Unruh Effect for Mixed Neutrinos and the KMS Condition
Abstract
1. Introduction
2. Nonextensive Tsallis Statistics in Unruh Effect for Mixed Neutrino Fields
3. Unruh Effect in Accelerated Proton Decay
3.1. Laboratory Frame
3.2. Comoving Frame
4. Discussion and Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
QFT | Quantum Field Theory |
QG | Quantum Gravity |
KMS | Kubo–Martin–Schwinger |
References
- Green, M.; Schwarz, J.; Witten, E. Superstring Theory; Cambridge University Press: Cambridge, UK, 1987. [Google Scholar]
- Maldacena, J.M.; Nunez, C. Supergravity description of field theories on curved manifolds and a no go theorem. Int. J. Mod. Phys. A 2001, 16, 822. [Google Scholar] [CrossRef]
- Conde, E.; Gaillard, J.; Nunez, C.; Piai, M.; Ramallo, A.V. A Tale of Two Cascades: Higgsing and Seiberg-Duality Cascades from type IIB String Theory. J. High Energy Phys. 2012, 02, 145. [Google Scholar] [CrossRef]
- Rovelli, C. Quantum Gravity; Cambridge University Press: Cambridge, UK, 2004. [Google Scholar]
- Connes, A. Noncommutative Geometry; Academic Press: Sand Diego, CA, USA, 1994. [Google Scholar]
- Lizzi, F.; Szabo, R.J. Noncommutative geometry and space-time gauge symmetries of string theory. Chaos Solitons Fractals 1999, 10, 445. [Google Scholar] [CrossRef]
- Aschieri, P.; Dimitrijevic, M.; Kulish, P.; Wess, J.; Lizzi, F. Noncommutative spacetimes: Symmetries in noncommutative geometry and field theory. Lect. Notes Phys. 2009, 774, 1. [Google Scholar]
- De Cesare, M.; Sakellariadou, M.; Vitale, P. Noncommutative gravity with self-dual variables. Class. Quant. Grav. 2018, 35, 215009. [Google Scholar] [CrossRef]
- Weinberg, S. Ultraviolet divergences in quantum theories of gravitation. In General Relativity: An Einstein Centenary Survey; Hawking, S.W., Israel, W., Eds.; Cambridge University Press: Cambridge, UK, 1979. [Google Scholar]
- Niedermaier, M.; Reuter, M. The Asymptotic Safety Scenario in Quantum Gravity. Living Rev. Rel. 2006, 9, 5. [Google Scholar] [CrossRef]
- Bonanno, A.; Platania, A. Asymptotically safe inflation from quadratic gravity. Phys. Lett. B 2015, 750, 638. [Google Scholar] [CrossRef]
- Platania, A.; Wetterich, C. Non-perturbative unitarity and fictitious ghosts in quantum gravity. Phys. Lett. B 2020, 811, 135911. [Google Scholar] [CrossRef]
- Donoghue, J.F. A Critique of the Asymptotic Safety Program. Front. Phys. 2020, 8, 56. [Google Scholar] [CrossRef]
- Kiefer, C. The semiclassical approximation to quantum gravity. In Canonical Gravity: From Classical to Quantum, Lecture Notes in Physics; Ehlers, J., Friedrich, H., Eds.; Springer: Berlin/Heidelberg, Germany, 1994. [Google Scholar]
- Zurek, W.H. Decoherence, einselection, and the quantum origins of the classical. Rev. Mod. Phys. 2003, 75, 715. [Google Scholar] [CrossRef]
- Mavromatos, N.E. CPT Violation and Decoherence in Quantum Gravity. J. Phys. Conf. Ser. 2009, 171, 012007. [Google Scholar] [CrossRef]
- Kiefer, C. Quantum Gravity; Oxford Science Publications: Oxford, UK, 2012. [Google Scholar]
- Ashtekar, A.; Corichi, A.; Kesavan, A. Emergence of classical behavior in the early universe. Phys. Rev. D 2020, 102, 023512. [Google Scholar] [CrossRef]
- Petruzziello, L.; Illuminati, F. Quantum gravitational decoherence from fluctuating minimal length and deformation parameter at the Planck scale. Nat. Commun. 2021, 12, 4449. [Google Scholar] [CrossRef] [PubMed]
- Jizba, P.; Lambiase, G.; Luciano, G.G.; Petruzziello, L. Decoherence limit of quantum systems obeying generalized uncertainty principle: New paradigm for Tsallis thermostatistics. arXiv 2022, arXiv:2201.07919. [Google Scholar]
