Mixed symmetry tensors in the worldline formalism

Olindo Corradini, James Edwards

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

Abstract: We consider the first quantised approach to quantum field theory coupled to a non-Abelian gauge field. Representing the colour degrees of freedom with a single family of auxiliary variables the matter field transforms in a reducible representation of the gauge group which — by adding a suitable Chern-Simons term to the particle action — can be projected onto a chosen fully (anti-)symmetric representation. By considering F families of auxiliary variables, we describe how to extend the model to arbitrary tensor products of F reducible representations, which realises a U(F) “flavour” symmetry on the world-line particle model. Gauging this symmetry allows the introduction of constraints on the Hilbert space of the colour fields which can be used to project onto an arbitrary irreducible representation, specified by a certain Young tableau. In particular the occupation numbers of the wavefunction — i.e. the lengths of the columns (rows) of the Young tableau — are fixed through the introduction of Chern-Simons terms. We verify this projection by calculating the number of colour degrees of freedom associated to the matter field. We suggest that, using the worldline approach to quantum field theory, this mechanism will allow the calculation of one-loop scattering amplitudes with the virtual particle in an arbitrary representation of the gauge group.

Original languageEnglish
Article number56
JournalJournal of High Energy Physics
Volume2016
Issue number5
DOIs
Publication statusPublished - 10 May 2016

Keywords

  • Gauge Symmetry
  • Scattering Amplitudes
  • Wilson
  • ’t Hooft and Polyakov loops

Fingerprint

Dive into the research topics of 'Mixed symmetry tensors in the worldline formalism'. Together they form a unique fingerprint.

Cite this