TY - JOUR

T1 - Mixed symmetry tensors in the worldline formalism

AU - Corradini, Olindo

AU - Edwards, James

PY - 2016/5/10

Y1 - 2016/5/10

N2 - 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.

AB - 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.

KW - Gauge Symmetry

KW - Scattering Amplitudes

KW - Wilson

KW - ’t Hooft and Polyakov loops

UR - http://www.scopus.com/inward/record.url?scp=84971278875&partnerID=8YFLogxK

UR - http://dx.doi.org/10.1007/JHEP05(2016)056

UR - http://dx.doi.org/10.1007/JHEP05(2016)056

U2 - 10.1007/JHEP05(2016)056

DO - 10.1007/JHEP05(2016)056

M3 - Article

AN - SCOPUS:84971278875

SN - 1126-6708

VL - 2016

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 5

M1 - 56

ER -