Related papers: On the Fermionic Sector of Quantum Holonomy Theory
We study magnetic Schrodinger operators with random or almost periodic electric potentials on the hyperbolic plane, motivated by the quantum Hall effect in which the hyperbolic geometry provides an effective Hamiltonian. In addition we add…
Motivated by quantum simulation, we consider lattice Hamiltonians for Yang-Mills gauge theories with finite gauge group, for example a finite subgroup of a compact Lie group. We show that the electric Hamiltonian admits an interpretation as…
The correct Hamiltonian for an extended Hubbard model with quantum group symmetry as introduced by A. Montorsi and M. Rasetti is derived for a D-dimensional lattice. It is shown that the superconducting SUq(2) holds as a true quantum…
We study a non-autonomous, non-linear evolution equation on the space of operators on a complex Hilbert space. We specify assumptions that ensure the global existence of its solutions and allow us to derive its asymptotics at temporal…
The machinery of noncommutative geometry is applied to a space of connections. A noncommutative function algebra of loops closely related to holonomy loops is investigated. The space of connections is identified as a projective limit of…
We study two-dimensional celestial conformal field theory describing four-dimensional ${\cal N}=1$ supergravity/Yang-Mills systems and show that the underlying symmetry is a supersymmetric generalization of BMS symmetry. We construct…
We consider the quantum theory of a two-form gauge field on a space-time which is a direct product of time and a spatial manifold, taken to be a compact five-manifold with no torsion in its cohomology. We show that the Hilbert space of this…
Modular parallel transport is a generalization of Berry phases, applied to modular (entanglement) Hamiltonians. Here we initiate the study of modular parallel transport for disjoint field theory regions. We study modular parallel transport…
The volume operator plays a central role in both the kinematics and dynamics of canonical approaches to quantum gravity which are based on algebras of generalized Wilson loops. We introduce a method for simplifying its spectral analysis,…
A proof is given for the Fourier transform for functions in a quantum mechanical Hilbert space on a non-compact manifold in general relativity. In the (configuration space) Newton-Wigner representation we discuss the spectral decomposition…
Quantum homogeneous supervector bundles arising from the quantum general linear supergoup are studied. The space of holomorphic sections is promoted to a left exact covariant functor from a category of modules over a quantum parabolic…
We consider $1+1$ dimensional Yang-Mills theory with gauge group $G$ coupled to a massive Majorana fermion field in an adjoint representation and a number of massless Dirac or Majorana fermions transforming in arbitrary representations of…
We use the freedom available in hybrid loop quantum cosmology to split the degrees of freedom between the geometry and the matter fields so as to build a quantum field theory for the matter content with good quantum properties. We…
The Zeeman-Hamilton operators of free charged particles are identified with the Laplacians of certain Riemannian manifolds, called Zeeman manifolds. The quantum Hilbert space decomposes into subspaces (Zeeman zones) which are invariant…
Starting from a general $N$-band Hamiltonian with weak spatial and temporal variations, we derive a low energy effective theory for transport within one or several overlapping bands. To this end, we use the Wigner representation that allows…
The loop quantization of Brans-Dicke theory (with coupling parameter $\omega\neq-3/2$) is studied. In the geometry-dynamical formalism, the canonical structure and constraint algebra of this theory are similar to those of general relativity…
This paper reviews progress on the Fractional Quantum Hall Effect (FQHE) based on what we term hamiltonian theories, i.e., theories that proceed from the microscopic electronic hamiltonian to the final solution via a sequence of…
We reexamine the massless spectrum of a heterotic string vacuum at large radius and present two results. The first result is to construct a vector bundle $\mathcal{Q}$ and operator $\overline{\mathcal{D}}$ whose kernel amounts to…
We examine an extension of the ideas of quantum cosmology and, in particular, the proposal of Hartle and Hawking for the boundary conditions of the Universe, to models which incorporate Yang-Mills fields. Inhomogeneous perturbations about a…
Using Serre's adelic interpretation of cohomology, we develop a `differential and integral calculus' on an algebraic curve X over an algebraically closed filed k of constants of characteristic zero, define algebraic analogs of additive…