Moyal brackets, star products and the generalised Wigner function

The Wigner-Weyl-Moyal approach to Quantum Mechanics is recalled, and simila rities 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 Wign er functions are shown to solve a BPS generalised Moyal-Nahm equation. (C) 1999 Elsevier Science Ltd. All rights reserved.