相关论文: On Symmetric Operators in Noncommutative Geometry

In high-energy physics, coordinate noncommutativity represents the core idea that space itself can be quantized, as expressed through the frameworks of string theory and noncommutative field theory. Influence of such a noncommutativity on…

This is an expanded version of the notes to a course taught by the first author at the 1995 Les Houches Summer School. Constraints on a tentative reconciliation of quantum theory and general relativity are reviewed. It is explained what…

We present a generally covariant approach to quantum mechanics in which generalized positions, momenta and time variables are treated as coordinates on a fundamental "phase-spacetime." We show that this covariant starting point makes…

In this expository paper we describe the study of certain non-self-adjoint operator algebras, the Hardy algebras, and their representation theory. We view these algebras as algebras of (operator valued) functions on their spaces of…

We review some selected aspects of the construction of gauge invariant operators in field theories on non-commutative spaces and their relation to the energy momentum tensor as well as to the non-commutative loop equations.

The formulation of Geometric Quantization contains several axioms and assumptions. We show that for real polarizations we can generalize the standard geometric quantization procedure by introducing an arbitrary connection on the…

We consider noncommutative geometries obtained from a triangular Drinfeld twist. This allows to construct and study a wide class of noncommutative manifolds and their deformed Lie algebras of infinitesimal diffeomorphisms. This way symmetry…

We develop the formalism for noncommutative differential geometry and Riemmannian geometry to take full account of the *-algebra structure on the (possibly noncommutative) coordinate ring and the bimodule structure on the differential…

In this article, we give conditions guaranteeing the commutativity of a bounded self-adjoint operator with an unbounded closed symmetric operator.

Working towards an algebra for operators of strongly interacting quantum fields, a nonassociative decomposition of field operators is proposed. In the demonstrated case, quantum corrections appear from the possible bracket permutations. A…

It is shown that in presence of certain external fields a well defined self-adjoint time operator exists, satisfying the standard canonical commutation relations with the Hamiltonian. Examples include uniform electric and gravitational…

We consider both the co-ordinates and momenta to be non-commutative and define a non-commutative version of Lorentz symmetry which has a smooth limit to the standard Lorentz symmetry. The Poincar\acute{e} algebra in this spacetime has also…

The anti self-adjoint operators of imaginary coordinate and momentum, together with the self-adjoint operators of real coordinate, momentum, energy and time are used in construction of the quantum field theory in operator form. This…

Physical considerations strongly indicate that spacetime at Planck scales is noncommutative. A popular model for such a spacetime is the Moyal plane. The Poincar\`e group algebra acts on it with a Drinfel'd-twisted coproduct. But the latter…

After an introduction to some basic issues in non-commutative geometry (Gel'fand duality, spectral triples), we present a "panoramic view" of the status of our current research program on the use of categorical methods in the setting of…

Quiver varieties have recently appeared in various different areas of Mathematics such as representation theory of Kac-Moody algebras and quantum groups, instantons on 4-manifolds, and resolutions Kleinian singularities. In this paper, we…

We study the properties of a quantum field with time as a dynamical variable. Temporal vibrations are introduced to restore the symmetry between time and space in a matter field. The system with vibrations of matter in time and space obeys…

In quantum theory, real degrees of freedom are usually described by operators which are self-adjoint. There are, however, exceptions to the rule. This is because, in infinite dimensional Hilbert spaces, an operator is not necessarily…

We investigate the kinetics of a nonrelativistic particle interacting with a constant external force on a Lie-algebraic noncommutative space. The structure constants of a Lie algebra, also called noncommutative parameters, are constrained…

We introduce a self-adjoint operator that indicates the direction of time within the framework of standard quantum mechanics. That is, as a function of time its expectation value decreases monotonically for any initial state. This operator…