Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1106.0469 · Modern Physics Letters A

A GENERAL FORMULATION OF THE MOYAL AND VOROS PRODUCTS AND ITS PHYSICAL INTERPRETATION

Laure Gouba, DOMAGOJ KOVACEVIC, STJEPAN MELJANAC

Published Dec 30, 2011• 4 citations
arXivHTMLPDF

Abstract

A unifying perspective on the Moyal and Voros products and their physical meanings has been recently presented in the literature, where the Voros formulation admits a consistent physical interpretation. We define a star product ⋆, in terms of an antisymmetric fixed matrix Θ, and an arbitrary symmetric matrix Φ, that is a generalization of the Moyal and the Voros products. We discuss the quantum mechanics and the physical meaning of the generalized star product.

DOI
10.1142/s0217732312500058

Related papers

A unifying perspective on the Moyal and Voros products and their physical meanings

Prasad Basu, Biswajit Chakraborty, Frederik G. Scholtz

The Moyal and Voros formulations of non-commutative quantum field theory has been a point of controversy in the recent past. Here we address this issue in the context of non-commutative non-relativistic quantum mechanics. In particular we show that the two formulations simply correspond to two different representations associated with two different choices of basis on the quantum Hilbert space. From a mathematical perspective the two formulations are therefore completely equivalent, but we also argue that only the Voros formulaton admits a consistent physical interpretation. These considerations are elucidated by considering the free particle transition amplitude in the two representations.

arXiv:1101.2495•Journal of Physics A Mathematical and Theoretical•Jun 10, 2011•30 citations

Chemical building blocks in quantum chemical calculations. Perspective on “The density matrix in many-electron quantum mechanics I. Generalized product functions. Factorization and physical interpretation of the density matrices”

János G. Ángyán

Springer eBooks•Jan 1, 2000•10 citations

Chemical building blocks in quantum chemical calculations. Perspective on "The density matrix in many-electron quantum mechanics I. Generalized product functions. Factorization and physical interpretation of the density matrices"

János G. Ángyán

Theoretical Chemistry Accounts•Feb 9, 2000•4 citations

The Weyl--Wigner--Moyal Formalism. III. The Generalized Moyal Product in the Curved Phase Space

Maciej Przanowski, Jaromir Tosiek

Acta Physica Polonica B•Feb 1, 1999•8 citations

Multicomponent WKB and Quantization

C. Emmrich, Hartmann Römer

Hamiltonians whose symbols are not simply real valued, but matrix or, more generally, endomorphism valued functions appear in many places in physics, examples being the Dirac equation, multicomponent wave equations like electrodynamics in media, and Yang-Mills theories, and the Born-Oppenheimer approximation in molecular physics. The aim of this paper is to give a completely geometric approach to the WKB approximation od such systems, and to reduce the problem ``as far as possible'' to the scalar case. A star-product formulation of quantum mechanics proves to be particularly useful in this context. As opposed to other approaches in the literature which restrict themselves to the use of the Moyal product and thus to the study of trivial bundles (or local trivializations) over $\real^{2n}$, we will consider general bundles over arbitrary symplectic manifolds. Here, Fedosov's construction \cite{fedosov} will be the adequate tool, since it gives an explicit construction for star products in this general setting.

arXiv:hep-th/9601138•Jan 25, 1996•0 citations

Generalized Quantum Mechanics

James B. Hartle

A unified framework for different formulations of quantum theoery is introduced specifying what is meant by a quantum mechanical theory in general.

arXiv:2110.11268•Oct 21, 2021•0 citations
A unifying perspective on the Moyal and Voros products and their physical meanings has been recently presented in the literature, where the Voros formulation admits a consistent physical interpretation. We define a star product ⋆, in terms of an antisymmetric fixed matrix Θ, and an arbitrary symmetric matrix Φ, that is a generalization of the Moyal and the Voros products. We discuss the quantum mechanics and the physical meaning of the generalized star product.
The Moyal and Voros formulations of non-commutative quantum field theory has been a point of controversy in the recent past. Here we address this issue in the context of non-commutative non-relativistic quantum mechanics. In particular we show that the two formulations simply correspond to two different representations associated with two different choices of basis on the quantum Hilbert space. From a mathematical perspective the two formulations are therefore completely equivalent, but we also argue that only the Voros formulaton admits a consistent physical interpretation. These considerations are elucidated by considering the free particle transition amplitude in the two representations.
Hamiltonians whose symbols are not simply real valued, but matrix or, more generally, endomorphism valued functions appear in many places in physics, examples being the Dirac equation, multicomponent wave equations like electrodynamics in media, and Yang-Mills theories, and the Born-Oppenheimer approximation in molecular physics. The aim of this paper is to give a completely geometric approach to the WKB approximation od such systems, and to reduce the problem ``as far as possible'' to the scalar case. A star-product formulation of quantum mechanics proves to be particularly useful in this context. As opposed to other approaches in the literature which restrict themselves to the use of the Moyal product and thus to the study of trivial bundles (or local trivializations) over ℜ2n\real^{2n}ℜ2n, we will consider general bundles over arbitrary symplectic manifolds. Here, Fedosov's construction \cite{fedosov} will be the adequate tool, since it gives an explicit construction for star products in this general setting.