King's College London

Research portal

Complete normal ordering 1: Foundations

Research output: Contribution to journalArticle

Original languageEnglish
Pages (from-to)840-879
Number of pages40
JournalNuclear Physics, Section B
Early online date18 Jul 2016
Publication statusPublished - Aug 2016


  • Complete normal ordering_ELLIS_Accepted 24May2016_GOLD VoR

    Complete_normal_ordering_ELLIS_Accepted_24May2016_GOLD_VoR.pdf, 1.05 MB, application/pdf


    Final published version

    CC BY

    Open Access funded by SCOAP³ - Sponsoring Consortium for Open Access Publishing in Particle Physics. Under a Creative Commons license

King's Authors


We introduce a new prescription for quantising scalar field theories (in generic spacetime dimension and background) perturbatively around a true minimum of the full quantum effective action, which is to ‘complete normal order’ the bare action of interest. When the true vacuum of the theory is located at zero field value, the key property of this prescription is the automatic cancellation, to any finite order in perturbation theory, of all tadpole and, more generally, all ‘cephalopod’ Feynman diagrams. The latter are connected diagrams that can be disconnected into two pieces by cutting one internal vertex, with either one or both pieces free from external lines. In addition, this procedure of ‘complete normal ordering’ (which is an extension of the standard field theory definition of normal ordering) reduces by a substantial factor the number of Feynman diagrams to be calculated at any given loop order. We illustrate explicitly the complete normal ordering procedure and the cancellation of cephalopod diagrams in scalar field theories with non-derivative interactions, and by using a point splitting ‘trick’ we extend this result to theories with derivative interactions, such as those appearing as non-linear σ-models in the world-sheet formulation of string theory. We focus here on theories with trivial vacua, generalising the discussion to non-trivial vacua in a follow-up paper.

Download statistics

No data available

View graph of relations

© 2018 King's College London | Strand | London WC2R 2LS | England | United Kingdom | Tel +44 (0)20 7836 5454