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Gauging Higher-Spin-Like Symmetries Using the Moyal Product
2022Well established approaches to gauging U(1) transformations or spacetime translations lead to theories of interacting bosons of spin 1 or spin 2. We describe a novel approach to gauging their higher derivative generalizations (i.e. higher-spin-like symmetries), leading to a Yang-Mills like theory defined over a symplectic manifold dubbed “master space”.
Cvitan, Maro +4 more
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Generalised Deformations, Koszul Resolutions, Moyal Products
Reviews in Mathematical Physics, 1998We generalise Gerstenhaber's theory of deformations, by dropping the assumption that the deformation parameter should commute with the elements of the original algebra. We give the associated cohomology and construct a Koszul resolution for the polynomial algebra [Formula: see text] in the "homogeneous" case.
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An Explicit Moyal Product Realization of Quantum Deformation
Communications in Theoretical Physics, 1996The -deformation and q-deformation were estimated completely under the concrete Moyal *-product and induced Moyal product version.
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Analysis of the Moyal product in a flat space
Journal of Mathematical Physics, 1986This paper studies the mathematical properties of Moyal product defined in the space R2n. They correspond to the properties of quantum mechanics and permit us to consider classical mechanics as a limit of quantum mechanics when Planck’s constant vanishes.
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Stochastic differential calculus, the Moyal *-product, and noncommutative geometry
Letters in Mathematical Physics, 1993The authors present a reformulation of the Itõ calculus of stochastic differentials in terms of a differential calculus in the sense of noncommutative geometry. In this calculus, differentials do not commute with functions. The relation between both types of differential calculi is mediated by a generalized Moyal *-product.
Dimakis, Aristophanes +1 more
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MOYAL STAR PRODUCT OF μ-HOLOMORPHIC j-DIFFERENTIALS
International Journal of Geometric Methods in Modern Physics, 2008It was shown in [1], only for scalar conformal fields, that the Moyal–Weyl star product can introduce the quantum effect as the phase factor to the ordinary product. In this paper we show that, even on the same complex structure, the Moyal–Weyl star product of two j-differentials (conformal fields of weights (j, 0)) does not vanish but it generates ...
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Open Superstring Star as a Continuous Moyal Product with B Field
Communications in Theoretical Physics, 2003In this paper, we recast the matter part of the open superstring star in the present of a constant B field. By using a different coordinate representation the matter part of the open superstring star is identified with the continuous Moyal product of functions of anti-commuting variables.
Wang Xiao-Hui +3 more
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Deformation quantization of Fréchet-Poisson algebras: Convergence of the Moyal product
2000Beyond formal deformation quantization, i.e., deformation quantization of Poisson algebras with a formal deformation parameter [1], one can ask whether the formal parameter converges. In this direction, Rieffel [7] presented a notion of strict deformation quantization: Deformation quantization with a convergent product in the C*-algebras sense.
Hideki Omori +3 more
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Higher Spin Theories with The Moyal Product
2018Overview of the recent attempts to construct higher spin field theories in Minkowski spacetime is presented. It is shown that, despite the negative expectations comming from no-go theorems, we have found one candidate: higher-spin Yang-Mills theory. The properties and unknowns of HS-YM theory are presented.
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MOYAL STAR-PRODUCT ON A HILBERT SPACE
Topics in Mathematical Physics, General Relativity and Cosmology in Honor of Jerzy Plebanski, 2006openaire +1 more source