Narrow Results

The gauge symmetry inherent in the concept of manifold has been discussed. Within the scope of this symmetry the linear connection or displacement field can be considered as a natural gauge field on the manifold. The gauge-invariant equations for the displacement field have been derived. It has been shown that the energy–momentum tensor of this field conserves and hence the displacement field can be treated as one that transports energy and gravitates. To show the existence of the solutions of the field equations, we have derived the general form of the displacement field in Minkowski space–time which is invariant under rotation and space and time inversion. With this ansatz we found spherically-symmetric solutions of the equations in question.

A new doublet variable is proposed to decompose non-Abelian gauge field for describing the topological effects of instantons due to the defects in appropriate phase of SU(2) Yang–Mills theory. It is shown that the instanton number can be directly related to the isospin defects of the doublet order parameter and contributed from topological charges of these defects. The θ-term in instanton action is found to be the delta-function form of the doublet and the Lagrangian of instantons in terms of new variables is also presented.

The free spinor field on a fuzzy sphere is described within Watamura approach to Dirac operator. Except of the highest mode, its spectrum is the same but truncated as in the commutative case. We present a simple gauge extension of the model with usual polynomial interaction. The gauge symmetry is exact, and the chiral properties of the field modes are standard except the highest mode.

The higher order symmetries are investigated in a covariant Hamiltonian formulation. The covariant phase-space approach is extended to include the presence of external gauge fields and scalar potentials. The special role of the Killing–Yano tensors is pointed out. Some nontrivial examples involving Runge–Lenz type conserved quantities are explicitly worked out.

We consider a possibility that the recent OPERA results on neutrinos' superluminality could be caused by a local effect of a new gauge field sourced by the earth. If neutrinos couple to this gauge field via a gauge-invariant but non-renormalizable interaction, the coupling effectively changes a background metric, thereby leading to superluminality of neutrinos. This possibility might naturally explain why neutrinos from CERN CNGS beam to Gran Sasso Laboratory become superluminal while those from SN1987A to Earth become subluminal.

In this paper, we study how geometrical coupling can be adapted to localize a model with kinetic gauge mixing on a thin membrane. The model discussed is a theory for millicharged particles, proposed by Holdom in 1985, and that now is object of study in the LHC. We propose a geometrical coupling between the gauge fields, the Ricci scalar and the Ricci tensor. We show that it is possible to localize such a model by regarding specific values for the coupling constants. We find the solutions for the two gauge fields and discuss the localization for scalar fields that appears naturally in the process. We show that not necessarily the gauge and scalar fields are localized at the same time.

Gauge field theory with rank-one field $T_{\mu }$ is a quantum field theory that describes the interaction of elementary spin-1 particles, of which being massless to preserve gauge symmetry. In this paper, we give a generalized, extended study of abelian gauge field theory under successive rotor model in general $D$-dimensional flat spacetime for spin-1 particles in the context of higher-order derivatives. We establish a theorem that $n$ rotor contributes to the ${\square }^n{T}^{\mu }$ fields in the integration-by-parts formalism of the action. This corresponds to the transformation of gauge field $T^{\mu }\to {\square }^n{T}^{\mu }$ and gauge field strength $G_{\mu \nu }\to {\square }^n{G}_{\mu \nu }$ in the action. The $n=0$ case restores back to the standard abelian gauge field theory. The equation of motion and Noether’s conserved current of the theory are also studied.

Low energy theorems of Nambu–Goldstone fermion associated with spontaneously broken supersymmetry are studied for gauge supermultiplets. Two possible terms in the effective Lagrangian are needed to deal with massless gaugino and/or massless gauge boson. As an illustrative example, a concrete model is worked out which can interpolate massless as well as massive gaugino and/or gauge boson to examine the low energy effective interaction of NG-fermion.

We present a simple mechanism for mass generation of gauge fields for the Yang–Mills theory, where two gauge SU(N)-connections are introduced to incorporate the mass term. Variations of these two sets of gauge fields compensate each other under local gauge transformations with the local gauge transformations of the matter fields, preserving gauge invariance. In this way the mass term of gauge fields is introduced without violating the local gauge symmetry of the Lagrangian. Because the Lagrangian has strict local gauge symmetry, the model is a renormalizable quantum model. This model, in the appropriate limit, comes from a class of universal Lagrangians which define a new massive Yang–Mills theories without Higgs bosons.

