Duality in scalar field theory on noncommutative phase spaces
By E. Langmann, R. Szabo. 2002
221 citations recorded by the source corpus.
Abstract We describe a novel duality symmetry of Φ 2 n 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. Using a particular regularization we show, to all orders of perturbation theory, that this duality also persists at the quantum level. We also point out various other properties of this class of noncommutative field theories.
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/43e3f06cdb7c17df83d650be111864547561f33b
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Citations in the corpus
- Vanishing of beta function of non-commutative Φ 4 4 theory to all orders (2006, background): “Grosse and Wulkenhaar solved the difficult problem of ultraviolet/infrared mixing by introducing a new harmonic potential term inspired by the Langmann-Szabo (LS) duality [8] between positions and momenta.”
- Power-Counting Theorem for Non-Local Matrix Models and Renormalisation (2003, unknown): “The oscillator potential makes the φ(4)-action covariant with respect to a duality transformation [15] between positions and momenta.”
- Exact Solution of Quantum Field Theory on Noncommutative Phase Spaces (2003, methodology): “For example, as discussed in [12], a finite matrix rank N provides both a short distance and low momentum cutoff simultaneously, and thereby avoids the mixing of ultraviolet and infrared divergences which seem to make the analysis of noncommutative perturbation theory to all orders hopeless.”