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We complete the formulation of the equations of motion of a non-Abelian gauge field coupled to fermions on a finite-element lattice in four space-time dimensions. This is accomplished by a straightforward iterative approach, in which…
A relatively simple approach to noncommutative gravity utilizes the gauge theory formulation of general relativity and involves replacing the Lorentz gauge group by a larger group. This results in additional field degrees of freedom which…
We revisit a propagating torsion gravity theory obtained by introducing a field coupled to the Holst term in the first-order Einstein-Cartan action. The resulting theory has second order field equations, no adjustable coupling constants,…
Recent experiments demonstrate that antiferromagnets exhibit the spin Hall effect. We study a tight-binding model of an antiferromagnet on a square lattice with Rashba spin-orbit coupling and disorder. By exact diagonalization of a finite…
The spin-rotationally invariant SU(2) approach to the Hubbard model is extended to accommodate the charge degrees of freedom. Both U(1) and SU(2) gauge transformation are useed to factorize the charge and spin contribution to the original…
A generalized Heisenberg-Euler formula is given for an Abelian gauge theory having vector as well as axial vector couplings to a massive fermion. So, the formula is applicable to a parity-violating theory. The gauge group is chosen to be…
This paper follows the previous work on generalized abelian gauge field theory of higher-order derivatives under rotor model and extends the study to the most generalized non-abelian case. We find that the rotor mechanism from the abelian…
We investigate the possibility of hidden non-Abelian Local Phase symmetries in large-U doped planar Hubbard antiferromagnets, believed to simulate the physics of two-dimensional (magnetic) superconductors. We present a spin-charge…
We provide a fully general-relativistic treatment of cosmological perturbations in a universe permeated by a large-scale primordial magnetic field, using the Ellis-Bruni gauge-invariant formalism. The exact non-linear equations for general…
We describe a $n$ component abelian Hall fluid as a system of {\it composite bosons} moving in an average null field given by the external magnetic field and by the statistical flux tubes located at the position of the particles. The…
This paper studies nonlinear deformations of the linear gauge theory of any number of spin-2 and spin-3/2 fields with general formal multiplication rules in place of standard Grassmann rules for manipulating the fields, in four spacetime…
We show that a two-dimensional spin-orbit-coupled system in the presence of a charge/spin-density wave with a wave-vector perpendicular to an applied electric field supports bulk manifestations of the direct/inverse spin-Hall effect. We…
The ordinary Hall effect is driven by the Lorentz force, while its anomalous counterpart occurs in ferromagnets. Here we show that the Berry curvature monopole of non-magnetic 2D spin-3/2 holes leads to a novel Hall effect linear in an…
A microscopic kinetic theory is developed which allows to investigate non-Abelian SU(2) systems interacting with meanfields and spin-orbit coupling under magnetic fields in one, two, and three dimensions. The coupled kinetic equations for…
The concept of gauge field is a cornerstone of modern physics and the synthetic gauge field has emerged as a new way to manipulate particles in many disciplines. In optics, several schemes of Abelian synthetic gauge fields have been…
We study two-dimensional systems with Galilean invariance gapped under magnetic fields. When such quantum Hall systems are coupled with external sources for charge, energy, and momentum currents, they exhibit invariance under the Milne…
Consistent interactions that can be added to a free, Abelian gauge theory comprising a BF model and a finite set of massless real scalar fields are constructed from the deformation of the solution to the master equation based on specific…
The Hamiltonian formulation of the Holst action in presence of a massless fermion field with a non-minimal Lagrangian is performed without any restriction on the local Lorentz frame. It is outlined that the phase space structure does not…
The nonlinear Hall effect, which is the second-order harmonic charge Hall effect from the Berry curvature dipole in momentum space, has received much attention recently. As the responses to higher harmonics of the driving ac electric field…
We use linear response theory to study the transverse force generated by an external electric field and hence possible charge Hall effect in spin-orbit coupled systems. In addition to the Lorentz force that is parallel to the electric…