The theory of quantum field theory in curved spacetime may be considered as an intermediate step towards quantum gravity. These predictions are calculated using the Bunch–Davies vacuum or modifications thereto. This formalism is also used to predict the primordial density perturbation spectrum arising in different models of cosmic inflation. Other prediction of quantum fields in curved spaces include, for example, the radiation emitted by a particle moving along a geodesic and the interaction of Hawking radiation with particles outside black holes. The latter can be understood as a manifestation of the Unruh effect where an accelerating observer observes black body radiation. 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 and Hawking radiation. Using perturbation theory in quantum field theory in curved spacetime geometry is known as the semiclassical approach to quantum gravity. 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. Several rigorous results concerning QFT in the presence of a black hole have been obtained. Indeed, the viewpoint of local quantum physics is suitable to generalize the renormalization procedure to the theory of quantum fields developed on curved backgrounds. 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. 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. Creation operators correspond to positive frequencies, while annihilation operators correspond to negative frequencies.
If t′( t) is a diffeomorphism, in general, the Fourier transform of exp will contain negative frequencies even if k > 0. This is because a mode decomposition of a field into positive and negative frequency modes is not invariant under diffeomorphisms. The concept of a vacuum is not invariant under diffeomorphisms. 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).Īnother 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. 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. These theories rely on general relativity to describe a curved background spacetime, and define a generalized quantum field theory to describe the behavior of quantum matter within that spacetime.įor non-zero cosmological constants, on curved spacetimes quantum fields lose their interpretation as asymptotic particles. In order to describe situations in which gravity is strong enough to influence (quantum) matter, yet not strong enough to require quantization itself, physicists have formulated quantum field theories in curved spacetime. Ordinary quantum field theories, which form the basis of standard model, are defined in flat Minkowski space, which is an excellent approximation when it comes to describing the behavior of microscopic particles in weak gravitational fields like those found on Earth. The most famous example of the latter is the phenomenon of Hawking radiation emitted by black holes. A general prediction of this theory is that particles can be created by time-dependent gravitational fields (multi graviton pair production), or by time-independent gravitational fields that contain horizons. This theory treats spacetime as a fixed, classical background, while giving a quantum-mechanical description of the matter and energy propagating through that spacetime. 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.
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