Gauge invariance for extended objects |
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| Affiliation: | 1. Centro de Estudios Cientificos de Santiago, Casilla 16443, Santiago 9, Chile;2. Center for Theoretical Physics, The University of Texas at Austin, Austin, TX 78712, USA;1. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China;2. School of Sciences, Jimei University, Xiamen 361021, China;1. CPHT, Ecole Polytechnique, 91128 Palaiseau cedex, France;2. Centre for High Energy Physics, Indian Institute of Science, Bangalore- 560012, India;1. Irving K. Barber School of Arts and Sciences, University of British Columbia - Okanagan, Kelowna, British Columbia V1V 1V7, Canada;2. Department of Physics and Astronomy, University of Lethbridge, Lethbridge, Alberta, T1K 3M4, Canada;3. Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, United Kingdom;1. IFSA Collaborative Innovation Center, Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China;2. Instituto de Física, Universidade de São Paulo, C.P. 66318, 05315-970 São Paulo, SP, Brazil |
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| Abstract: | Just as the vector potential (one-form) couples to charged point-particles, antisymmetric tensor fields of higher rank (p-forms) couple to elementary objects of higher dimensionality (strings, membranes, …). It is shown that the only possible gauge invariant interaction of such an extended object with a gauge field in spacetime is based on the abelian group U(1). This is unlike the situation for particles where Yang-Mills actions based on any gauge group may be written down. The properties of the abelian theory are explored. It is pointed out that a compact object is analogous to a particle-antiparticle pair and its quantum rate of production in a constant external field is calculated semiclassically. The analysis is performed keeping generic both the dimension of the object and that of spacetime. |
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