• Corpus ID: 119557786

K\"ahler Representation Theory

@article{Roberts2016KahlerRT,
  title={K\"ahler Representation Theory},
  author={Bryan W. Roberts and Nicholas J. Teh},
  journal={arXiv: Mathematical Physics},
  year={2016}
}
We show that Jordan-Lie-Banach algebras, which provide an abstract characterization of quantum theory equivalent to C^* algebras, can always be canonically represented in terms of smooth functions on a K\"ahler manifold. 

Figures from this paper

References

SHOWING 1-10 OF 27 REFERENCES

Reduction of Lie--Jordan algebras: Quantum

In this paper we present a theory of reduction of quantum systems in the presence of symmetries and constraints. The language used is that of Lie--Jordan Banach algebras, which are discussed in some

Pure states as a dual object forC*-algebras

We consider the set of pure states of aC*-algebra as a uniform space equipped with transition probabilities and orientation, and show that the pure states with this structure determine theC*-algebra

On Orientation and Dynamics in Operator Algebras.¶Part I

Abstract:This paper characterizes the self-adjoint part of C*-algebras and von Neumann algebras among normed Jordan algebras. It also explains how the associative product is determined by a general

Geometrization of quantum mechanics

We show that various descriptions of quantum mechanics can be represented in geometric terms. In particular, starting with the space of observables and using the momentum map associated with the

Geometry Of State Spaces Of Operator Algebras

Preface * JB-Algebras * JBW-Algebras * Structure of JBW-Algebras * Representations of JB-Algebras * State Spaces of Jordan Algebras * Dynamical Correspondences * General Compressions * Spectral

Typical states and density matrices

Geometry of quantum mechanics

Quantum mechanics is formulated on the true space of physical states—the projective Hilbert space. It is found that the postulates of quantum mechanics assume an intrinsically geometric form. In

On an Algebraic generalization of the quantum mechanical formalism

One of us has shown that the statistical properties of the measurements of a quantum mechanical system assume their simplest form when expressed in terms of a certain hypercomplex algebra which is

Mathematical Topics Between Classical and Quantum Mechanics

Introductory Overview.- I. Observables and Pure States.- Observables.- Pure States.- From Pure States to Observables.- II. Quantization and the Classical Limit.- Foundations.- Quantization on Flat