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Unitary quantization of a scalar charged field and Schwinger effect. (English) Zbl 1436.83029
Summary: Quantum field theory in curved spacetimes suffers in general from an infinite ambiguity in the choice of Fock representation and associated vacuum. In cosmological backgrounds, the requirement of a unitary implementation of the field dynamics in the physical Hilbert space of the theory is a good criterion to ameliorate such ambiguity. Indeed, this criterion, together with a unitary implementation of the symmetries of the equations of motion, leads to an equivalence class of unitarily equivalent quantizations that, even though it is still formed by an infinite number of Fock representations, is unique. In this work, we apply the procedure developed for fields in cosmological settings to analyze the quantization of a scalar field in the presence of an external electromagnetic classical field in a flat background. We find a natural Fock representation that admits a unitary implementation of the quantum field dynamics. It automatically allows to define a particle number density at all times in the evolution with the correct asymptotic behavior, when the electric field vanishes. Moreover we show the unitary equivalence of all the quantizations that fulfill our criteria, so that they form a unique equivalence class. Although we perform the field quantization in a specific gauge, we also show the equivalence between the procedures taken in different gauges.
83C47 Methods of quantum field theory in general relativity and gravitational theory
81T16 Nonperturbative methods of renormalization applied to problems in quantum field theory
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[1] F. Sauter, Über das Verhalten eines Elektrons im homogenen elektrischen Feld nach der relativistischen Theorie Diracs, Z. Phys.69 (1931) 742 [INSPIRE]. · JFM 57.1218.06
[2] W. Heisenberg and H. Euler, Consequences of Dirac’s theory of positrons, Z. Phys.98 (1936) 714 [physics/0605038] [INSPIRE]. · JFM 62.1002.03
[3] V. Weisskopf, The electrodynamics of the vacuum based on the quantum theory of the electron, Kong. Dan. Vid. Sel. Mat. Fys. Med.14N6 (1936) 1.
[4] J.S. Schwinger, On gauge invariance and vacuum polarization, Phys. Rev.82 (1951) 664 [INSPIRE]. · Zbl 0043.42201
[5] G.V. Dunne, Heisenberg-euler effective lagrangians: Basics and extensions, in From Fields to Strings: Circumnavigating Theoretical Physics (2005), pp. 445-522, [DOI]. · Zbl 1081.81116
[6] X.-L. Sheng, R.-H. Fang, Q. Wang and D.H. Rischke, Wigner function and pair production in parallel electric and magnetic fields, Phys. Rev.D 99 (2019) 056004 [arXiv:1812.01146] [INSPIRE].
[7] F. Hebenstreit, A. Ilderton, M. Marklund and J. Zamanian, Strong field effects in laser pulses: the Wigner formalism, Phys. Rev.D 83 (2011) 065007 [arXiv:1011.1923] [INSPIRE].
[8] Y. Kluger, E. Mottola and J.M. Eisenberg, The Quantum Vlasov equation and its Markov limit, Phys. Rev.D 58 (1998) 125015 [hep-ph/9803372] [INSPIRE].
[9] A.M. Fedotov, E.G. Gelfer, K.Yu. Korolev and S.A. Smolyansky, On the kinetic equation approach to pair production by time-dependent electric field, Phys. Rev.D 83 (2011) 025011 [arXiv:1008.2098] [INSPIRE].
[10] A. Huet, S.P. Kim and C. Schubert, Vlasov equation for Schwinger pair production in a time-dependent electric field, Phys. Rev.D 90 (2014) 125033 [arXiv:1411.3074] [INSPIRE].
[11] S.P. Gavrilov and D.M. Gitman, Vacuum instability in external fields, Phys. Rev.D 53 (1996) 7162 [hep-th/9603152] [INSPIRE].
[12] K. Rajeev, S. Chakraborty and T. Padmanabhan, Generalized Schwinger effect and particle production in an expanding universe, Phys. Rev.D 100 (2019) 045019 [arXiv:1904.03207] [INSPIRE].
[13] F. Gelis and N. Tanji, Schwinger mechanism revisited, Prog. Part. Nucl. Phys.87 (2016) 1 [arXiv:1510.05451] [INSPIRE].
[14] V. Yakimenko et al., Prospect of Studying Nonperturbative QED with Beam-Beam Collisions, Phys. Rev. Lett.122 (2019) 190404 [arXiv:1807.09271] [INSPIRE].
[15] G. Breit and J.A. Wheeler, Collision of two light quanta, Phys. Rev.46 (1934) 1087 [INSPIRE]. · JFM 60.0792.01
[16] R. Alkofer, M.B. Hecht, C.D. Roberts, S.M. Schmidt and D.V. Vinnik, Pair creation and an x-ray free electron laser, Phys. Rev. Lett.87 (2001) 193902 [nucl-th/0108046] [INSPIRE].
[17] R. Schutzhold, H. Gies and G. Dunne, Dynamically assisted Schwinger mechanism, Phys. Rev. Lett.101 (2008) 130404 [arXiv:0807.0754] [INSPIRE]. · Zbl 1228.81274
[18] J. Magnusson et al., Multiple-colliding laser pulses as a basis for studying high-field high-energy physics, Phys. Rev.A 100 (2019) 063404 [arXiv:1906.05235] [INSPIRE].
