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Exact quantisation of the relativistic Hopfield model. (English) Zbl 1377.81243

Summary: We investigate the quantisation in the Heisenberg representation of a relativistically covariant version of the Hopfield model for dielectric media, which entails the interaction of the quantum electromagnetic field with the matter dipole fields, represented by a mesoscopic polarisation field. A full quantisation of the model is provided in a covariant gauge, with the aim of maintaining explicit relativistic covariance. Breaking of the Lorentz invariance due to the intrinsic presence in the model of a preferred reference frame is also taken into account. Relativistic covariance forces us to deal with the unphysical (scalar and longitudinal) components of the fields, furthermore it introduces, in a more tricky form, the well-known dipole ghost of standard QED in a covariant gauge. In order to correctly dispose of this contribution, we implement a generalised Lautrup trick. Furthermore, causality and the relation of the model with the Wightman axioms are also discussed.

MSC:

81V10 Electromagnetic interaction; quantum electrodynamics
81T70 Quantization in field theory; cohomological methods
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[1] Luks, A.; Perinová, V., Quantum Aspects of Light Propagation (2009), Springer · Zbl 1238.81137
[2] Hawking, S. W., Comm. Math. Phys., 43, 199-220 (1975) · Zbl 1378.83040
[3] Unruh, W. G., Phys. Rev. Lett., 46, 1351-1353 (1981)
[4] Barcelo, Carlos; Liberati, Stefano; Visser, Matt, Living Rev. Relativ.. Living Rev. Relativ., Living Rev. Relativ., 14, 3 (2011) · Zbl 1316.83022
[5] Philbin, Thomas G.; Kuklewicz, Chris; Robertson, Scott; Hill, Stephen; Konig, Friedrich; Leonhardt, Ulf, Science, 319, 1367-1370 (2008)
[6] Belgiorno, F.; Cacciatori, S. L.; Clerici, M.; Gorini, V.; Ortenzi, G.; Rizzi, L.; Rubino, E.; Sala, V. G.; Faccio, D., Phys. Rev. Lett., 105, Article 203901 pp. (2010)
[7] Belgiorno, F.; Cacciatori, S. L.; Clerici, M.; Gorini, V.; Ortenzi, G.; Rizzi, L.; Rubino, E.; Sala, V. G.; Faccio, D., Phys. Rev. Lett., 107, Article 149402 pp. (2011)
[8] Rubino, E.; Belgiorno, F.; Cacciatori, S. L.; Clerici, M.; Gorini, V.; Ortenzi, G.; Rizzi, L.; Sala, V. G.; Kolesik, M.; Faccio, D., New J. Phys., 13, Article 085005 pp. (2011)
[9] Petev, M.; Westerberg, N.; Moss, D.; Rubino, E.; Rimoldi, C.; Cacciatori, S. L.; Belgiorno, F.; Faccio, D., Phys. Rev. Lett., 111, Article 043902 pp. (2013)
[10] Hopfield, J. J., Phys. Rev., 112, 1555-1567 (1958)
[11] Huttner, B.; Barnett, S. M., Phys. Rev. A, 46, 4306 (1992)
[12] Suttorp, L. G.; van Wonderen, A. J., Europhys. Lett., 67, 766-772 (2004)
[13] Suttorp, L. G., J. Phys. A: Math. Theor., 40, 3697-3719 (2007) · Zbl 1113.81117
[14] Kheirandish, F.; Soltani, M., Phys. Rev. A, 78, Article 012102 pp. (2008)
[15] Amooshahi, M.; Kheirandish, F., J. Phys. A: Math. Theor., 41, Article 275402 pp. (2008) · Zbl 1149.81376
[16] Philbin, T. G., New J. Phys., 12, Article 123008 pp. (2010) · Zbl 1448.81386
[17] Horsley, S. A.R., Phys. Rev. A, 86, Article 023830 pp. (2012)
[18] Belgiorno, F.; Cacciatori, S. L.; Dalla Piazza, F., Phys. Scr., 91, 1, Article 015001 pp. (2016)
[19] Belgiorno, Francesco; Cacciatori, Sergio Luigi; Dalla Piazza, Francesco, Eur. Phys. J. D, 68, 134 (2014)
[20] Belgiorno, F.; Cacciatori, S. L.; Dalla Piazza, F., Phys. Rev. D, 91, 12, Article 124063 pp. (2015)
[21] Belgiorno, F.; Cacciatori, S. L.; Dalla Piazza, F.; Doronzo, M., Eur. Phys. J. C, 76, 6, 308 (2016)
[22] Nakanishi, N.; Ojima, I., World Sci. Lecture Notes Phys., 27, 1-434 (1990)
[23] Greiner, W.; Reinhardt, J., Field Quantization (1996), Springer: Springer Berlin, Germany · Zbl 0844.00006
[24] Lautrup, B., Kong. Dan. Vid. Sel. Mat. Fys. Med., 35, 11 (1967)
[25] Anderson, J. L., Principles of Relativity Physics (1967), Academic Press: Academic Press New York
[26] Sundermeyer, Kurt, (Symmetries in Fundamental Physics. Symmetries in Fundamental Physics, Fundamental Theories of Physics, vol. 176 (2014), Springer, Cham: Springer, Cham Switzerland) · Zbl 1301.81006
[27] Jauch, J. M.; Watson, K. M., Phys. Rev., 74, 950 (1948) · Zbl 0036.27201
[28] Dereziński, Jan; Gérard, Christian, Mathematics of Quantization and Quantum Fields (2013), Cambridge University Press · Zbl 1271.81004
[29] Wiener, N., Ann. of Math., 33, 1-100 (1932) · JFM 58.0226.02
[30] Strocchi, F., (Selected Topics on the General Properties of Quantum Field Theory. Selected Topics on the General Properties of Quantum Field Theory, Lect. Notes Phys., vol. 51 (1993), World Scientific: World Scientific Singapore) · Zbl 0817.46073
[31] Watson, K. M.; Jauch, J. M., Phys. Rev., 75, 1249-1261 (1949) · Zbl 0036.27203
[32] Belgiorno, F.; Cacciatori, S. L.; Dalla Piazza, F.; Doronzo, M., Phys. Rev. D, 93, Article 065020 pp. (2016)
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