相关论文: Deformation Quantization of Classical Fields

Foundations of the formal series $*$ -- calculus in deformation quantisation are discussed. Several classes of continuous linear functionals over algebras applied in classical and quantum physics are introduced. The notion of nonnegativity…

The main objective of this article is to develop the theory of deformation of $C^*$-algebras endowed with a group action, from the perspective of non-formal equivariant quantization. This program, initiated in \cite{Bieliavsky-Gayral}, aims…

In the first part of this thesis we study the generalization of the recent algebraic approach to classical field theory by proposing a more general setting based on the manifold of smooth sections of a non-trivial fiber bundle. Central is…

Classical physics is reformulated as a constrained Hamiltonian system in the history phase space. Dynamics, i.e. the Euler-Lagrange equations, play the role of first-class constraints. This allows us to apply standard methods from the…

We elaborate the generalizations of the approach to gauge-invariant deformations of the gauge theories developed in our previous work [1]. In the given paper we construct the exact transformations defying the gauge-invariant deformed theory…

Starting from deformation quantization (star-products), the quantization problem of Nambu Mechanics is investigated. After considering some impossibilities and pushing some analogies with field quantization, a solution to the quantization…

In this paper, we analyze the polymer representation of the real-valued scalar field theory within the deformation quantization formalism. Specifically, we obtain the polymer Wigner functional by taking the limit of Gaussian measures in the…

The Weyl quantization of classical observables on the torus (as phase space) without regularity assumptions is explicitly computed. The equivalence class of symbols yielding the same Weyl operator is characterized. The Heisenberg equation…

Affine quantization is a parallel procedure to canonical quantization, which is ideally suited to deal with non-renormalizable scalar models as well as quantum gravity. The basic applications of this approach lead to the common goals of any…

We discuss a quantum-theoretical aspect of the massive Abelian antisymmetric tensor gauge theory with antisymmetric tensor current. To this end, an Abelian rank-2 antisymmetric tensor field is quantized both in the covariant gauge with an…

We argue that the quantized non-Abelian gauge theory can be obtained as the infrared limit of the corresponding classical gauge theory in a higher dimension. We show how the transformation from classical to quantum dynamics emerges and…

The most general gauge-invariant marginal deformation of four-dimensional abelian BF-type topological field theory is studied. It is shown that the deformed quantum field theory is topological and that its observables compute, in addition…

Deformation quantization (sometimes called phase-space quantization) is a formulation of quantum mechanics that is not usually taught to undergraduates. It is formally quite similar to classical mechanics: ordinary functions on phase space…

We show that a suitable deformation of the algebra $h_k(1)$ of the creation and annihilation operators for a complex scalar field, initially quantized in Minkowski space--time, induces the canonical quantization of the same field in a…

We present a first attempt to apply the approach of deformation quantization to linearized Einstein's equations. We use the analogy with Maxwell equations to derive the field equations of linearized gravity from a modified Maxwell…

We consider SU(2) gauge potentials over a space with a compactified dimension. A non-Abelian Fourier transform of the gauge potential in the compactified dimension is defined in such a way that the Fourier coefficients are (almost) gauge…

Deformational structures, in many aspects generalizing standard elasticity theory, are investigated in abstract form. Within free deformational structures we define algebra of deformations, classify them by its special properties, define…

We first introduce the Wigner-Weyl-Moyal formalism for a theory whose phase-space is an arbitrary Lie algebra. We also generalize to quantum Lie algebras and to supersymmetric theories. It turns out that the non-commutativity leads to a…

Consistent interactions that can be added to a two-dimensional, free abelian gauge theory comprising a special class of BF-type models and a collection of vector fields are constructed from the deformation of the solution to the master…

We discuss the tight-binding models of solid state physics with the $Z_2$ sublattice symmetry in the presence of elastic deformations, and their important particular case -the tight binding model of graphene. In order to describe the…