Tadpoles, Cephalopods, and `Complete Normal Ordering'

TL;DR

This paper introduces 'complete normal ordering,' a method to cancel tadpole and cephalopod Feynman diagrams in scalar field theories, simplifying calculations by reducing diagram counts to all orders in perturbation theory.

Contribution

It proposes a novel extension of normal ordering that eliminates specific Feynman diagrams, streamlining perturbative computations in scalar field theories.

Findings

Reduces the number of Feynman diagrams by a factor of two or more.

Achieves tadpole- and cephalopod-free Greens functions.

Applicable to generic interacting scalar field theories.

Abstract

We describe how to cancel (when this is desirable) all tadpole and more generally all cephalopod Feynman diagrams in generic interacting scalar field theories to all orders in perturbation theory. This cancelation reduces the number of Feynman diagrams at a given loop order by a factor of two or more, and is accomplished by introducing the notion of 'complete normal ordering' (an extension of the standard field theory definition of normal ordering) which when applied to the bare action of the theories of interest results in tadpole- and cephalopod-free Greens functions.