相关论文: Questions on quantization

We describe an algebra for composing automata which includes both classical and quantum entities and their communications. We illustrate by describing in detail a quantum protocol.

Quantum computation has received great attention in recent years for its possible application to difficult problem in classical calculation. Despite the experimental problems of implementing quantum devices, theoretical physicists have…

This chapter surveys the advances of the past decade arising from the contributions of Indian mathematicians in the broad areas of operator algebras and operator theory. It brings together the work of twenty mathematicians and their…

Jordan operator algebras are norm-closed spaces of operators on a Hilbert space with a^2 in A for all a in A. In two recent papers by the authors and Neal, a theory for these spaces was developed. It was shown there that much of the theory…

It is shown here and in the preceeding paper (quant-ph/0201129) that vector coherent state theory, the theory of induced representations, and geometric quantization provide alternative but equivalent quantizations of an algebraic model. The…

We derive several formulae for the spectra of the second quantization operators in abstract fermionic Fock spaces.

It is shown how the theory of the fields can be constructed in a consistent way in quantized spaces. All constructions are connected with unitary irreducible representations of real forms of six dimensional rotation algebras O(1,5), O(2,4),…

Operator quantum error-correction is a technique for robustly storing quantum information in the presence of noise. It generalizes the standard theory of quantum error-correction, and provides a unified framework for topics such as quantum…

Using geometric quantization procedure, the quantization of algebra of observables for physical system with Ricci-flat phase space is obtained. In the classical case the appointed physical system is reduced to harmonic oscillator when the…

Under some hypotheses (symmetry, confluence), we enumerate all quadratically presented algebras, generated by creation and destruction operators, in which number operators exist. We show that these are algebras of bosons, fermions, their…

The present text surveys some relevant situations and results where basic Module Theory interacts with computational aspects of operator algebras. We tried to keep a balance between constructive and algebraic aspects.

We present some general theorems about operator algebras that are algebras of functions on sets, including theories of local algebras, residually finite dimensional operator algebras and algebras that can be represented as the scalar…

A practical method is developed to deal with the second quantization of the many-body system containing the composite particles. In our treatment, the modes associated with composite particles are regarded approximately as independent ones…

In this note we present a brief overview of variational methods to solve homogenization problems. The purpose is to give a first insight on the subject by presenting some fundamental theoretical tools, both classical and modern. We conclude…

We introduce a quantization of the graded algebra of functions on the canonical cone of an algebraic curve C, based on the theory of formal pseudodifferential operators. When C is a complex curve with Poincar\'e uniformization, we propose…

This is a survey of the author's recent results on the Kadison and Halmos similarity problems and the closely connected notion of ``length'' of an operator algebra.

A general framework for obtaining certain types of contracted and centrally extended algebras is presented. The whole process relies on the existence of quadratic algebras, which appear in the context of boundary integrable models.

A long-standing problem in quantum gravity and cosmology is the quantization of systems in which time evolution is generated by a constraint that must vanish on solutions. Here, an algebraic formulation of this problem is presented,…

Polynomial relations between the generators of the classical and quantum Heisenberg algebras are presented. Some of those relations can have a meaning of the formulas of the normal ordering for the creation/annihilation operators occurred…

We introduce the new problems of quantum packing, quantum covering, and quantum paving. These problems arise naturally when considering an algebra of non-commutative operators that is deeply rooted in quantum physics as well as in Gabor…