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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
M.J. Strassler, Field theory without Feynman diagrams: one loop effective actions, Nucl. Phys. B 385 (1992) 145 [hep-ph/9205205] [INSPIRE].
C. Schubert, Perturbative quantum field theory in the string inspired formalism, Phys. Rept. 355 (2001) 73 [hep-th/0101036] [INSPIRE].
Z. Bern and D.A. Kosower, Efficient calculation of one loop QCD amplitudes, Phys. Rev. Lett. 66 (1991) 1669 [INSPIRE].
H.-T. Sato and M.G. Schmidt, Worldline approach to the Bern-Kosower formalism in two loop Yang-Mills theory, Nucl. Phys. B 560 (1999) 551 [hep-th/9812229] [INSPIRE].
G.V. Dunne and C. Schubert, Multiloop information from the QED effective Lagrangian, J. Phys. Conf. Ser. 37 (2006) 59 [hep-th/0409021] [INSPIRE].
M.G. Schmidt and C. Schubert, On the calculation of effective actions by string methods, Phys. Lett. B 318 (1993) 438 [hep-th/9309055] [INSPIRE].
F. Bastianelli and A. Zirotti, Worldline formalism in a gravitational background, Nucl. Phys. B 642 (2002) 372 [hep-th/0205182] [INSPIRE].
F. Bastianelli, J.M. Davila and C. Schubert, Gravitational corrections to the Euler-Heisenberg Lagrangian, JHEP 03 (2009) 086 [arXiv:0812.4849] [INSPIRE].
F. Bastianelli, O. Corradini and E. Latini, Higher spin fields from a worldline perspective, JHEP 02 (2007) 072 [hep-th/0701055] [INSPIRE].
F. Bastianelli, O. Corradini and E. Latini, Spinning particles and higher spin fields on (A)dS backgrounds, JHEP 11 (2008) 054 [arXiv:0810.0188] [INSPIRE].
J.P. Edwards, Contact interactions between particle worldlines, JHEP 01 (2016) 033 [arXiv:1506.0813].
N. Ahmadiniaz, F. Bastianelli and O. Corradini, Dressed scalar propagator in a non-abelian background from the worldline formalism, Phys. Rev. D 93 (2016) 025035 [arXiv:1508.0514].
N. Ahmadiniaz, C. Schubert and V.M. Villanueva, String-inspired representations of photon/gluon amplitudes, JHEP 01 (2013) 132 [arXiv:1211.1821] [INSPIRE].
F. Bastianelli, A. Huet, C. Schubert, R. Thakur and A. Weber, Integral representations combining ladders and crossed-ladders, JHEP 07 (2014) 066 [arXiv:1405.7770] [INSPIRE].
P. Mansfield, The fermion content of the Standard Model from a simple world-line theory, Phys. Lett. B 743 (2015) 353 [arXiv:1410.7298] [INSPIRE].
J.P. Edwards, Unified theory in the worldline approach, Phys. Lett. B 750 (2015) 312 [arXiv:1411.6540] [INSPIRE].
F. Bastianelli, R. Bonezzi, O. Corradini and E. Latini, Particles with non abelian charges, JHEP 10 (2013) 098 [arXiv:1309.1608] [INSPIRE].
F. Bastianelli, R. Bonezzi, O. Corradini, E. Latini and K.H. Ould-Lahoucine, A worldline approach to colored particles, arXiv:1504.0361.
A.P. Balachandran, P. Salomonson, B.-S. Skagerstam and J.-O. Winnberg, Classical description of particle interacting with nonabelian gauge field, Phys. Rev. D 15 (1977) 2308 [INSPIRE].
A. Barducci, R. Casalbuoni and L. Lusanna, Classical scalar and spinning particles interacting with external Yang-Mills fields, Nucl. Phys. B 124 (1977) 93 [INSPIRE].
E. D’Hoker and D.G. Gagne, Worldline path integrals for fermions with general couplings, Nucl. Phys. B 467 (1996) 297 [hep-th/9512080] [INSPIRE].
F. Bastianelli, P. Benincasa and S. Giombi, Worldline approach to vector and antisymmetric tensor fields, JHEP 04 (2005) 010 [hep-th/0503155] [INSPIRE].
F. Bastianelli and R. Bonezzi, Quantum theory of massless (p, 0)-forms, JHEP 09 (2011) 018 [arXiv:1107.3661] [INSPIRE].
L. Brink, P. Di Vecchia and P.S. Howe, A Lagrangian formulation of the classical and quantum dynamics of spinning particles, Nucl. Phys. B 118 (1977) 76 [INSPIRE].
L. Brink, S. Deser, B. Zumino, P. Di Vecchia and P.S. Howe, Local supersymmetry for spinning particles, Phys. Lett. B 64 (1976) 435 [Erratum ibid. B 68 (1977) 488] [INSPIRE].
F. Bastianelli, O. Corradini and A. Waldron, Detours and paths: BRST complexes and worldline formalism, JHEP 05 (2009) 017 [arXiv:0902.0530] [INSPIRE].
P. Howe, S. Penati, M. Pernici and P.K. Townsend, A particle mechanics description of antisymmetric tensor fields, Class. Quant. Grav. 6 (1989) 1125.
H. Georgi, Lie algebras in particle physics, Frontiers in Physics, Perseus Books, Reading U.S.A. (1999).
J.P. Edwards and P. Mansfield, Delta-function interactions for the bosonic and spinning strings and the generation of abelian gauge theory, JHEP 01 (2015) 127 [arXiv:1410.3288] [INSPIRE].
J.P. Edwards and P. Mansfield, QED as the tensionless limit of the spinning string with contact interaction, Phys. Lett. B 746 (2015) 335 [arXiv:1409.4948] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1603.07929
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Corradini, O., Edwards, J.P. Mixed symmetry tensors in the worldline formalism. J. High Energ. Phys. 2016, 56 (2016). https://doi.org/10.1007/JHEP05(2016)056
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2016)056