ON THE STRUCTURE OF HOMOGENENOUS WICK IDEALS IN WICK *-ALGEBRAS WITH BRAIDED COEFFICIENTS

We study a Wick ideal structure of quadratic *-algebras allowing Wick ordering with braided operator of coefficients. A construction of nested sequence of homogeneous Wick ideals of growing degree is presented. Representations of a Wick analogue of the CCR algebra with two degrees of freedom, annihilating certain homogeneous Wick ideals are described.

Functional Representations for Fock Superalgebras

The Fock space of bosons and fermions and its underlying superalgebra are represented by algebras of functions on a superspace. We define Gaussian integration on infinite-dimensional superspaces, and construct super-analogs of the classical function spaces with a reproducing kernel — including the Bargmann–Fock representation — and of the Wiener–Segal representation. The latter representation requires the investigation of Wick ordering on Z2-graded algebras. As application we derive a Mehler formula for the Ornstein–Uhlenbeck semigroup on the Fock space.

Quantum White Noises and Free Fields

Nuclear Wick algebra of generalized operators generated by quantum white noise is introduced in order to formulate the formal manipulations in free fields at rigorous mathematical level. Solutions of second quantized field equations and various physical observables such as energy and momenta of the fields are realized as generalized operators adn the renormalizations through Wick ordering procedure are investigated from functional analytical point of view.

GENERALIZED CANONICAL QUANTIZATION OF BOSONIC STRING IN BACKGROUND FIELDS

The theory of a closed bosonic string interacting with background fields, namely, with metric, antisymmetric tensor of second rank and dilaton, is considered. The classical formulation of the constrained theory is developed and the canonical quantization is carried out. The combined symbols of the Virasoro operators corresponding to the Weyl ordering of zero string modes and to the Wick ordering of oscillating ones are constructed. The quantum Virasoro algebra is formulated by means of star-commutators corresponding to these symbols and the nonlocal first quantum correction in the algebra is calculated. The local part of the correction linear in curvature is derived and effective equations of motion for background fields are obtained in the lowest order.