- Bassi, A.; Lochan, K.; Satin, S.; Singh, T.P.; Ulbricht, H. Models of Wave-function Collapse, Underlying Theories, and Experimental Tests. Rev. Mod. Phys. 2013, 85, 471. [Google Scholar] [CrossRef]
- Singh, T.P. Possible role of gravity in collapse of the wave-function: A brief survey of some ideas. J. Phys. Conf. Ser. 2015, 626, 012009. [Google Scholar] [CrossRef]
- Amati, D.; Ciafaloni, M.; Veneziano, G. Superstring collisions at planckian energies. Phys. Lett. B 1987, 197, 81. [Google Scholar] [CrossRef]
- Maggiore, M. The algebraic structure of the generalized uncertainty principle. Phys. Lett. B 1993, 319, 83. [Google Scholar] [CrossRef]
- Kempf, A.; Mangano, G.; Mann, R.B. Hilbert space representation of the minimal length uncertainty relation. Phys. Rev. D 1995, 52, 1108. [Google Scholar] [CrossRef]
- Scardigli, F. Generalized Uncertainty Principle in Quantum Gravity from Micro-Black Hole Gedanken Experiment. Phys. Lett. B 1999, 452, 39. [Google Scholar] [CrossRef]
- Capozziello, S.; Lambiase, G.; Scarpetta, G. Generalized Uncertainty Principle from Quantum Geometry. Int. J. Theor. Phys. 2000, 39, 15. [Google Scholar] [CrossRef]
- Scardigli, F.; Casadio, R. Generalized uncertainty principle, extra dimensions and holography. Class. Quant. Grav. 2003, 20, 3915. [Google Scholar] [CrossRef]
- Das, S.; Vagenas, E.C. Universality of Quantum Gravity Corrections. Phys. Rev. Lett. 2008, 101, 221301. [Google Scholar] [CrossRef] [PubMed]
- Hossenfelder, S. Minimal Length Scale Scenarios for Quantum Gravity. Living Rev. Rel. 2013, 16, 2. [Google Scholar] [CrossRef] [PubMed]
- Scardigli, F.; Lambiase, G.; Vagenas, E. GUP parameter from quantum corrections to the Newtonian potential. Phys. Lett. B 2017, 767, 242. [Google Scholar] [CrossRef]
- Kanazawa, T.; Lambiase, G.; Vilasi, G.; Yoshioka, A. Noncommutative Schwarzschild geometry and generalized uncertainty principle. Eur. Phys. J. C 2019, 79, 2. [Google Scholar] [CrossRef]
- Bosso, P.; Das, S. Generalized Uncertainty Principle and Angular Momentum. Ann. Phys. 2017, 383, 416. [Google Scholar] [CrossRef]
- Petruzziello, L.; Wagner, F. Gravitationally induced uncertainty relations in curved backgrounds. Phys. Rev. D 2021, 103, 104061. [Google Scholar] [CrossRef]
- Bosso, P.; Luciano, G.G. Generalized uncertainty principle: From the harmonic oscillator to a QFT toy model. Eur. Phys. J. C 2021, 81, 982. [Google Scholar] [CrossRef]
- Luciano, G.G. Primordial big bang nucleosynthesis and generalized uncertainty principle. Eur. Phys. J. C 2021, 81, 1086. [Google Scholar] [CrossRef]
- Giné, J.; Luciano, G.G. Gravitational effects on the Heisenberg Uncertainty Principle: A geometric approach. Results Phys. 2022, 38, 105594. [Google Scholar] [CrossRef]
- Amelino-Camelia, G. Testable scenario for relativity with minimum length. Phys. Lett. B 2001, 510, 255. [Google Scholar] [CrossRef]
- Magueijo, J.; Smolin, L. Lorentz Invariance with an Invariant Energy Scale. Phys. Rev. Lett. 2002, 88, 190403. [Google Scholar] [CrossRef] [PubMed]
- Barcelo, C.; Liberati, S.; Visser, M. Analogue gravity. Living Rev. Rel. 2005, 8, 12. [Google Scholar] [CrossRef] [PubMed]
- Pikovski, I.; Vanner, M.R.; Aspelmeyer, M.; Kim, M.S.; Brukner, Č. Probing Planck-scale physics with quantum optics. Nat. Phys. 2012, 8, 393. [Google Scholar] [CrossRef]
- Marin, F.; Marino, F.; Bonaldi, M.; Cerdonio, M.; Conti, L.; Falferi, P. Gravitational bar detectors set limits to Planck-scale physics on macroscopic variables. Nat. Phys. 2013, 9, 71. [Google Scholar] [CrossRef]
- Iorio, A.; Lambiase, G. The Hawking-Unruh phenomenon on graphene. Phys. Lett. B 2012, 716, 334. [Google Scholar] [CrossRef]
