Jump to content

Quantum field theory in curved spacetime: Difference between revisions

From Wikipedia, the free encyclopedia
Browse history interactively
← Previous editNext edit →
Content deleted Content added
VisualWikitext
No edit summary
Tag: Reverted
Tag: Reverted
Line 24: Line 24:


==Relation to quantum gravity==
==Relation to quantum gravity==
Quantum field theory in curved space-time geometry by construction is a systematic tool to study quantum phenomena in a curved spacetime geometry. It neglects the quantum fluctuations of the spacetime geometry from outset. It, therefore, can not be extended to a regime where quantum fluctuations of the space-time geometry is as important as the quantum fluctuations of other fields. So it should not be understood as a substitute or an approximation to [[quantum gravity]]. Its predictions such as [[Hawking radiation]] serve as [[smoking gun]]s in order to discover the theory of [[quantum gravity]].
Quantum field theory in curved space-time geometry by construction neglects the quantum fluctuations of the spacetime geometry from outset. It, therefore, can not be extended to a regime where quantum fluctuations of the space-time geometry is as important as the quantum fluctuations of other fields. So it should not be understood as a substitute or an approximation to [[quantum gravity]]. Its predictions such as [[Hawking radiation]] serve as [[smoking gun]]s in order to discover the theory of [[quantum gravity]].


==See also==
==See also==

Revision as of 23:20, 14 January 2022

Quantum field theory
Feynman diagram
History
Background
Symmetries
Tools
Equations
Standard Model
Incomplete theories
Scientists

.

In theoretical physics, quantum field theory in curved spacetime (QFTCS) is an extension of quantum field theory from Minkowski spacetime to a general curved spacetime. It provides a systematic mathematical framework to investigate how a fixed background space-time geometry affects quantum mechanical phenomena. It circumvents the non-renormalizability of general relativity by neglecting quantum fluctuations of the space-time geometry while keeping into account the quantum fluctuations of all other fields present in the theory. It is best known for the prediction of Hawking radiation near the event horizon of black holes.

Overview

Interesting new phenomena occur; owing to the equivalence principle[clarification needed] the quantization procedure locally resembles that of normal coordinates where the affine connection at the origin is set to zero and a nonzero Riemann tensor in general once the proper (covariant) formalism is chosen; however, even in flat spacetime quantum field theory, the number of particles is not well-defined locally[clarification needed]. For non-zero cosmological constants, on curved spacetimes quantum fields lose their interpretation as asymptotic particles.[1] Only in certain situations, such as in asymptotically flat spacetimes (zero cosmological curvature), can the notion of incoming and outgoing particle be recovered, thus enabling one to define an S-matrix. Even then, as in flat spacetime, the asymptotic particle interpretation depends on the observer (i.e., different observers may measure different numbers of asymptotic particles on a given spacetime).

Another observation is that unless the background metric tensor has a global timelike Killing vector, there is no way to define a vacuum or ground state canonically. The concept of a vacuum is not invariant under diffeomorphisms. This is because a mode decomposition of a field into positive and negative frequency modes is not invariant under diffeomorphisms. If t′(t) is a diffeomorphism, in general, the Fourier transform of exp[ikt′(t)] will contain negative frequencies even if k > 0. Creation operators correspond to positive frequencies, while annihilation operators correspond to negative frequencies. This is why a state which looks like a vacuum to one observer cannot look like a vacuum state to another observer; it could even appear as a heat bath under suitable hypotheses.

Since the end of the 1980s, the local quantum field theory approach due to Rudolf Haag and Daniel Kastler has been implemented in order to include an algebraic version of quantum field theory in curved spacetime. Indeed, the viewpoint of local quantum physics is suitable to generalize the renormalization procedure to the theory of quantum fields developed on curved backgrounds. Several rigorous results concerning QFT in the presence of a black hole have been obtained. In particular the algebraic approach allows one to deal with the problems mentioned above arising from the absence of a preferred reference vacuum state, the absence of a natural notion of particle and the appearance of unitarily inequivalent representations of the algebra of observables.[2][3]

Applications

Using perturbation theory in quantum field theory in curved space-time geometry is known as the semiclassical approach to quantum gravity. This approach studies the interaction of quantum fields in a fixed classical spacetime and among other thing predicts the creation of particles by time-varying spacetimes[4] and Hawking radiation.[5] The latter can be understood as a manifestation of the Unruh effect where an accelerating observer observes black body radiation.[6] Other prediction of quantum fields in curved spaces include,[7] for example, the radiation emitted by a particle moving along a geodesic[8][9][10][11] and the interaction of Hawking radiation with particles outside black holes.[12][13][14][15]

This formalism is also used to predict the primordial density perturbation spectrum arising in different models of cosmic inflation. These predictions are calculated using the Bunch–Davies vacuum or modifications thereto.[16]

Relation to quantum gravity

Quantum field theory in curved space-time geometry by construction neglects the quantum fluctuations of the spacetime geometry from outset. It, therefore, can not be extended to a regime where quantum fluctuations of the space-time geometry is as important as the quantum fluctuations of other fields. So it should not be understood as a substitute or an approximation to quantum gravity. Its predictions such as Hawking radiation serve as smoking guns in order to discover the theory of quantum gravity.

