Moyal Brackets, Star Products and the Generalised Wigner Function

Abstract

The Wigner-Weyl- Moyal approach to Quantum Mechanics is recalled, and similarities to classical probability theory emphasised. The Wigner distribution function is generalised and viewed as a construction of a bosonic object, a target space co-ordinate, for example, in terms of a bilinear convolution of two fermionic objects, e.g. a quark antiquark pair. This construction is essentially non-local, generalising the idea of a local current. Such Wigner functions are shown to solve a BPS generalised Moyal-Nahm equation.

7 pages, LaTeX, to appear in special issue of the J. of Chaos, Solitons and Fractals

References in corpus (4)

• Matrix String Theory
• Features of Time-independent Wigner Functions
• Moyal Brackets in M-Theory
• Higher-dimensional Generalisations of the Euler Top Equations

Cited by in corpus (11)

• Non-Hermitian Hamiltonians with real eigenvalues coupled to electric fields: from the time-independent to the time dependent quantum mechanical formulation
• Isospectral Hamiltonians from Moyal products
• Metrics and isospectral partners for the most generic cubic PT-symmetric non-Hermitian Hamiltonian
• Moyal Nahm Equations
• Chern-Simons Hadronic Bag from Quenched Large-N QCD
• Noncommutative Geometry Framework and The Feynman's Proof of Maxwell Equations
• Derivatives and the Role of the Drinfel'd Twist in Noncommutative String Theory
• Moyal Noncommutative Integrability and the Burgers-KdV Mapping
• Generalized dynamical theories in phase space and the hydrogen atom
• Gauging the higher-spin-like symmetries by the Moyal product
• Master equations for Wigner functions with spontaneous collapse and their relation to thermodynamic irreversibility