- Weinfurtner, S.; Tedford, E.W.; Penrice, M.C.J.; Unruh, W.G.; Lawrence, G.A. Classical aspects of Hawking radiation verified in analogue gravity experiment. Lect. Notes Phys. 2013, 870, 167. [Google Scholar]
- Belenchia, A.; Benincasa, D.; Liberati, S.; Marin, F.; Marino, F.; Ortolan, A. Testing Quantum Gravity Induc. Nonlocality Via Optomech. Quantum Oscillators. Phys. Rev. Lett. 2016, 116, 161303. [Google Scholar] [CrossRef]
- Bose, S.; Mazumdar, A.; Morley, G.W.; Ulbricht, H.; Toros, M.; Paternostro, M.; Geraci, A.; Barker, P.; Kim, M.S.; Milburn, G. Spin Entanglement Witness Quantum Gravity. Phys. Rev. Lett. 2017, 119, 240401. [Google Scholar] [CrossRef]
- Marletto, C.; Vedral, V. Gravitationally-induced entanglement between two massive particles is sufficient evidence of quantum effects in gravity. Phys. Rev. Lett. 2017, 119, 240402. [Google Scholar] [CrossRef] [PubMed]
- Carney, D.; Stamp, P.C.E.; Taylor, J.M. Tabletop experiments for quantum gravity: A user’s manual. Class. Quant. Grav. 2019, 36, 034001. [Google Scholar] [CrossRef]
- Hu, J.; Feng, L.; Zhang, Z.; Chin, C. Quantum simulation of Unruh radiation. Nat. Phys. 2019, 15, 785. [Google Scholar] [CrossRef]
- Kumar, S.P.; Plenio, M.B. On Quantum Gravity Tests with Composite Particles. Nat. Commun. 2020, 11, 3900. [Google Scholar] [CrossRef] [PubMed]
- Šoda, B.; Sudhir, V.; Kempf, A. Acceleration-induced effects in stimulated light-matter interactions. Phys. Rev. Lett. 2022, 128, 163603. [Google Scholar] [CrossRef] [PubMed]
- Singh, A. Probing the Quantum Nature of Gravity in the Microgravity of Space. arXiv 2021, arXiv:2111.01711. [Google Scholar]
- Addazi, A.; Alvarez-Muniz, J.; Batista, R.A.; Amelino-Camelia, G.; Antonelli, V.; Arzano, M.; Asorey, M.; Atteia, J.L.; Bahamonde, S.; Bajardi, F.; et al. Quantum gravity phenomenology at the dawn of the multi-messenger era—A review. Prog. Part. Nucl. Phys. 2022, 103948. [Google Scholar] [CrossRef]
- ’t Hooft, G. Quantum gravity as a dissipative deterministic system. Class. Quant. Grav. 1999, 16, 3263. [Google Scholar] [CrossRef]
- ’t Hooft, G. The Cellular Automaton Interpretation of Quantum Mechanics; Springer: Berlin/Heidelberg, Germany, 2016. [Google Scholar]
- Elze, H.T. Are Quantum Spins but Small Perturbations of Ontological Ising Spins? Found. Phys. 2020, 50, 1875. [Google Scholar] [CrossRef]
- Blasone, M.; Jizba, P.; Vitiello, G. Dissipation and quantization. Phys. Lett. A 2001, 287, 205. [Google Scholar] [CrossRef]
- Birrell, N.D.; Davies, P.C.W. Quantum Fields in Curved Space; Cambridge University Press: Cambridge, UK, 1982. [Google Scholar]
- Buchbinder, I.L.; Odintsov, S.D.; Shapiro, I.L. Effective Action in Quantum Gravity; IOP: London, UK, 1992. [Google Scholar]
- Hawking, S.W. Particle Creation by Black Holes. Commun. Math. Phys. 1975, 43, 199. [Google Scholar] [CrossRef]
- Unruh, W.G. Notes on black-hole evaporation. Phys. Rev. D 1976, 14, 870. [Google Scholar] [CrossRef]
- ’t Hooft, G. On the Quantum Structure of a Black Hole. Nucl. Phys. B 1985, 256, 727. [Google Scholar] [CrossRef]
- Banados, M.; Teitelboim, C.; Zanelli, J. The Black hole in three-dimensional space-time. Phys. Rev. Lett. 1992, 69, 1849. [Google Scholar] [CrossRef] [PubMed]
- Carlip, S. The (2+1)-Dimensional black hole. Class. Quant. Grav. 1995, 12, 2853. [Google Scholar] [CrossRef]
- Loll, R. Discrete approaches to quantum gravity in four-dimensions. Living Rev. Rel. 1998, 1, 13. [Google Scholar] [CrossRef] [PubMed]
- Mathur, S.D. The Quantum structure of black holes. Class. Quant. Grav. 2006, 23, R115. [Google Scholar] [CrossRef]
- Mannheim, P.D. Intrinsically Quantum-Mechanical Gravity and the Cosmological Constant Problem. Mod. Phys. Lett. A 2011, 26, 2375. [Google Scholar] [CrossRef]