See also

References

  1. ^ Wald, R. M. (1995). Quantum field theory in curved space-time and black hole thermodynamics. Chicago U. ISBN 0-226-87025-1.
  2. ^ Fewster, C. J. (2008). "Lectures on quantum field theory in curved spacetime (Lecture Note 39/2008 Max Planck Institute for Mathematics in the Natural Sciences (2008))" (PDF).
  3. ^ Khavkine, Igor; Moretti, Valter (2015), Brunetti, Romeo; Dappiaggi, Claudio; Fredenhagen, Klaus; Yngvason, Jakob (eds.), "Algebraic QFT in Curved Spacetime and Quasifree Hadamard States: An Introduction", Advances in Algebraic Quantum Field Theory, Cham: Springer International Publishing, pp. 191–251, arXiv:1412.5945, Bibcode:2014arXiv1412.5945K, doi:10.1007/978-3-319-21353-8_5, ISBN 978-3-319-21352-1, retrieved 2022-01-14
  4. ^ Parker, L. (1968-08-19). "Particle Creation in Expanding Universes". Physical Review Letters. 21 (8): 562–564. doi:10.1103/PhysRevLett.21.562.
  5. ^ Hawking, S. W. (1993-05-01), "Particle Creation by Black Holes", Euclidean Quantum Gravity, WORLD SCIENTIFIC, pp. 167–188, doi:10.1142/9789814539395_0011, ISBN 978-981-02-0515-7, retrieved 2021-08-15
  6. ^ Crispino, Luís C. B.; Higuchi, Atsushi; Matsas, George E. A. (2008-07-01). "The Unruh effect and its applications". Reviews of Modern Physics. 80 (3): 787–838. doi:10.1103/RevModPhys.80.787. hdl:11449/24446.
  7. ^ Birrell, N. D. (1982). Quantum fields in curved space. P. C. W. Davies. Cambridge [Cambridgeshire]: Cambridge University Press. ISBN 0-521-23385-2. OCLC 7462032.
  8. ^ Crispino, L. C. B.; Higuchi, A.; Matsas, G. E. A. (November 1999). "Scalar radiation emitted from a source rotating around a black hole". Classical and Quantum Gravity. 17 (1): 19–32. arXiv:gr-qc/9901006. doi:10.1088/0264-9381/17/1/303. ISSN 0264-9381.
  9. ^ Crispino, L. C. B.; Higuchi, A.; Matsas, G. E. A. (September 2016). "Corrigendum: Scalar radiation emitted from a source rotating around a black hole (2000 Class. Quantum Grav. 17 19)". Classical and Quantum Gravity. 33 (20): 209502. doi:10.1088/0264-9381/33/20/209502. hdl:11449/162073. ISSN 0264-9381.
  10. ^ Oliveira, Leandro A.; Crispino, Luís C. B.; Higuchi, Atsushi (2018-02-16). "Scalar radiation from a radially infalling source into a Schwarzschild black hole in the framework of quantum field theory". The European Physical Journal C. 78 (2): 133. doi:10.1140/epjc/s10052-018-5604-8. ISSN 1434-6052.
  11. ^ Brito, João P. B.; Bernar, Rafael P.; Crispino, Luís C. B. (2020-06-11). "Synchrotron geodesic radiation in Schwarzschild--de Sitter spacetime". Physical Review D. 101 (12): 124019. arXiv:2006.08887. doi:10.1103/PhysRevD.101.124019.
  12. ^ Higuchi, Atsushi; Matsas, George E. A.; Sudarsky, Daniel (1998-10-22). "Interaction of Hawking radiation with static sources outside a Schwarzschild black hole". Physical Review D. 58 (10): 104021. arXiv:gr-qc/9806093. doi:10.1103/PhysRevD.58.104021. hdl:11449/65552.
  13. ^ Crispino, Luís C. B.; Higuchi, Atsushi; Matsas, George E. A. (1998-09-22). "Interaction of Hawking radiation and a static electric charge". Physical Review D. 58 (8): 084027. arXiv:gr-qc/9804066. doi:10.1103/PhysRevD.58.084027. hdl:11449/65534.
  14. ^ Castiñeiras, J.; Costa e Silva, I. P.; Matsas, G. E. A. (2003-03-27). "Do static sources respond to massive scalar particles from the Hawking radiation as uniformly accelerated ones do in the inertial vacuum?". Physical Review D. 67 (6): 067502. arXiv:gr-qc/0211053. doi:10.1103/PhysRevD.67.067502. hdl:11449/23239.
  15. ^ Castiñeiras, J.; Costa e Silva, I. P.; Matsas, G. E. A. (2003-10-31). "Interaction of Hawking radiation with static sources in de Sitter and Schwarzschild--de Sitter spacetimes". Physical Review D. 68 (8): 084022. arXiv:gr-qc/0308015. doi:10.1103/PhysRevD.68.084022. hdl:11449/23527.
  16. ^ Greene, Brian R.; Parikh, Maulik K.; van der Schaar, Jan Pieter (28 April 2006). "Universal correction to the inflationary vacuum". Journal of High Energy Physics. 2006 (4): 057. arXiv:hep-th/0512243. Bibcode:2006JHEP...04..057G. doi:10.1088/1126-6708/2006/04/057. S2CID 16290999.

Further reading

Retrieved from "https://en.wikipedia.org/enwiki/w/index.php?title=Quantum_field_theory_in_curved_spacetime&oldid=1065719490"