Worldline approach to the Grosse-Wulkenhaar model

Abstract

We apply the worldline formalism to the Grosse-Wulkenhaar model and obtain an expression for the one-loop effective action which provides an efficient way for computing Schwinger functions in this theory. Using this expression we obtain the quantum corrections to the effective background and the $\beta$-functions, which are known to vanish at the self-dual point. The case of degenerate noncommutativity is also considered. Our main result can be straightforwardly applied to any polynomial self-interaction of the scalar field and we consider that the worldline approach could be useful for studying effective actions of noncommutative gauge fields as well as in other non-local models or in higher-derivative field theories.

arXiv comment22 pages, 2 figures. Matches the published version. New section added where the degenerate case is also considered

References in corpus (11)

• Noncommutative Perturbative Dynamics
• Renormalisation of ϕ^4-theory on noncommutative R^4 in the matrix base
• Constant External Fields in Gauge Theory and the Spin 0, 1/2, 1 Path Integrals
• Renormalisation of ϕ^4-theory on noncommutative R^2 in the matrix base
• Vanishing of Beta Function of Non Commutative ${\Phi }_4^4$ Theory to all orders
• Renormalization of noncommutative phi 4-theory by multi-scale analysis
• Non-commutative heat kernel
• Worldgraph Approach to Yang-Mills Amplitudes from N=2 Spinning Particle
• String-inspired representations of photon/gluon amplitudes
• Solvable 4D noncommutative QFT: phase transitions and quest for reflection positivity
• Trace anomalies and the string-inspired definition of quantum-mechanical path integrals in curved space

Cited by in corpus (1)

• The Snyder-de Sitter Scalar ${\phi }_{\star }^4$ Quantum Field Theory in D=2