Quantum field theory in curved spacetime is an extension of standard, Minkowski-space 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 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, 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 (i.e., different observers may measure different numbers of asymptotic particles on a given spacetime).
Another observation is that unless the background metric 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 is a diffeomorphism, in general, the Fourier transform of will contain negative frequencies even if . 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 can look like a heat bath to another accelerating with respect to the former observer.
The most striking application of the theory is Hawking's prediction that Schwarzschild 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, i.e. the Bunch–Davies vacuum. 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).
Read more about Quantum Field Theory In Curved Spacetime: Suggested Reading
Famous quotes containing the words quantum, field, theory and/or curved:
“The receipt to make a speaker, and an applauded one too, is short and easy.Take of common sense quantum sufficit, add a little application to the rules and orders of the House, throw obvious thoughts in a new light, and make up the whole with a large quantity of purity, correctness, and elegancy of style.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (16941773)
“Every woman who visited the Fair made it the center of her orbit. Here was a structure designed by a woman, decorated by women, managed by women, filled with the work of women. Thousands discovered women were not only doing something, but had been working seriously for many generations ... [ellipsis in source] Many of the exhibits were admirable, but if others failed to satisfy experts, what of it?”
—Kate Field (18381908)
“The human species, according to the best theory I can form of it, is composed of two distinct races, the men who borrow and the men who lend.”
—Charles Lamb (17751834)
“Our life is a faint tracing on the surface of mystery, like the idle, curved tunnels of leaf miners on the face of a leaf. We must somehow take a wider view, look at the whole landscape, really see it, and describe whats going on here. Then we can at least wail the right question into the swaddling band of darkness, or, if it comes to that, choir the proper praise.”
—Annie Dillard (b. 1945)