Exact solution of quantum field theory on noncommutative phase spaces

• We present the exact solution of a scalar field theory defined with noncommuting position and momentum variables. The model describes charged particles in a uniform magnetic field and with an interaction defined by the Groenewold-Moyal star-product. Explicit results are presented for all Green's functions in arbitrary even spacetime dimensionality. Various scaling limits of the field theory are analysed non-perturbatively and the renormalizability of each limit examined. A supersymmetric extension of the field theory is also constructed in which the supersymmetry transformations are parametrized by differential operators in an in finite-dimensional noncommutative algebra.

Ämnesord

NATURVETENSKAP  -- Fysik (hsv//swe)

NATURAL SCIENCES  -- Physical Sciences (hsv//eng)

Nyckelord

renormalization regularization and renormalons

non-commutative geometry

matrix models

kontsevich-penner model

matrix models

interacting fermions

landau problem

mechanics

limit

superspace

plane

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