Heriot-Watt Mathematics Report Series
HWM02-3, 6 February 2002
Duality in Scalar Field Theory on Noncommutative Phase Spaces
E Langmann and R J Szabo
Abstract
We describe a novel duality symmetry of Phi(4)-theory defined on
noncommutative Euclidean space and with noncommuting momentum coordinates.
This duality acts on the fields by Fourier transformation and scaling.
It is an extension, to interactions defined with a star-product, of
that which arises in quantum field theories of non-interacting
scalar particles coupled to a constant background electromagnetic field. The
dual models are in general of the same original form but with
transformed coupling parameters, while in certain special cases
all parameters are essentially unchanged. We
show that this duality persists to all orders of perturbation theory in the
full quantum field theory. We also point out various other
properties of this class of noncommutative field theories.
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