相关论文: Classical Spinor Structures on Quantum Spaces

Building on the universal covering group of the general linear group, we introduce the composite spinor bundle whose subbundles are Lorentz spin structures associated with different gravitational fields. General covariant transformations of…

Linear spinor fields are a generalization of the Dirac field that have transparent cluster decomposability properties needed for classical correspondence of relativistic quantum systems. The algebra of these fields directly incorporate…

We develop notions of twisted spinor bundle and twisted pre-quantum bundle on quasi-Hamiltonian G-spaces. The main result of this paper is that we construct a Dirac operator with index given by positive energy representation of loop group.…

Although intrinsic spin is usually viewed as a purely quantum property with no classical analog, we present evidence here that fermion spin has a classical origin rooted in the geometry of three-dimensional physical space. Our approach to…

Building on the theory of noncommutative complex structures, the notion of a noncommutative K\"ahler structure is introduced. In the quantum homogeneous space case many of the fundamental results of classical K\"ahler geometry are shown to…

A generalized Clifford manifold is proposed in which there are coordinates not only for the basis vector generators, but for each element of the Clifford group, including the identity scalar. These new quantities are physically interpreted…

The theory of spinors is developed for locally anisotropic (la) spaces, in brief la-spaces, which in general are modeled as vector bundles provided with nonlinear and distinguished connections and metric structures (such la-spaces contain…

Basic notions of Dirac theory of constrained systems have their analogs in differential geometry. Combination of the two approaches gives more clear understanding of both classical and quantum mechanics, when we deal with a model with…

Recent progress to construct Dirac operators and spinors on compact quantum groups is discussed. The case $SU_q(2)$ is studied carefully and the relationship between known approaches is explained. New examples are given.

The spin-base invariant formalism of Dirac fermions in curved space maintains the essential symmetries of general covariance as well as similarity transformations of the Clifford algebra. We emphasize the advantages of the spin-base…

We present general mappings between classical spin systems and quantum physics. More precisely, we show how to express partition functions and correlation functions of arbitrary classical spin models as inner products between quantum…

Operator fields in the bundle of Dirac spinors and their conversion to spatial fields are considered. Some commutator equations are studied with the use of the conversion technique.

The closed homogeneous and isotropic universe is considered. The bundles of Weyl and Dirac spinors for this universe are explicitly described. Some explicit formulas for the basic fields and for the connection components in stereographic…

Dirac's method of classical analogy is employed to incorporate quantum degrees of freedom into modern nonequilibrium thermodynamics. The proposed formulation of dissipative quantum mechanics builds entirely upon the geometric structures…

We clarify the structure obtained in H\'elein and Vey's proposition for a variational principle for the Einstein-Cartan gravitation formulated on a frame bundle starting from a structure-less differentiable 10-manifold. The obtained…

A construction of the noncommutative-geometric counterparts of classical classifying spaces is presented, for general compact matrix quantum structure groups. A quantum analogue of the classical concept of the classifying map is introduced…

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 the work some relations between three techniques, Hopf's bundle, Kustaanheimo-Stiefel's bundle, 3-space with spinor structure have been examined. The spinor space is viewed as a real space that is minimally (twice as much) extended in…

Based on the observation that Cacic [10]'s characterization of almost commutative spectral triples as Clifford module bundles can be pushed to endomorphim algebras of Dirac bundles, with the geometric Dirac operator related to the Dirac…

A geometric framework for describing quantum particles on a possibly curved background is proposed. Natural constructions on certain distributional bundles (`quantum bundles') over the spacetime manifold yield a quantum ``formalism'' along…