Two mass generation mechanisms for gauge theories are studied. It is proved that in the Abelian case the topological mass generation mechanism introduced in Refs. 4, 12 and 15 is equivalent to the mass generation mechanism defined in Refs. 5 and 20 with the help of "localization" of a nonlocal gauge invariant action. In the non-Abelian case the former mechanism is known to generate a unitary renormalizable quantum field theory, describing a massive vector field.

The topological properties of quantum electron plasmas in three-dimensional space are presented. Starting from ϕ-mapping topological current theory, the vortex lines are just at the core of wave function obtained. It is shown that the vorticity of the vortex can be expressed by the Hopf index and the Brouwer degree. We find that the vortex lines are unstable in some conditions and the evolution of vortex lines at the bifurcation points is given.

Electron hopping models on the honeycomb lattice are studied. The lattice consists of two triangular sublattices, and it is non-Bravais. The dual space has non-trivial topology. The gauge fields of Bloch electrons have the U(1) symmetry and thus represent superconducting states in the dual space. Two quantized Abrikosov fluxes exist at the Dirac points and have fluxes 2π and -2π, respectively. We define the non-Abelian SO(3) gauge theory in the extended 3d dual space and it is shown that a monopole and anti-monoplole solution is stable. The SO(3) gauge group is broken down to U(1) at the 2d boundary. The Abrikosov fluxes are related to quantized Hall conductance by the topological expression. Based on this, monopole confinement and deconfinement are discussed in relation to time reversal symmetry and QHE. The Jahn–Teller effect is briefly discussed.

We have studied the ground state properties of hard-core bosons in a two-leg optical ladder in the presence of uniform and staggered frustrations due to an artificial gauge field. By calculating the ground state via the Lanczos method, we find first-order phase transitions tuned by the staggered gauge field between the Meissner and the vortex states. The momentum distributions show that the Meissner state has edge and staggered currents, while the vortex states have vortex-solid or vortex-glass phases in the presence of a staggered field.

For the Bose–Einstein condensate in the non-Abelian gauge field, the atomic wavefunction obtains helical modulation, which would lead to nontrivial objects, such as three-dimensional Skyrmion. The spin–orbit coupled condensate is usually capable of supporting Skyrmion ground states, which can be well understood through the wavefunction modulation vector concept. In the present manuscript, the modulation vector is characterized both analytically and numerically with respect to the spin–orbit coupling strength. For the SU(2) symmetric condensate, the modulation vector of the wavefunction is linearly proportional to the spin–orbit coupling strength. In the presence of spin-dependent interaction, the modulus of the modulation vector is predicted to increase or decrease according to the sign of the interaction parameter, resulting in a shrunken or expanded Skyrmion. However, the Skyrmion is unstable for a certain area of the parameter space of the spin–orbit coupling and spin-dependent interaction. The condensate favors a single Skyrmion state or the Skyrmion lattice state according to the strength of the spin–orbit coupling.

We review the historical development and physical ideas of topological Yang–Mills theory and explain how quantum field theory, a physical framework describing subatomic physics, can be used as a tool to study differential geometry. We further emphasize that this phenomenon demonstrates that the inter-relation between theoretical physics and mathematics have come into a new stage.

Magnetic electric effects in ferromagnetic metals are discussed from the viewpoint of effective spin electromagnetic field that couples to conduction electron spin. The effective field in the adiabatic limit is the spin Berry’s phase in space and time, and it leads to spin motive force (voltage generated by magnetization dynamics) and topological Hall effect due to spin chirality. Its gauge coupling to spin current describes the spin transfer effect, where magnetization structure is driven by an applied spin current. The idea of effective gauge field can be extended to include spin relaxation and Rashba spin-orbit interaction. Voltage generation by the inverse Edelstein effect in junctions is interpreted as due to the electric component of Rashba-induced spin gauge field. The spin gauge field arising from the Rashba interaction turns out to coincides with toroidal moment, and causes asymmetric light propagation (directional dichroism) as a result of the Doppler shift. Rashba conductor without magnetization is shown to be natural metamaterial exhibiting negative refraction.

Interplay between magnetization dynamics and electric current in a conducting ferromagnet is theoretically studied based on a microscopic model calculation. First, the effects of the current on magnetization dynamics (spin torques) are studied with special attention to the "dissipative" torques arising from spin-relaxation processes of conduction electrons. Next, an analysis is given of the "spin motive force", namely, a spin-dependent 'voltage' generation due to magnetization dynamics, which is the reaction to spin torques. Finally, an attempt is presented of a unified description of these effects.