Weighted power counting and chiral dimensional regularization

Abstract

We define a modified dimensional-regularization technique that overcomes several difficulties of the ordinary technique, and is specially designed to work efficiently in chiral and parity violating quantum field theories, in arbitrary dimensions greater than 2. When the dimension of spacetime is continued to complex values, spinors, vectors and tensors keep the components they have in the physical dimension, therefore the $\gamma$ matrices are the standard ones. Propagators are regularized with the help of evanescent higher-derivative kinetic terms, which are of the Majorana type in the case of chiral fermions. If the new terms are organized in a clever way, weighted power counting provides an efficient control on the renormalization of the theory, and allows us to show that the resulting chiral dimensional regularization is consistent to all orders. The new technique considerably simplifies the proofs of properties that hold to all orders, and makes them suitable to be generalized to wider classes of models. Typical examples are the renormalizability of chiral gauge theories and the Adler-Bardeen theorem. The difficulty of explicit computations, on the other hand, may increase.

41 pages; v2: minor changes, PRD version

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Cited by in corpus (12)

• Super-renormalizable & Finite Gravitational Theories
• Universally Finite Gravitational & Gauge Theories
• Finite quantum gauge theories
• Quantum Field Theory, Feynman-, Wheeler Propagators, Dimensional Regularization in Configuration Space and Convolution of Lorentz Invariant Tempered Distributions
• Aspects of perturbative unitarity
• Dimensionally regularized Tsallis' Statistical Mechanics and two-body Newton's gravitation
• Remarks on the renormalization properties of Lorentz and CPT violating quantum electrodynamics
• Dimensionally regularized Boltzmann-Gibbs Statistical Mechanics and two-body Newton's gravitation
• Newton's gravitation-force's classical average proof of a Verlinde's conjecture
• Classical and Quantum Nonlocal Supergravity
• Adler-Bardeen theorem and cancellation of gauge anomalies to all orders in nonrenormalizable theories
• Ward identities and gauge independence in general chiral gauge theories