Quantum field theory: Finiteness and Effectiveness

TL;DR

This paper proposes that quantum field theories can be made UV finite by viewing them as low-energy effective theories derived from a complete underlying theory, simplifying the renormalization process and addressing longstanding issues.

Contribution

It introduces a novel approach where the underlying theory determines low-energy effective theories through ambiguity definitions, differing from traditional renormalization methods.

Findings

Applicable to any interaction model and space-time dimension

Simpler and more straightforward than traditional renormalization

Includes nonperturbative examples demonstrating effectiveness

Abstract

A new attempt is demonstrated that QFTs can be UV finite if they are viewed as the low energy effective theories of a fundamental underlying theory (that is complete and well-defined in all respects) according to the modern standard point of view. This approach works for any interaction model and space-time dimension. It is much simpler in principle and in technology comparing to any known renormalization program.Unlike the known renormalization methods, the importance of the procedure for defining the ambiguities (corresponding to the choice of the renormalization conditions in the conventional program) is fully appreciated in the new approach. It is shown that the high energy theory(s) or the underlying theory(s) in fact 'stipulates (stipulate)' the low energy and effective ones through these definitions within our approach while all the conventional methods miss this important point. Some simple but important nonperturbative examples are discussed to show the power and plausibility of the new approach. Other related issues (especially the IR problem and the implication of our new approach for the canonical quantization procedure) are briefly touched.