Naoya Miyazaki

Star exponential functions as two-valued elements

We propose a relatively new notion of two-valued elements, which arise naturally in constructing star exponential functions of the quadratics in the Weyl algebra over the complex number. This notion enables us to describe group-like objects of the set of star exponential functions of quadratics in the Weyl algebra.

Deformation Quantizations of the Poisson Algebra of Laurent Polynomials

It is well known that the Moyal bracket gives a unique deformation quantization of the canonical phase space R2n up to equivalence. In his presentation of an interesting deformation quantization of the Poisson algebra of Laurent polynomials, Ovsienko discusses the equivalences of deformation quantizations of these algebras. We show that under suitable conditions, deformation quantizations of this algebra are equivalent. Though Ovsienko showed that there exists a deformation quantization of the Poisson algebra of Laurent polynomials which is not equivalent to the Moyal product, this is not correct. We show this equivalence by two methods: a direct construction of the intertwiner via the star exponential and a more standard approach using Hochschild 2-cocycles.

ON NON(ANTI)COMMUTATIVE SUPER TWISTOR SPACES

The main purpose of this article is a proposal of non(anti)commutative super twistor space by making the odd coordinates θ not anticommuting, but satisfying Clifford algebra relations. Despite the deformation, we can introduce a deformed associative product which is globally defined on P3|N.

A Lie Group Structure for Automorphisms of a Contact Weyl Manifold

In the present article, we are concerned with the automorphisms of a contact Weyl manifold, and we introduce an infinite-dimensional Lie group structure for the automorphism group.

Singular Systems of Exponential Functions

We attempt to establish a calculus of the Moyal product treating the deformation parameter as a parameter moving in positive reals. We show strange phenomenas different from formal deformation quantization by studying the convergence of the parameter in computing the product of the exponential functions of the quadratic form. In the case of deformation quantization with the positive real parameters, the associativity for the Moyal product fails for a wider class of functions.

Expressions of algebra elements and transcendental noncommutative calculus

Ideas from deformation quantization are applied to deform the expression of elements of an algebra. Extending these ideas to certain transcendental elements implies that

Noncommutative 3-sphere as an example of noncommutative contact algebras

\frac{1}{i\h}uv

Lifts of symplectic diffeomorphisms as automorphisms of a weyl algebra bundle with fedosov connection

in the Weyl algebra is naturally viewed as an indeterminate living in a discrete set

Remarks on the Characteristic Classes Associated with the Group of Fourier Integral Operators

\mathbb{N}{+}{1/2}

Strange phenomena related to ordering problems in quantizations

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