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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