- Pourhassan, B.; Faizal, M.; Capozziello, S. Testing Quantum Gravity through Dumb Holes. Ann. Phys. 2017, 377, 108. [Google Scholar] [CrossRef]
- Bambi, C.; Modesto, L.; Porey, S.; Rachwał, L. Formation and evaporation of an electrically charged black hole in conformal gravity. Eur. Phys. J. C 2018, 78, 116. [Google Scholar] [CrossRef]
- Bellucci, S.; Bonanno, A.; Gabriele Gionti, S.J.; Scardigli, F. Black Holes, Gravitational Waves and Space Time Singularities. Found. Phys. 2018, 48, 1131. [Google Scholar] [CrossRef]
- Buoninfante, L.; Cornell, A.S.; Harmsen, G.; Koshelev, A.S.; Lambiase, G.; Marto, J.; Mazumdar, A. Towards nonsingular rotating compact object in ghost-free infinite derivative gravity. Phys. Rev. D 2018, 98, 084041. [Google Scholar] [CrossRef]
- Almheiri, A.; Engelhardt, N.; Marolf, D.; Maxfield, H. The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole. J. High Energy Phys. 2019, 12, 063. [Google Scholar] [CrossRef]
- Cooper, S.; Rozali, M.; Swingle, B.; Van Raamsdonk, M.; Waddell, C.; Wakeham, D. Black hole microstate cosmology. J. High Energy Phys. 2019, 7, 065. [Google Scholar] [CrossRef]
- Buoninfante, L.; Luciano, G.G.; Petruzziello, L. Generalized Uncertainty Principle and Corpuscular Gravity. Eur. Phys. J. C 2019, 79, 663. [Google Scholar] [CrossRef]
- Maldacena, J. Black holes and quantum information. Nat. Rev. Phys. 2020, 2, 123. [Google Scholar] [CrossRef]
- Acquaviva, G.; Iorio, A.; Smaldone, L. Bekenstein bound from the Pauli principle. Phys. Rev. D 2020, 102, 106002. [Google Scholar] [CrossRef]
- Salucci, P.; Esposito, G.; Lambiase, G.; Battista, E.; Yunge, A. Einstein, Planck and Vera Rubin: Relevant encounters between the Cosmological and the Quantum Worlds. Front. Phys. 2021, 8, 603190. [Google Scholar] [CrossRef]
- Buoninfante, L.; Di Filippo, F.; Mukohyama, S. On the assumptions leading to the information loss paradox. J. High Energy Phys. 2021, 10, 81. [Google Scholar] [CrossRef]
- Liu, H.; Vardhan, S. Entanglement entropies of equilibrated pure states in quantum many-body systems and gravity. PRX Quantum 2021, 2, 010344. [Google Scholar] [CrossRef]
- Bittencourt, V.A.S.V.; Blasone, M.; Illuminati, F.; Lambiase, G.; Luciano, G.G.; Petruzziello, L. Quantum nonlocality in extended theories of gravity. Phys. Rev. D 2021, 103, 044051. [Google Scholar] [CrossRef]
- Alonso-Serrano, A.; Dabrowski, M.P.; Gohar, H. Nonextensive Black Hole Entropy and Quantum Gravity Effects at the Last Stages of Evaporation. Phys. Rev. D 2021, 103, 026021. [Google Scholar] [CrossRef]
- Casadio, R. Quantum black holes and resolution of the singularity. arXiv 2021, arXiv:2103.00183. [Google Scholar] [CrossRef]
- Gaddam, N.; Groenenboom, N.; Hooft, G.T. Quantum gravity on the black hole horizon. J. High Energy Phys. 2022, 1, 023. [Google Scholar] [CrossRef]
- Buoninfante, L.; Luciano, G.G.; Petruzziello, L.; Scardigli, F. Bekenstein bound and uncertainty relations. Phys. Lett. B 2022, 824, 136818. [Google Scholar] [CrossRef]
- Singleton, D.; Wilburn, S. Hawking radiation, Unruh radiation and the equivalence principle. Phys. Rev. Lett. 2011, 107, 081102. [Google Scholar] [CrossRef]
- Crispino, L.C.B.; Higuchi, A.; Matsas, G.E.A. Comment on Hawking Radiation, Unruh Radiation, and the Equivalence Principle. Phys. Rev. Lett. 2021, 108, 049001. [Google Scholar] [CrossRef]
- Giacomini, F.; Castro-Ruiz, E.; Brukner, Č. Quantum mechanics and the covariance of physical laws in quantum reference frames. Nat. Commun. 2019, 10, 494. [Google Scholar] [CrossRef]
- From the talk given by W., G. Unruh at TGTG2021 Conference (Link to the Youtube Page of the Conference. Available online: https://www.youtube.com/watch?v=4tqsrJJVm74&t=16289s (accessed on 23 May 2022).
