Gauge symmetries indicate redundancies in the description of the relevant degrees of freedom of a given field theory and restrict the nature of observable quantities. One of the problems faced by emergent theories of relativistic fields is to understand how gauge symmetries can show up in systems that contain no trace of these symmetries at a more fundamental level. In this paper we start a systematic study aimed to establish a satisfactory mathematical and physical picture of this issue, dealing first with abelian field theories. We discuss how the trivialization, due to the decoupling and lack of excitation of some degrees of freedom, of the Noether currents associated with physical symmetries leads to emergent gauge symmetries in specific situations. An example of a relativistic field theory of a vector field is worked out in detail in order to make explicit how this mechanism works and to clarify the physics behind it. The interplay of these ideas with well-known results of importance to the emergent gravity program, such as the Weinberg-Witten theorem, are discussed.
T. Thiemann, Modern canonical quantum general relativity, Cambridge University Press (2008).
S. Weinberg and E. Witten, Limits on Massless Particles, Phys. Lett. B 96 (1980) 59 [INSPIRE].
G. Baskaran and P.W. Anderson, Gauge theory of high temperature superconductors and strongly correlated Fermi systems, Phys. Rev. B 37 (1988) 580 [INSPIRE].
M. Henneaux and C. Teitelboim, Quantization of gauge systems, Princeton University Press, U.S.A. (1992).
C.W. Misner, K.S. Thorne and J.A. Wheeler, Gravitation, W.H. Freeman, San Francisco U.S.A. (1973).
B. Julia and S. Silva, Currents and superpotentials in classical gauge invariant theories. 1. Local results with applications to perfect fluids and general relativity, Class. Quant. Grav. 15 (1998) 2173 [gr-qc/9804029] [INSPIRE].
V. Aldaya, M. Calixto, J. Guerrero and F.F. Lopez-Ruiz, Symmetries of non-linear systems: group approach to their quantization, Int. J. Geom. Meth. Mod. Phys. 8 (2011) 1329 [arXiv:1012.3681] [INSPIRE].
C. Itzykson and J.B. Zuber, Quantum Field Theory, Dover Books on Physics, Dover Publications (2012).
S. Weinberg, Gravitation and Cosmology: principles and applications of the general theory of relativity, John Wiley and Sons, New York U.S.A (1972).
G.E. Volovik, The Universe in a Helium Droplet, International Series of Monographs on Physics, Oxford University Press, Oxford (2009).
F. Loebbert, The Weinberg-Witten theorem on massless particles: an essay, Ann. Phys. 17 (2008) 803 [INSPIRE].
J.F. Donoghue, M.M. Anber and U. Aydemir, Gauge noninvariance as tests of emergent gauge symmetry, in proceedings of the 5th Meeting on CPT and Lorentz Symmetry (CPT 10), Bloomington, Indiana U.S.A., June 28 - July 2 2010, p. 113 [arXiv:1007.5049] [INSPIRE].
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ArXiv ePrint: 1608.07473
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Barceló, C., Carballo-Rubio, R., Di Filippo, F. et al. From physical symmetries to emergent gauge symmetries. J. High Energ. Phys. 2016, 84 (2016). https://doi.org/10.1007/JHEP10(2016)084
- Gauge Symmetry
- Global Symmetries
- Models of Quantum Gravity
- Effective field theories