zbMATH — the first resource for mathematics

Fermionic one-particle states in curved spacetimes. (English) Zbl 1395.83034
Summary: We show that a notion of one-particle state and the corresponding vacuum state exists in general curved backgrounds for spin $$\frac{1}{2}$$ fields. A curved spacetime can be equipped with a coordinate system in which the metric component $$g_{--} = 0$$. We separate the component of the left-handed massless Dirac field which is annihilated by the null vector $$\partial_-$$ and compute the corresponding Feynman propagator. We find that the propagating modes are localized on two dimensional subspaces and the Feynman propagator is similar to the Feynman propagator of chiral fermions in two dimensional Minkowski spacetime. Therefore, it can be interpreted in terms of one-particle states and the corresponding vacuum state similarly to the second quantization in Minkowski spacetime.

MSC:
 83C47 Methods of quantum field theory in general relativity and gravitational theory 81T16 Nonperturbative methods of renormalization applied to problems in quantum field theory 81S40 Path integrals in quantum mechanics
Full Text:
References:
 [1] L. Parker, Quantized fields and particle creation in expanding universes. II, Phys. Rev.D 3 (1971) 346 [Erratum ibid.D 3 (1971) 2546] [INSPIRE]. [2] Bunch, TS; Parker, L., Feynman propagator in curved space-time: a momentum space representation, Phys. Rev., D 20, 2499, (1979) [3] M.M. Anber and E. Sabancilar, Chiral gravitational waves from chiral fermions, Phys. Rev.D 96 (2017) 023501 [arXiv:1607.03916] [INSPIRE]. [4] J. Cortez, B. Elizaga Navascués, M. Martín-Benito, G.A.M. 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 [5] A. Eichhorn and S. Lippoldt, Quantum gravity and Standard-Model-like fermions, Phys. Lett.B 767 (2017) 142 [arXiv:1611.05878] [INSPIRE]. [6] D. Singh and N. Mobed, Breakdown of Lorentz invariance for spin-1$$/$$2 particle motion in curved space-time with applications to muon decay, Phys. Rev.D 79 (2009) 024026 [arXiv:0807.0937] [INSPIRE]. · Zbl 1222.81223 [7] N.D. Birrell and P.C.W. Davies, Quantum fields in curved space, Cambridge University Press, Cambridge, U.K., (1982) [INSPIRE]. · Zbl 0476.53017 [8] S.A. Fulling, Aspects of quantum field theory in curved space-time, London Math. Soc. Student Texts17, Cambridge University Press, Cambridge, U.K., (1989), pg. 1. · Zbl 0677.53081 [9] M.E. Peskin and D.V. Schroeder, An introduction to quantum field theory, Addison-Wesley, U.S.A., (1995) [INSPIRE]. [10] R.M. Wald, Quantum field theory in curved space-time and black hole thermodynamics, University of Chicago Press, Chicago, U.S.A., (1994) [INSPIRE]. · Zbl 0842.53052 [11] S.A. Fulling, Nonuniqueness of canonical field quantization in Riemannian space-time, Phys. Rev.D 7 (1973) 2850 [INSPIRE]. [12] L. Susskind and J. Lindesay, An introduction to black holes, information and the string theory revolution: the holographic universe, World Scientific, U.S.A., (2005) [INSPIRE]. · Zbl 1069.83005 [13] L. Álvarez-Gaumé and E. Witten, Gravitational anomalies, Nucl. Phys.B 234 (1984) 269 [INSPIRE]. [14] W. Walter, Ordinary differential equations, Springer-Verlag, New York, U.S.A., (1998). · Zbl 0991.34001 [15] P.H. Ginsparg, Applied conformal field theory, in Les Houches Summer School in Theoretical Physics: fields, strings, critical phenomena, Les Houches, France, 28 June-5 August 1988, pg. 1 [hep-th/9108028] [INSPIRE]. [16] S.V. Ketov, Conformal field theory, World Scientific, Singapore, (1995). · Zbl 0875.00029 [17] F. Loran, Chiral fermions on 2D curved space-times, Int. J. Mod. Phys.A 32 (2017) 1750092 [arXiv:1608.06899] [INSPIRE]. · Zbl 1372.81137 [18] W.A. Bardeen and B. Zumino, Consistent and covariant anomalies in gauge and gravitational theories, Nucl. Phys.B 244 (1984) 421 [INSPIRE]. [19] L. Álvarez-Gaumé and P.H. Ginsparg, The structure of gauge and gravitational anomalies, Annals Phys.161 (1985) 423 [Erratum ibid.171 (1986) 233] [INSPIRE]. · Zbl 0579.58038 [20] H. Leutwyler, Gravitational anomalies: a soluble two-dimensional model, Phys. Lett.B 153 (1985) 65 [Erratum ibid.B 155 (1985) 469] [INSPIRE]. [21] S.W. Hawking and G.F.R. Ellis, The large scale structure of space-time, Cambridge University Press, Cambridge, U.K., (1973) [INSPIRE]. · Zbl 0265.53054
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.