- Vanzella, D.A.T.; Matsas, G.E.A. Decay of accelerated protons and the existence of the Fulling-Davies-Unruh effect. Phys. Rev. Lett. 2001, 87, 151301. [Google Scholar] [CrossRef]
- Muller, R. Decay of accelerated particles. Phys. Rev. D 1997, 56, 953. [Google Scholar] [CrossRef]
- Suzuki, H.; Yamada, K. Analytic evaluation of the decay rate for accelerated proton. Phys. Rev. D 2003, 67, 065002. [Google Scholar] [CrossRef]
- Ahluwalia, D.V.; Labun, L.; Torrieri, G. Neutrino mixing in accelerated proton decays. Eur. Phys. J. A 2016, 52, 189. [Google Scholar] [CrossRef]
- Blasone, M.; Lambiase, G.; Luciano, G.G.; Petruzziello, L. Role of neutrino mixing in accelerated proton decay. Phys. Rev. D 2018, 97, 105008. [Google Scholar] [CrossRef]
- Cozzella, G.; Fulling, S.A.; Landulfo, A.G.S.; Matsas, G.E.A.; Vanzella, D.A.T. Unruh effect for mixing neutrinos. Phys. Rev. D 2018, 97, 105022. [Google Scholar] [CrossRef]
- Blasone, M.; Lambiase, G.; Luciano, G.G.; Petruzziello, L. Neutrino oscillations in Unruh radiation. Phys. Lett. A 2020, 800, 135083. [Google Scholar] [CrossRef]
- Blasone, M.; Lambiase, G.; Luciano, G.G.; Petruzziello, L. On the β-decay of the accelerated proton and neutrino oscillations: A three-flavor description with CP violation. Eur. Phys. J. C 2020, 80, 130. [Google Scholar] [CrossRef]
- Luciano, G.G. On the Very Nature of Neutrinos: The β-Decay as a Test Bench. Available online: https://pos.sissa.it/376/033/pdf (accessed on 23 May 2022).
