Unfolded Dynamics Approach and Quantum Field Theory

Abstract

We study quantization of a self-interacting scalar field within the unfolded dynamics approach. To this end we find and analyze a classical unfolded system describing 4d off-shell scalar field with a general self-interaction potential. Then we systematically construct three different but related unfolded formulations of the corresponding quantum field theory, supporting them with illustrative calculations: an unfolded functional Schwinger-Dyson system, an unfolded system for correlation functions and an unfolded effective system for vertex functions. The most curious feature we reveal is that an unfolded quantum commutator gets naturally regularized: a standard delta-function is replaced with a heat kernel, parameterized by the unfolded proper time. We also identify an auxiliary 5d system, having this proper time as a physical time, which generates 4d scalar action as its on-shell action.

27 pages. V4: brief explanatory comment after (3.5) added; presentation in the Introduction and the Conclusion improved; references added. This version has been accepted for publication in JHEP

References in corpus (9)

• Gauge Invariant Lagrangians for Free and Interacting Higher Spin Fields. A Review of the BRST formulation
• Light-Front Higher-Spin Theories in Flat Space
• Higher spins in AdS_5 at one loop: vacuum energy, boundary conformal anomalies and AdS/CFT
• Chiral Higher Spin Theories and Self-Duality
• Off-Shell Spinor-Helicity Amplitudes from Light-Cone Deformation Procedure
• Spinor-Helicity Formalism for Massless Fields in AdS${}_4$ III: Contact Four-Point Amplitudes
• A remark on the Lagrange structure of the unfolded field theory
• One Loop Tests of Supersymmetric Higher Spin $Ad{S}_4/CF{T}_3$
• Quantum Off-Shell Recursion Relation

Cited by in corpus (2)

• Scalar Electrodynamics and Higgs Mechanism in the Unfolded Dynamics Approach
• Unfolded hypermultiplet in harmonic superspace