Related papers: The operator algebra of the discrete state operato…
We study the interactions of the discrete states with nonzero ghost number in $c=1$ two-dimensional ($2D$) quantum gravity. By using the vertex operator representations, it is shown that their interactions are given by the structure…
The noncritical $4D$ $\cW_3$ string is a model of $\cW_3$ gravity coupled to two free scalar fields. In this paper we discuss its BRST quantization in direct analogy with that of the $2D$ (Virasoro) string. The physical operators form a…
We study the discrete state structure of $\hat c=1$ superconformal matter coupled to 2-D supergravity. Factorization properties of scattering amplitudes are used to identify these states and to construct the corresponding vertex operators.…
We show that 2D periodic operators with local and perpendicular defects form an algebra. We provide an algorithm of finding spectrum for such operators. While the continuous spectral components can be computed by simple algebraic operations…
Some elaboration is given to the structure of physical states in 2D gravity coupled to $C \leq 1$ matter, and to the chiral algebra ($w_{\infty}$) of $C_{M} = 1$ theory which has been found recently, in the continuum approach, by Witten and…
We summarize and deepen recent results on systems of orthogonal pure states on operator algebras. Especially, we focus on noncommutative generalizations of some principles of topology of locally compact spaces such as exposining points by…
We investigate some properties of geometric operators in canonical quantum gravity in the connection approach \`a la Ashtekar, which are associated with volume, area and length of spatial regions. We motivate the construction of analogous…
This paper is a survey of our recent work on operator algebras associated to dynamical systems that lead to classification results for the systems in terms of algebraic invariants of the operator algebras.
The article is devoted to the investigation of operators on a non locally compact group algebra. Their isomorphisms are also studied.
The matrix normed structure of the unitization of a (non-selfadjoint) operator algebra is determined by that of the original operator algebra. This yields a classification up to completely isometric isomorphism of two-dimensional unital…
A new functional calculus, developed recently for a fully non-perturbative treatment of quantum gravity, is used to begin a systematic construction of a quantum theory of geometry. Regulated operators corresponding to areas of 2-surfaces…
We investigate the spectral properties of the volume operator in quantum gravity in the framework of a previously introduced lattice discretization. The presence of a well-defined scalar product in this approach permits us to make definite…
This note aims to offer a non-technical and self-contained introduction to gravitational algebras and their applications in the nonequilibrium physics of gravitational systems. We begin by presenting foundational concepts from operator…
Structure constants of Operator Algebras for the SL(2) degenerate conformal field theories are calculated.
We present a non-physical interpretation of the Cosmological Constant based on a particular algebraic analysis. This also introduces some novel algebraic structures, such as ``unital norms", ``uncurling metrics", and ``partial wedge…
Constants of motion are calculated for 2+1 dimensional gravity with topology R x T^2 and negative cosmological constant. Certain linear combinations of them satisfy the anti - de Sitter algebra so(2,2) in either ADM or holonomy variables.…
Lecture notes to a one-term course on operator algebras and their application in physics. Very brief and basic introduction to the subject of Banach- and C-star algebras complemented with their appearance in physics. The course is intended…
This work gives value to the importance of Hilbert-Schmidt operators in the formulation of a noncommutative quantum theory. A system of charged particle in a constant magnetic field is investigated in this framework.
We use the theory of functions of noncommuting operators (noncommutative analysis) to solve an asymptotic problem for a partial differential equation and show how, starting from general constructions and operator formulas that seem to be…
We describe an algebra of observables for a static patch in de Sitter space, with operators gravitationally dressed to the worldline of an observer. The algebra is a von Neumann algebra of Type II$_1$. There is a natural notion of entropy…