We study contact interactions for long world-lines on a curved surface, focusing on the average number of times two world-lines intersect as a function of their end-points. The result can be used to extend the concept of path-ordering, as employed in the Wilson loop, from a closed curve into the interior of a surface spanning the curve. Taking this surface as a string world-sheet yields a generalisation of the string contact interaction previously used to represent the Abelian Wilson loop as a tensionless string. We also describe a supersymmetric generalisation.
J.C. Maxwell, A treatise on electricity and magnetism, Clarendon Press, Oxford U.K. (1998).
M. Faraday, Thoughts on ray-vibrations. Letter to Richard Phillips, Esq. Phil. Mag. 28 (1846) 345, reprinted in Experimental researches in chemistry and physics, M. Faraday, R. Taylor and W. Francis, London U.K. (1859).
P.A.M. Dirac, Gauge-invariant formulation of quantum electrodynamics, Canadian J. Phys. 33 (1955) 650.
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].
S. Samuel, Color Zitterbewegung, Nucl. Phys. B 149 (1979) 517 [INSPIRE].
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].
P. Salomonson, B.-S. Skagerstam and J.-O. Winnberg, On the equations of motion of a Yang-Mills particle, Phys. Rev. D 16 (1977) 2581 [INSPIRE].
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ArXiv ePrint: 1712.04760
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Curry, C., Mansfield, P. Intersection of world-lines on curved surfaces and path-ordering of the Wilson loop. J. High Energ. Phys. 2018, 81 (2018). https://doi.org/10.1007/JHEP06(2018)081
- Bosonic Strings
- Long strings
- Wilson, ’t Hooft and Polyakov loops
- Field Theories in Lower Dimensions