相关论文: Generalized "bra-ket" formalism

General Relativity formulated with Noncommutative geometry allows one to obtain, via the fluctuation of Dirac operator, an exact equivalence principle: generation of curvature and torsion from flat space. The fluctuation method presented in…

The definition of a non-trivial space of generalized functions of a complex variable allowing to consider derivatives of continuous functions is a non-obvious task, e.g. because of Morera theorem, because distributional Cauchy-Riemann…

The most general dilaton gravity theory in 2 spacetime dimensions is considered. A Hamiltonian analysis is performed and the reduced phase space, which is two dimensional, is explicitly constructed in a suitable parametrization of the…

Dirac operators on curved space-times are introduced with the help of a new point-view that observers have to be included in the formulation of natural laws. The class of Dirac operators are Lorentz invariant in the sense that the…

This paper introduces the expanded real numbers as an ordered subring of the hyperreal number field that does not contain any infinitesimals, and defines the set of all integrable functions from the real numbers to the expanded real…

In this paper the approximation of Dirac operators with general $\delta$-shell potentials supported on $C^2$-curves in $\mathbb{R}^2$ or $C^2$-surfaces in $\mathbb{R}^3$, which may be bounded or unbounded, is studied. It is shown under…

We review the basic elements of the geometrical formalism for description of gauge fields and the theory of invariant connections, and their applications to the coset space dimensional reduction of Yang-Mills theories. We also discuss the…

The notion of a generalized product, refining that of a (symmetric and smooth) simplicial space is introduced and shown to imply the existence of an algebra of pseudodifferential operators. This encompasses many constructions of such…

Full details are given for the definition and construction of the wreath product of two arbitrary Lie algebras, in the hope that it can lead to the definition of a suitable Lie group to be the wreath product of two given Lie groups. In the…

A geometric description is given for the Sp(2) covariant version of the field-antifield quantization of general constrained systems in the Lagrangian formalism. We develop differential geometry on manifolds in which a basic set of…

The BRST quantization of the Abelian Proca model is performed using the Batalin-Fradkin-Tyutin and the Batalin-Fradkin-Vilkovisky formalism. First, the BFT Hamiltonian method is applied in order to systematically convert a second class…

Motivated by computational efficiency in algebraic automata theory here we define the cascade product of permutation groups as an external product, as a generic extension. It is the most general hierarchical product that uses arbitrary…

We establish the coarse relative trace formulae of Jacquet-Rallis for linear and unitary groups. Both formulae are of the form: a sum of spectral distributions equals a sum of geometric distributions. In order to obtain the spectral…

In this paper we use topological techniques to construct generalized trace and modified dimension functions on ideals in certain ribbon categories. Examples of such ribbon categories naturally arise in representation theory where the usual…

We use the method of similar operators to study a general Dirac operator $L$ and its spectral properties. We find a similar operator to the Dirac operator that is an orthogonal direct sum of simpler operators. The result is used to describe…

Coordinate formalism on Hilbert manifolds developed in Kryukov is reviewed. The results of Kryukov are applied to the simpliest case of a Hilbert manifold: the abstract Hilbert space. In particular, functional transformations preserving…

In this paper, we propose a generalization of an improved gauge unfixing formalism in order to generate gauge symmetries in the non-Abelian valued systems. This generalization displays a proper and formal reformulation of second-class…

There are certain countably generated sigma-algebras of sets in the real line which do not admit any non-zero, sigma-finite, diffused (or, continuous) measure. Such countably generated sigma-algebras can be obtained by the use of some…

Extending the methods from our previous work on quantum knots and quantum graphs, we describe a general procedure for quantizing a large class of mathematical structures which includes, for example, knots, graphs, groups, algebraic…

In this paper, we consider a generalization of variational calculus which allows us to consider in the same framework different cases of mechanical systems, for instance, Lagrangian mechanics, Hamiltonian mechanics, systems subjected to…