Quantum field theory in curved spacetime
Quantum field theory |
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History |
In theoretical physics, quantum field theory in curved spacetime (QFTCS) [1] is an extension of quantum field theory from Minkowski spacetime to a general curved spacetime. This theory uses a semi-classical approach; it treats spacetime as a fixed, classical background, while giving a quantum-mechanical description of the matter and energy propagating through that spacetime. A general prediction of this theory is that particles can be created by time-dependent gravitational fields (multigraviton pair production), or by time-independent gravitational fields that contain horizons. The most famous example of the latter is the phenomenon of Hawking radiation emitted by black holes.
Overview
Ordinary
For non-zero cosmological constants, on curved spacetimes quantum fields lose their interpretation as asymptotic particles.[2] 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
Since the end of the 1980s, the
Applications
Using
This formalism is also used to predict the primordial density
Approximation to quantum gravity
The theory of quantum field theory in curved spacetime may be considered as an intermediate step towards quantum gravity.[18] QFT in curved spacetime is expected to be a viable approximation to the theory of quantum gravity when spacetime curvature is not significant on the Planck scale.[19][20][21] However, the fact that the true theory of quantum gravity remains unknown means that the precise criteria for when QFT on curved spacetime is a good approximation are also unknown.[2]: 1
Gravity is not
See also
References
- ^ Kay, B.S. (2023). "Quantum Field Theory in Curved Spacetime (2nd Edition) (article prepared for the second edition of the Encyclopaedia of Mathematical Physics, edited by M. Bojowald and R.J. Szabo, to be published by Elsevier)" (PDF).
- ^ ISBN 0-226-87025-1.
- ^ 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).
- S2CID 119179440, retrieved 2022-01-14
- .
- ISBN 978-981-02-0515-7, retrieved 2021-08-15
- S2CID 119223632.
- OCLC 7462032.
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- S2CID 126192949.
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- S2CID 33007353.
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- S2CID 16290999.
- S2CID 55608399.
Quantum field theory on curved spacetime, which might be considered as an intermediate step towards quantum gravity, already has no distinguished particle interpretation.
- ISBN 9783642027802.
In particular, due to the weakness of gravitational forces, the back reaction of the spacetime metric to the energy momentum tensor of the quantum fields may be neglected, in a first approximation, and one is left with the problem of quantum field theory on Lorentzian manifolds. Surprisingly, this seemingly modest approach leads to far-reaching conceptual and mathematical problems and to spectacular predictions, the most famous one being the Hawking radiation of black holes.
- arXiv:gr-qc/0601008.
One expects it to be a good approximation to full quantum gravity provided the typical frequencies of the gravitational background are very much less than the Planck frequency [...] and provided, with a suitable measure for energy, the energy of created particles is very much less than the energy of the background gravitational field or of its matter sources.
- S2CID 218502756.
Quantum field theory in curved spacetime is a semiclassical approximation to quantum gravity theory, where the curved background spacetime is treated classically, while the matter fields in the curved spacetime are quantized.
Further reading
- Birrell, N. D.; Davies, P. C. W. (1982). Quantum fields in curved space. CUP. ISBN 0-521-23385-2.
- Fulling, S. A. (1989). Aspects of quantum field theory in curved space-time. CUP. ISBN 0-521-34400-X.
- Mukhanov, V.; Winitzki, S. (2007). Introduction to Quantum Effects in Gravity. CUP. ISBN 978-0-521-86834-1.
- ISBN 978-0-521-87787-9.
External links
- Summary Chart of Intro Steps to Quantum Fields in Curved Spacetime A two-page chart outline of the basic principles governing the behavior of quantum fields in general relativity.