[19] S.W. Hawking, Black hole explosions, Nature248 (1974) 30 [INSPIRE]. · Zbl 1370.83053
[20] L. Parker, Particle creation in expanding universes, Phys. Rev. Lett.21 (1968) 562 [INSPIRE]. · Zbl 0186.58603
[21] G.W. Gibbons and S.W. Hawking, Cosmological Event Horizons, Thermodynamics and Particle Creation, Phys. Rev.D 15 (1977) 2738 [INSPIRE].
[22] R.M. Wald, Existence of the s-matrix in quantum field theory in curved space-time, Annals Phys.118 (1979) 490 [INSPIRE].
[23] R. Dabrowski and G.V. Dunne, Time dependence of adiabatic particle number, Phys. Rev.D 94 (2016) 065005 [arXiv:1606.00902] [INSPIRE].
[24] F. Hebenstreit, R. Alkofer and H. Gies, Pair Production Beyond the Schwinger Formula in Time-Dependent Electric Fields, Phys. Rev.D 78 (2008) 061701 [arXiv:0807.2785] [INSPIRE].
[25] S.P. Kim, Schwinger Pair Production in Solitonic Gauge Fields, arXiv:1110.4684 [INSPIRE].
[26] R. Wald, Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics, Chicago Lectures in Physics, University of Chicago Press, (1994). · Zbl 0842.53052
[27] J. Cortez, G.A. Mena Marugán and J.M. Velhinho, Quantum unitary dynamics in cosmological spacetimes, Annals Phys.363 (2015) 36 [arXiv:1509.06171] [INSPIRE]. · Zbl 1360.83087
[28] J. Cortez, G.A. Mena Marugán and J.M. Velhinho Quantum linear scalar fields with time dependent potentials: Overview and applications to cosmology, Mathematics8 (2020) 115.
[29] L. Castelló Gomar, J. Cortez, D. Martín-de Blas, G.A. Mena Marugán and J.M. Velhinho, Uniqueness of the Fock quantization of scalar fields in spatially flat cosmological spacetimes, JCAP11 (2012) 001 [arXiv:1211.5176] [INSPIRE].
[30] J. Cortez, L. Fonseca, D. Martín-de Blas and G.A. Mena Marugán, Uniqueness of the Fock quantization of scalar fields under mode preserving canonical transformations varying in time, Phys. Rev.D 87 (2013) 044013 [arXiv:1212.3947] [INSPIRE].
[31] J. Cortez, B. Elizaga Navascués, M. Martín-Benito, G.A. Mena Marugán and J.M. Velhinho, Unique Fock quantization of a massive fermion field in a cosmological scenario, Phys. Rev.D 93 (2016) 084053 [arXiv:1603.00037] [INSPIRE]. · Zbl 1364.81194
[32] J. Cortez, B. Elizaga Navascués, M. Martín-Benito, G.A. Mena Marugán and J.M. Velhinho, Dirac fields in flat FLRW cosmology: Uniqueness of the Fock quantization, Annals Phys.376 (2017) 76 [arXiv:1609.07904] [INSPIRE]. · Zbl 1364.81194
[33] J. Cortez, B. Elizaga Navascués, M. Martín-Benito, G.A. Mena Marugán, J. Olmedo and J.M. Velhinho, Uniqueness of the Fock quantization of scalar fields in a Bianchi I cosmology with unitary dynamics, Phys. Rev.D 94 (2016) 105019 [arXiv:1610.06797] [INSPIRE]. · Zbl 1364.81194
[34] S.N.M. Ruijsenaars, Charged Particles in External Fields. 1. Classical Theory, J. Math. Phys.18 (1977) 720 [INSPIRE].
[35] B. Thaller, The Dirac equation, Texts and monographs in physics. Springer-Verlag, (1992).
[36] P. Beltrán-Palau, A. Ferreiro, J. Navarro-Salas and S. Pla, Breaking of adiabatic invariance in the creation of particles by electromagnetic fields, Phys. Rev.D 100 (2019) 085014 [arXiv:1905.07215] [INSPIRE].
[37] J. Lee and R.M. Wald, Local symmetries and constraints, J. Math. Phys.31 (1990) 725 [INSPIRE]. · Zbl 0704.70013
[38] D. Shale, Linear symmetries of free boson fields, Trans. Am. Math. Soc.103 (1962) 149. · Zbl 0171.46901
[39] R. Honegger and A. Rieckers, Squeezing Bogoliubov transformations on the infinite mode CCR-algebra, J. Math. Phys.37 (1996) 4292. · Zbl 0904.46059
[40] S.N.M. Ruijsenaars, On Bogolyubov Transformations. 2. The General Case, Annals Phys.116 (1978) 105 [INSPIRE].
[41] M. Abramowitz and I. Stegun, Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables, Applied mathematics series, Dover Publications, (1965).
[42] N. Tanji, Dynamical view of pair creation in uniform electric and magnetic fields, Annals Phys.324 (2009) 1691 [arXiv:0810.4429] [INSPIRE]. · Zbl 1168.81026
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