Asao Arai

HEISENBERG OPERATORS, INVARIANT DOMAINS AND HEISENBERG EQUATIONS OF MOTION

An abstract operator theory is developed on operators of the form AH(t) := eitHAe-itH, t ∈ ℝ, with H a self-adjoint operator and A a linear operator on a Hilbert space (in the context of quantum mechanics, AH(t) is called the Heisenberg operator of A with respect to H). The following aspects are discussed: (i) integral equations for AH(t) for a general class of A; (ii) a sufficient condition for D(A), the domain of A, to be left invariant by e-itH for all t ∈ ℝ; (iii) a mathematically rigorous formulation of the Heisenberg equation of motion in quantum mechanics and the uniqueness of its solutions; (iv) invariant domains in the case where H is an abstract version of Schrodinger and Dirac operators; (v) applications to Schrodinger operators with matrix-valued potentials and Dirac operators.

Spectral properties of a Dirac operator in the chiral quark soliton model

We consider a Dirac operator

Mathematical Analysis of a Generalized Chiral Quark Soliton Model

H

Ultra-Weak Time Operators of Schrödinger Operators

acting in the Hilbert space

A Special Class of Infinite Dimensional Dirac Operators on the Abstract Boson-Fermion Fock Space

L^2(\BbbR^3;\BbbC^4)\otimes \BbbC^2

FUNCTIONAL INTEGRAL REPRESENTATIONS AND GOLDEN–THOMPSON INEQUALITIES IN BOSON–FERMION SYSTEMS

, which describes a Hamiltonian of the chiral quark soliton model in nuclear physics. The mass term of

Hilbert Space Representations of Generalized Canonical Commutation Relations

H

A Class of d-Dimensional Dirac Operators with a Variable Mass

is a matrix-valued function formed out of a function

Generalized Weak Weyl Relation and Decay of Quantum Dynamics

F:\BbbR^3 \to \BbbR

Spectrum of Time Operators

, called a profile function, and a vector field