Electronic states in magnets are characterized by the quantum mechanical Berry phase defined in both the real and momentum spaces. This Berry phase constitutes the gauge fields, i.e. the emergent electromagnetic fields in solids, and affects the motion of the electrons. In momentum space, the band crossings act as the magnetic monopoles, i.e. the sources or sinks of the gauge flux. In real spac...

The recently developed families index theory for the overlap lattice Dirac operator is applied to demonstrate an interplay between topological features of the space of SU(N) lattice gauge fields on the 4-torus and the existence question for G0 gauge fixings which do not have the Gribov problem. The continuum version of our considerations leads to topological obstructions to the existence of suc...

A theory in which 16-dimensional curved Clifford space (C-space) provides a realization of Kaluza-Klein theory is investigated. No extra dimensions of spacetime are needed: “extra dimensions” are in C-space. We explore the spin gauge theory in C-space and show that the generalized spin connection contains the usual 4-dimensional gravity and Yang-Mills fields of the U(1)×SU(2)×SU(3) gauge group....

Apart from supersymmetric theories, the most interesting possibilities for unified theories beyond the standard model are models with large extra dimensions, that is, the brane-world scenario. The domain walls are the simplest branes on which realistic models can be constructed. However, localization of gauge fields on domain walls has been notoriously difficult in field theories, although scal...

The dynamics of Wilson lines integrated along a warped extra dimension has been unknown. We study a five dimensional SU(N) pure gauge theory with Randall-Sundrum warped compactification on S/Z2. We clarify the notion of large gauge transformations on the covering space for this setup. We obtain Kaluza-Klein expansions of gauge and ghost fields for the most general twists and background gauge fi...

We consider the gauging of space translations with time–dependent gauge functions. Using fixed time gauge of relativistic theory, we consider the gauge– invariant model describing the motion of nonrelativistic particles. When we use gauge–invariant nonrelativistic velocities as independent variables the translation gauge fields enter the equations through a d × (d + 1) matrix of vielbein fields...

We formulate a general gauge invariant Lagrangian construction describing the dynamics of massive higher spin fermionic fields in arbitrary dimensions. Treating the conditions determining the irreducible representations of Poincare group with given spin as the operator constraints in auxiliary Fock space, we built the BRST charge for the model under consideration and find the gauge invariant eq...

The loop transform in quantum gauge field theory can be recognized as the Fourier transform (or characteristic functional) of a measure on the space of generalized connections modulo gauge transformations. Since this space is a compact Hausdorff space, conversely, we know from the Riesz-Markov theorem that every positive linear functional on the space of continuous functions thereon qualifies a...

We investigate the possibility of doing momentum space lattice simulations as an alternative to the conventional method. The procedure is introduced and tested for quenched QED2 and quenched QED3. Interesting physical applications to unquenched QED3 and quenched QED4 are also briefly discussed.

This paper completes the argument that lattice simulations of partially quenched QCD can provide quantitative information about QCD itself, with the aid of partially quenched chiral perturbation theory. A barrier to doing this has been the inclusion of Φ0, the partially quenched generalization of the η ′, in previous calculations in the partially quenched effective theory. This invalidates the ...