- Blasone, M.; Vitiello, G. Quantum field theory of fermion mixing. Ann. Phys. 1995, 244, 283. [Google Scholar] [CrossRef]
- Blasone, M.; Lambiase, G.; Luciano, G.G. Nonthermal signature of the Unruh effect in field mixing. Phys. Rev. D 2017, 96, 025023. [Google Scholar] [CrossRef]
- Luciano, G.G.; Blasone, M. Nonextensive Tsallis statistics in Unruh effect for Dirac neutrinos. Eur. Phys. J. C 2021, 81, 995. [Google Scholar] [CrossRef]
- Luciano, G.G.; Blasone, M. q-generalized Tsallis thermostatistics in Unruh effect for mixed fields. Phys. Rev. D 2021, 104, 045004. [Google Scholar] [CrossRef]
- Tsallis, C. Possible generalization of Boltzmann-Gibbs statistics. J. Stat. Phys. 1988, 52, 479. [Google Scholar] [CrossRef]
- Rahaman, M.; Bhattacharyya, T.; Alam, J. Phenomenological Tsallis distribution from thermal field theory. Int. J. Mod. Phys. A 2021, 36, 2150154. [Google Scholar] [CrossRef]
- Biró, T.S.; Shen, K.M.; Zhang, B.W. Non-extensive quantum statistics with particle–hole symmetry. Phys. A 2015, 428, 410. [Google Scholar] [CrossRef][Green Version]
- Bilenky, S.M.; Pontecorvo, B. Lepton mixing and neutrino oscillations. Phys. Rep. 1978, 41, 225. [Google Scholar] [CrossRef]
- Blasone, M.; Lambiase, G.; Luciano, G.G. Non-thermal Unruh radiation for flavour neutrinos. J. Phys. Conf. Ser. 2018, 956, 012021. [Google Scholar] [CrossRef]
- Plastino, A.R.; Plastino, A. Stellar polytropes and Tsallis’ entropy. Phys. Lett. A 1993, 174, 384. [Google Scholar] [CrossRef]
- Hamity, V.H.; Barraco, D.E. Generalized Nonextensive Thermodynamics Applied to the Cosmic Background Radiation in a Robertson-Walker Universe. Phys. Rev. Lett. 1996, 76, 4664. [Google Scholar] [CrossRef]
- Tsallis, C.; Cirto, L.J.L. Black hole thermodynamical entropy. Eur. Phys. J. C 2013, 73, 2487. [Google Scholar] [CrossRef]
- Kaniadakis, G.; Lavagno, A.; Quarati, P. Generalized statistics and solar neutrinos. Phys. Lett. B 1996, 369, 308. [Google Scholar] [CrossRef]
- Saridakis, E.N.; Bamba, K.; Myrzakulov, R.; Anagnostopoulos, F.K. Holographic dark energy through Tsallis entropy. JCAP 2018, 12, 12. [Google Scholar] [CrossRef]
- Luciano, G.G. Tsallis statistics and generalized uncertainty principle. Eur. Phys. J. C 2021, 81, 672. [Google Scholar] [CrossRef]
- Cabo, A.; Cabo Bizet, N.G. About the neutrino oscillation-like effects in general physical systems: On interference between distinguishable particles. Eur. Phys. J. Plus 2021, 136, 1042. [Google Scholar] [CrossRef]
- Blasone, M.; Illuminati, F.; Luciano, G.G.; Petruzziello, L. Flavor vacuum entanglement in boson mixing. Phys. Rev. A 2021, 103, 032434. [Google Scholar] [CrossRef]
- Abe, S.; Martínez, S.; Pennini, F.; Plastino, A. Nonextensive thermodynamic relations. Phys. Lett. A 2001, 281, 126. [Google Scholar] [CrossRef]
- Büyükkiliç, F.; Demirhan, D. A fractal approach to entropy and distribution functions. Phys. Lett. A 1993, 181, 24. [Google Scholar] [CrossRef]
- Nojiri, S.; Odintsov, S.D.; Saridakis, E.N. Modified cosmology from extended entropy with varying exponent. Eur. Phys. J. C 2019, 79, 242. [Google Scholar] [CrossRef]
- Fulling, S.A. Nonuniqueness of Canonical Field Quantization in Riemannian Space-Time. Phys. Rev. D 1973, 7, 2850. [Google Scholar] [CrossRef]
- Davies, P.C.W. Scalar production in Schwarzschild and Rindler metric. J. Phys. A 1975, 8, 609. [Google Scholar] [CrossRef]
- Blasone, M.; Henning, P.A.; Vitiello, G. The Exact formula for neutrino oscillations. Phys. Lett. B 1999, 451, 140. [Google Scholar] [CrossRef]
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |
© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Blasone, M.; Lambiase, G.; Luciano, G.G.; Petruzziello, L. Unruh Effect for Mixed Neutrinos and the KMS Condition. Universe 2022, 8, 306. https://doi.org/10.3390/universe8060306
Blasone M, Lambiase G, Luciano GG, Petruzziello L. Unruh Effect for Mixed Neutrinos and the KMS Condition. Universe. 2022; 8(6):306. https://doi.org/10.3390/universe8060306
Chicago/Turabian StyleBlasone, Massimo, Gaetano Lambiase, Giuseppe Gaetano Luciano, and Luciano Petruzziello. 2022. "Unruh Effect for Mixed Neutrinos and the KMS Condition" Universe 8, no. 6: 306. https://doi.org/10.3390/universe8060306
APA StyleBlasone, M., Lambiase, G., Luciano, G. G., & Petruzziello, L. (2022). Unruh Effect for Mixed Neutrinos and the KMS Condition. Universe, 8(6), 306. https://doi.org/10.3390/universe8060306