Worldline approach to noncommutative field theory

Abstract

Abstract. The study of the heat-trace expansion in noncommutative field theory has shown the existence of Moyal nonlocal Seeley-DeWitt coefficients which are related to the UV/IR mixing and manifest, in some cases, the non-renormalizability of the theory. We show that these models can be studied in a worldline approach implemented in phase space and arrive at a master formula for the n-point contribution to the heat-trace expansion. This formulation could be useful in understanding some open problems in this area, as the heat-trace expansion for the noncommutative torus or the introduction of renormalizing terms in the action, as well as for generalizations to other nonlocal operators.

Noncommutative U(1) gauge theory from a worldline perspective

“…The three derivatives give a leading contribution (for small β) of the form i 2β δ µνĠ3j σ jτ , together with the corresponding permutations. The divergent contribution then reads After performing the derivatives, the leading contribution is given by − 11) which, as expected, is cancelled by the renormalization of the charge given by expression (8.13).…”

“…, t n }; the corresponding fields are then V a = A µ (x+ √ β x(t a ) ± a θp(t a )) and must be Lorentz-contracted with p µ (t a ). In terms of Fourier transforms this quantity can be written as 11) so that expression (6.10) results …”

Snyder-de Sitter Meets the Grosse-Wulkenhaar Model

“…This can be done using the well-known Feynman diagram's expansion-there exists however a specially well-suited technique called the Worldline or String-inspired formalism [27]. Some previous implementations of this technique in noncommutative theories may be found in [28,29,30,20], whereas details in the computation of the two-point function result that concerns us can be read in [31]. In particular, the one-loop divergent part of the two-point function in D = 4 − ε dimensions, Γ…”

Worldline colour fields and non-Abelian quantum field theory

“…Its origins can be traced to Feynman [6], with a revival of interest following Bern and Kosower's Master Formulae for field theory amplitudes derived from string theory [7,8]. It is recently finding application in a wide range of physical problems, including multi-loop effective actions and scattering amplitudes [3,9], constant field QED and the Schwinger effect [10,11], gravitational interactions [12,13], higher spin fields [14,15], quantum fields in non-commutative space-time [16,17] and the form factor decomposition of the four gluon vertex reported by Schubert elsewhere in these proceedings.…”