We formulate SU(3) Hamiltonian lattice QCD in terms of the plaquette variables and determine the relevant subspaces of the Hilbert space for the vacuum wave functional and its approximations. We analyze the oneand two-plaquette problems. In an earlier paper [1] we formulated the fully gauge-fixed SU(N) lattice gauge Hamiltonian and studied the one-plaquette problem for several values of N . Thi...

Abstract We develop a complete Hamiltonian approach to the theory of perturbations around any spatially homogeneous spacetime. employ Dirac method for constrained systems which is well-suited cosmological perturbations. refine via so-called Kuchař parametrization kinematical phase space. separate gauge-invariant dynamics three-surfaces from three-surface deformations induced by linear coordinat...

This extended write–up of my talk gives an introductory survey of mathematical problems of the quantization of gauge systems. Using the Schwinger model as an exactly tractable but nontrivial example which exhibits general features of gauge quantum field theory, I cover the following subjects: The axiomatics of quantum field theory, formulation of quantum field theory in terms of Wightman functi...

In this paper we study the structure of the Hilbert space for the recent noncommutative geometry models of gauge theories. We point out the presence of unphysical degrees of freedom similar to the ones appearing in lattice gauge theories (fermion doubling). We investigate the possibility of projecting out these states at the various levels in the construction, but we find that the results of th...

The classical moduli space M of a supersymmetric gauge theory with trivial superpotential can be stratified according to the unbroken gauge subgroup at different vacua. We apply known results about this stratification to obtain the W 6= 0 theory classical moduli space M ⊂ M, working entirely with the composite gauge invariant operators φ̂ that span M, assuming we do not know their elementary mat...

I discuss the indefinite metrical structure of the time-space translations asrealized in the indefinite inner products for relativistic quantum fields, familiarin the example of quantum gauge fields. The arising indefinite unitary nondiag-onalizable representations of the translations suggest as the positive unitaritycondition for the probability interpretable positive defin...

Conserved currents of any spin t > 0 built from bosonic symmetric massless gauge fields of arbitrary integer spins s1 + s2 > t in AdS4 are found. Analogous to the case of 4d Minkowski space, currents considered in this paper are not gauge invariant, but generate gauge-invariant conserved charges.

We write the SU(2) lattice gauge theory Hamiltonian in (d+1) dimensions in terms of prepotentials which are the SU(2) fundamental doublets of harmonic oscillators. The Hamiltonian in terms of prepotentials has SU(2)⊗U(1) local gauge invariance. In the strong coupling limit, the color confinement in this formulation is due to the U(1) gauge group. We further solve the SU(2) ⊗ U(1) Gauss law to c...

We solve the Gauss law and the corresponding Mandelstam constraints in the loop Hilbert space HL using the prepotential formulation of (d+1) dimensional SU(2) lattice gauge theory. The resulting orthonormal and complete loop basis, explicitly constructed in terms of the d(2d − 1) prepotential intertwining operators, is used to transcribe the gauge dynamics directly in HL without any redundant g...

Using noncommutative geometry, the standard tools of differential geometry can be extended to a broad class of spaces whose coordinates are noncommuting operators acting on a Hilbert space. In the simplest case of coordinates being matrix valued functions on space-time, the standard model of particle physics can be reconstructed out of a few basic principles. Following these ideas, we investiga...