Dispersion relations for the self-energy in non-commutative field theories

Abstract

We study the IR/UV connection in non-commutative ${\varphi }^3$ theory as well as in non-commutative QED from the point of view of the dispersion relation for the self-energy. We show that, although the imaginary part of the self-energy is well behaved as the parameter of non-commutativity vanishes, the real part becomes divergent as a consequence of the high energy behavior of the dispersion integral. Some other interesting features that arise from this analysis are also briefly discussed.

10 pages

References in corpus (7)

• Noncommutative Field Theory
• Quantum Field Theory on Noncommutative Spaces
• On the unitarity problem in space/time noncommutative theories
• The Meaning of Infrared Singularities in Noncommutative Gauge Theories
• Renormalization of the noncommutative photon self-energy to all orders via Seiberg-Witten map
• On the unitarity of quantum gauge theories on non-commutative spaces
• General structure of the photon self-energy in non-commutative QED

Cited by in corpus (4)

• Spectral Representation and Dispersion Relations in Field Theory on Noncommutative Space
• Chiral fermions in noncommutative electrodynamics: renormalizability and dispersion
• On space-time noncommutative theories at finite temperature
• Gauge-Invariant Resummation Formalism and Unitarity in Non-Commutative QED