Quantum field theory in curved spacetime
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Quantum field theory in curved spacetime is an extension of standard quantum field theory to curved 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.
Thanks to the equivalence principle the quantization procedure locally resembles that of Minkowski spacetime once the proper (covariant) formalism is chosen; however, interesting new phenomena occur. Even in flat spacetime quantum field theory, the number of particles is not well-defined locally. For non-zero cosmological constants, on curved spacetimes quantum fields lose their interpretation as asymptotic particles. 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 (ie, different observers may measure different numbers of asymptotic particles on a given spacetime).
The most striking application of the theory is Hawking's prediction that Schwarzchild black holes radiate with a thermal spectrum. A related prediction is the Unruh effect: accelerated observers in the vacuum measure a thermal bath of particles.
This formalism is also used to predict the primordial density perturbation spectrum arising from cosmic inflation. Since this spectrum is measured by a variety of cosmological measurements -- such as the CMB -- if inflation is correct this particular prediction of the theory has already been verified.
The theory of quantum field theory in curved spacetime can be considered as a first approximation to quantum gravity. A second step towards that theory would be semiclassical gravity, which would include the influence of particles created by a strong gravitational field on the spacetime (which is still considered classical and the equivalence principle still holds).
The current Big Bang Model is a QFT in a curved spacetime. Unfortunately, no such theory-in the sense of including QED or the Standard Model-is mathematically well-defined; in spite of this, theoreticians claim to extract information from this hypothetical theory. On the other hand, the super-classical limit of the not mathematically well-defined QED in a curved spacetime is the mathematically well-defined Einstein-Maxwell-Dirac system. (One could get a similar system for the standard model.) As a super theory, EMD violates the positivity condition in the Penrose-Hawking Singularity Theorem. Thus, it is possible that there would be complete solutions without any singularities. Furthermore, it is known that the Maxwell-Dirac system admits of solitonic solutions, i.e., classical electrons and photons. This is the kind of theory Einstein was hoping for. On the other hand, the matter field being a super-field probably doesn't admit of any realistic interpretation. One last comment, EMD is also a totally geometrized theory as a non-commutative geometry; here, the charge e and the mass m of the electron are geometric invariants of the non-commutative geometry analogous to pi!
[edit] Suggested reading
- R.M. Wald. Quantum field theory in curved space-time and black hole thermodynamics. Chicago U. (1995).
- S.A. Fulling. Aspects of quantum field theory in curved space-time. CUP (1989).
- N.D. Birrell & P.C.W. Davies. Quantum fields in curved space. CUP (1982).
- L. H. Ford Quantum Field Theory in Curved Spacetime (1997).
- V.Mukhanov and S.Winitzki. Introduction to Quantum Effects in Gravity. CUP (2007).
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