Related papers: Rigged Hilbert Space Treatment of Continuous Spect…
This paper establishes a link between Noncommutative Geometry and canonical quantum gravity. A semi-finite spectral triple over a space of connections is presented. The triple involves an algebra of holonomy loops and a Dirac type operator…
In conventional Schr\"{o}dinger representation the unitarity of the evolution of bound states is guaranteed by the Hermiticity of the Hamiltonian. A non-unitary isospectral simplification of the Hamiltonian, $\mathfrak{h} \to…
It is known that besides the usual unitary mappings $\Omega = 1/\Omega^\dagger$ between the equivalent representations of the physical Hilbert space of Quantum Mechanics (often, Fourier transformations), the generalized non-unitary maps…
Our main theorem is in the generality of the axioms of Hilbert space, and the theory of unbounded operators. Consider two Hilbert spaces such that their intersection contains a fixed vector space D. It is of interest to make a precise…
The concept of a Dirac algebroid, which is a linear almost Dirac structure on a vector bundle, was designed to generate phase equations for mechanical systems with linear nonholonomic constraints. We apply it to systems with magnetic-like…
We explore the superstring theory on AdS_3 x S^3 x T^4 in the framework given in hep-th/9806194. We argue on the Hilbert space of "space-time CFT", and especially construct a suitable vacuum of this CFT from the physical degrees of freedom…
The Hilbert spaces for stable scattering states and particles are determined by the representations of the characterizing Euclidean and Poincar\'e group and given, respectively, by the square integrable functions on the momentum 2-spheres…
Non-commutative electrodynamics obtained through the Seiberg-Witten map ceases to have equivalent action-level and equation-level realizations once fixed external currents are introduced, and in the action-level construction associated with…
We present a detailed study of the interplay between chiral symmetry and spectral properties of the Dirac operator in lattice gauge theories. We consider, in the framework of the Schwinger model, the fixed point action and a fermion action…
We study approximate solutions to the Schr\"odinger equation $i\epsi\partial\psi_t(x)/\partial t = H(x,-i\epsi\nabla_x) \psi_t(x)$ with the Hamiltonian given as the Weyl quantization of the symbol $H(q,p)$ taking values in the space of…
The functional Schr\"odinger representation of a scalar field on an $n$-dimensional static space-time background is argued to be a singular limiting case of the hypercomplex quantum theory of the same system obtained by the precanonical…
In this work, we present an abstract theory for the approximation of operator-valued Riccati equations posed on Hilbert spaces. It is demonstrated here that the error of the approximate solution to the operator-valued Riccati equation is…
We consider an off-diagonal self-adjoint finite rank perturbation of a self-adjoint operator in a complex separable Hilbert space $\mathfrak{H}_0 \oplus \mathfrak{H}_1$, where $\mathfrak{H}_1$ is finite dimensional. We describe the singular…
We introduce a systematically improvable family of variational wave functions for the simulation of strongly correlated fermionic systems. This family consists of Slater determinants in an augmented Hilbert space involving "hidden"…
The general Dirac equation in 1+1 dimensions with a potential with a completely general Lorentz structure is studied. Considering mixed vector-scalar-pseudoscalar square potentials, the states of relativistic fermions are investigated. This…
Intrinsic microphysical irreversibility is the time asymmetry observed in exponentially decaying states. It is described by the semigroup generated by the Hamiltonian $\QTR{it}{H}$ of the quantum physical system, not by the semigroup…
A linear operator in a Hilbert space defined through the form of Riesz representation naturally introduces a reproducing kernel Hilbert space structure over the range space. Such formulation, called H-HK formulation in this paper, possesses…
In general case of deformed Heisenberg algebra leading to the minimal length we present a definition of the square inverse position operator. Our proposal is based on the functional analysis of the square position operator. Using this…
We study the discrete Schr\"odinger operator $H$ in $\ZZ^d$ with the surface potential of the form $V(x)=g \delta(x_1) \tan \pi(\alpha \cdot x_2+ \omega)$, where for $x \in \ZZ^d$ we write $x=(x_1,x_2), \quad x_1 \in \ZZ^{d_1}, x_2 \in…
We discuss the detailed structure of the spectrum of the Hamiltonian for the polymerized harmonic oscillator and compare it with the spectrum in the standard quantization. As we will see the non-separability of the Hilbert space implies…