相关论文: Geometrical description of algebraic structures: A…

There have been several propositions for a geometric and essentially non-linear formulation of quantum mechanics. From a purely mathematical point of view, the point of view of Jordan algebra theory might give new strength to such…

We show how to formulate physical theory taking as a starting point the set of states (geometric approach). We discuss the relation of this formulation to the conventional approach to classical and quantum mechanics and the theory of…

Quantum mechanics is among the most important and successful mathematical model for describing our physical reality. The traditional formulation of quantum mechanics is linear and algebraic. In contrast classical mechanics is a geometrical…

In this paper we review a proposed geometrical formulation of quantum mechanics. We argue that this geometrization makes available mathematical methods from classical mechanics to the quantum frame work. We apply this formulation to the…

In this paper we will present an ongoing project which aims to use model theory as a suitable mathematical setting for studying the formalism of quantum mechanics. We will argue that this approach provides a geometric semantics for such…

The unsatisfactory status of the search for a consistent and predictive quantization of gravity is taken as motivation to study the question whether geometrical laws could be more fundamental than quantization procedures. In such an…

Jordan algebras were first introduced in an effort to restructure quantum mechanics purely in terms of physical observables. In this paper we explain why, if one attempts to reformulate the internal structure of the standard model of…

This is an overview of higher structural constructions in physics. The main motivations of our current attempt are as follows: (i) to provide a brief introduction to derived algebraic geometry, (ii) to understand how derived objects…

In the paper "Is there a Jordan geometry underlying quantum physics?" (Int. J. Theor. Phys., to appear; arXiv:0801.3069 [math-ph]), generalized projective geometries have been proposed as a framework for a geometric formulation of Quantum…

Over the past six years, a detailed framework has been constructed to unravel the quantum nature of the Riemannian geometry of physical space. A review of these developments is presented at a level which should be accessible to graduate…

The usual quantization of a classical space-time field does not touch the non-geometrical character of quantum mechanics. We believe that the deep problems of unification of general relativity and quantum mechanics are rooted in this poor…

We demonstrate how one can see quantization of geometry, and quantum algebraic structure in supersymmetric gauge theory.

The basic elements of the geometric approach to a consistent quantization formalism are summarized, with reference to the methods of the old quantum mechanics and the induced representations theory of Lie groups. A possible relationship…

In the last decade, the development of new ideas in quantum theory, including geometric and deformation quantization, the non-Abelian Berry factor, super- and BRST symmetries, non-commutativity, has called into play the geometric techniques…

The application of geometry to physics has provided us with new insightful information about many physical theories such as classical mechanics, general relativity, and quantum geometry (quantum gravity). The geometry also plays an…

These notes present an introduction to an analytic version of deformation quantization. The central point is to study algebras of physical observables and their irreducible representations. In classical mechanics one deals with real Poisson…

The geometry of the symplectic structures and Fubini-Study metric is discussed. Discussion in the paper addresses geometry of Quantum Mechanics in the classical phase space. Also, geometry of Quantum Mechanics in the projective Hilbert…

We review the main features of a mathematical framework encompassing some of the salient quantum mechanical and geometrical aspects of Hall systems with finite size and general boundary conditions. Geometrical as well as algebraic…

States of a quantum mechanical system are represented by rays in a complex Hilbert space. The space of rays has, naturally, the structure of a K\"ahler manifold. This leads to a geometrical formulation of the postulates of quantum mechanics…

Geometric quantization is an attempt at using the differential-geometric ingredients of classical phase spaces regarded as symplectic manifolds in order to define a corresponding quantum theory. Generally, the process of geometric…