We calculate the Green's functions for a scalar field theory with quartic interactions for which the fields are multiplied with a generic translation invariant star product. Our analysis involves both non-commutative products, for which there is the canonical commutation relation among coordinates, and nonlocal commutative products. We give explicit expressions for the one-loop corrections to the two- and four-point functions. We find that the phenomenon of ultraviolet/infrared mixing is always a consequence of the presence of non-commuting variables. The commutative part of the product does not have the mixing.

Green’s functions for translation invariant star products / Lizzi, Fedele; Rivera, Manolo; Vitale, Patrizia. - In: MODERN PHYSICS LETTERS A. - ISSN 0217-7323. - 30:36(2015), p. 1550194. [10.1142/S0217732315501941]

Green’s functions for translation invariant star products

LIZZI, FEDELE;VITALE, PATRIZIA
2015

Abstract

We calculate the Green's functions for a scalar field theory with quartic interactions for which the fields are multiplied with a generic translation invariant star product. Our analysis involves both non-commutative products, for which there is the canonical commutation relation among coordinates, and nonlocal commutative products. We give explicit expressions for the one-loop corrections to the two- and four-point functions. We find that the phenomenon of ultraviolet/infrared mixing is always a consequence of the presence of non-commuting variables. The commutative part of the product does not have the mixing.
2015
Green’s functions for translation invariant star products / Lizzi, Fedele; Rivera, Manolo; Vitale, Patrizia. - In: MODERN PHYSICS LETTERS A. - ISSN 0217-7323. - 30:36(2015), p. 1550194. [10.1142/S0217732315501941]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/612792
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