The Moyal product is the matrix product
S.A. Merkulov
TL;DR
This paper demonstrates that the Moyal algebra of functions on the plane is mathematically equivalent to an algebra of infinite-sized matrices, providing a new perspective on deformation quantization.
Contribution
It establishes a canonical isomorphism between the Moyal algebra and an algebra of infinite matrices, linking deformation quantization to matrix algebra.
Findings
Moyal algebra is isomorphic to an algebra of infinite matrices
Provides a new mathematical perspective on deformation quantization
Connects Moyal product with matrix algebra
Abstract
This is a short comment on the Moyal formula for deformation quantization. It is shown that the Moyal algebra of functions on the plane is canonically isomorphic to an algebra of matrices of infinite size.
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Taxonomy
TopicsAdvanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models