between the SU(1, 1)-related coherent fields and the moving atom by using the quantum reduced entropy and that between the SU(1, 1)-related coherent fields by using the quantum relative entropy. It is shown that we can obtain the maximal entangled state between the fields and the moving atom and the high degree of entanglement between the SU(1, 1)-related coherent fields can be preserved for some choiced system parameters.     

THE Hn SIGMA-MODELS AND SELF-DUAL SU(n) YANG-MILLS FIELDS IN FOUR-DIMENSIONAL EUCLIDEAN SFACE

The H_n σ-models. i.e., non-linear σ-models taking-values on the symetric coset space SL(n,c)/SU(n), both in two-dimensional and four-dimensional Euclidean space,.are formulated. The relations with self-duel SU(n) Yang-Mills fields are also discussed.     

piN and pipiN couplings of the Delta(1232) and its chiral partners

We investigate the interactions and chiral properties of the four spin-3/2 baryons N(-)(D13), N+(P13), Delta+(P33), and Delta(-)(D33) together with the nucleon. We construct the SU(2)R x SU(2)L invariant interactions between the spin-1/2 and spin-3/2 baryons with the aid of a new, specially developed spin and isospin projection technique for these baryon fields, where the chiral invariant interactions contain one- and two-pion couplings. We obtain simple relations for the coupling constants of the one- and two-pion spin-1/2-3/2 transitions terms. The relation for the one-pion interactions reasonably agrees with the experiments, which suggests that these spin-3/2 baryons are chiral partners.     

New gravitational instantons and universal spin structures

An infinite class of new gravitational instantons for the axial anomaly is found. It consists entirely of algebraic spin- manifolds. In theories that allow manifolds without ordinary spin structure we find the presence of spinorial matter fields to require the existence of a “universal” gauged SU(2) or higher internal symmetry (e.g., SU(2) × SU(2) × G) and of an “internal-spin” -statistics connection. The possible relation of this to the gauge theory of weak and electromagnetic interactions is explored.     

LEFT-RIGHT SYMMETRY MODEL IN WESS-ZUMINO-WITTEN EFFECTIVE ACTION

In the present paper we obtain the Wess-Zumino-Witten effective action of the Goldstone bosons coupling to electroweak fields within the left-right symmetry SU(2)_L×SU(2)_R×U(1) gauge theory with six quarks.     

Symmetry breaking and asymptotic freedom in colour SU(3) gauge models

A class of quark models based on the colour gauge group SU(3) is shown to be asymptotically free despite the conplete breakdown of local symmetry to guarantee infrared stability. The symmetry breakdown is achieved by the presence of elementary scalar fields either through the Higgs mechanism or dynamically as first proposed by Coleman and Weinberg. Asymptotic freedom is preserved by imposing eigenvalue conditions on the coupling constants as first proposed by Chang. New quark species must be present, but below their production threshold, colour can still be a global symmetry which is approximate under SU(3), but exact under SU(2). Among the many implications of this class of models is the possibility of producing isolated quarks and gluons of non-zero mass without altering the short-distance behaviour of the superstrong interaction which binds them.     

Classification of gauge fields: The Eigenspinor-Eigenvalue equation

The eigenspinor-eigenvalue equation for SU(2) gauge fields is presented. A classification of gauge fields is consequently obtained. The whole classification is described in terms of a diagram.