Canonical Quantization of a Massive Scalar Field in the Schwarzschild Spacetime
Tóm tắt
A consistent procedure of canonical quantization of a massive real scalar field in the Schwarzschild spacetime is carried out. An expansion of the field operator in states that are convenient from a physical point of view is proposed, the fulfillment of all necessary commutation relations is verified, and the Hamiltonian of the system under consideration is obtained explicitly. Some physical consequences of the resulting theory are discussed.
Tài liệu tham khảo
D. G. Boulware, “Quantum field theory in Schwarzschild and Rindler spaces,” Phys. Rev. D 11, 1404 (1975).
L. D. Landau and E. M. Lifshits, The Classical Theory of Fields (Nauka, Moscow, 1988; Butterworth-Heinemann, 1980)
N. Deruelle and R. Ruffini, “Quantum and classical relativistic energy states in stationary geometries,” Phys. Lett. B 52, 437 (1974).
A. Zecca, “Properties of radial equation of scalar field in Schwarzschild space-time,” Nuovo Cimento B 124, 1251 (2009).
J. Barranco, A. Bernal, J. C. Degollado, A. Diez-Tejedor, M. Megevand, M. Alcubierre, D. Nunez, and O. Sarbach, “Are black holes a serious threat to scalar field dark matter models?,” Phys. Rev. D 84, 083008 (2011).
P. V. Elyutin and V. D. Krivchenkov, Quantum Mechanics (with Problems) (Nauka, Moscow, 1976) [in Russian].
P. A. Anempodistov, “Remarks on the thermofield double state in 4D black hole background,” Phys. Rev. D 103, 105008 (2021).
K. V. Bazarov, “Notes on peculiarities of quantum fields in space-times with horizons,” Class. Quant. Grav. 39, 217001 (2022).
V. Egorov, M. Smolyakov, and I. Volobuev, “Doubling of physical states in the quantum scalar field theory for a remote observer in the Schwarzschild space-time,” (2022). arXiv:2209.02067 [gr-qc].
L. D. Landau and E. M. Lifshits, Quantum Mechanics: Non-Relativistic Theory (Fizmatgiz, Moscow, 1963; Butterworth-Heinemann, 1981)
G. ’t Hooft, “Virtual black holes and space-time structure,” Found. Phys. 48, 1134 (2018);
G. ’t Hooft, “The quantum black hole as a theoretical lab, a pedagogical treatment of a new approach,” (2019). arXiv: 1902.10469 [gr-qc].
G. ’t Hooft, “Quantum clones inside black holes,” (2022). arXiv:2206.04608 [gr-qc].