A class of interacting classical random fields is constructed using deformed ⋆-algebras of creation and annihilation operators. The fields constructed are classical random field versions of “Lie fields.” A vacuum vector is used to construct linear forms over the algebras, which are conjectured to be states over the algebras. Assuming this conjecture is true, the fields constructed are “quantum random fields” in the sense that they have Poincaré invariant vacua with a fluctuation scale determined by . A nonlocal particle interpretation of the formalism is shown to be the same as a particle interpretation of a quantum field theory.
Skip Nav Destination
Research Article| December 26 2007
Lie fields revisited
Peter Morgan; Lie fields revisited. J. Math. Phys. 1 December 2007; 48 (12): 122302. https://doi.org/10.1063/1.2825148
Download citation file: