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. Properties of quantum field theory in causality violating spacetimes.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. Some version of the ``averaged null energy condition'', and the formulation and A brief discussionĪlso is given of several open issues and questions in quantum field theory inĬurved spacetime regarding the treatment of ``back-reaction", the validity of The perspective of the theoretical framework adopted here. We briefly review the Unruh and Hawking effects from Vacuum state in Minkowski spacetime, and that the expected stress-energy tensor Insures that the ultra-violet behavior of the state be similar to that of the Requirement that their two-point function satisfy the Hadamard condition, which The physically nonsingular states are restricted by the Is accomplished via the algebraic approach, which, in essence, simultaneouslyĪdmits all states in all possible (unitarily inequivalent) Hilbert spaceĬonstructions. Linear field propagating in a globally hyperbolic spacetime. Wald Download PDF Abstract: We review the mathematically rigorous formulation of the quantum theory of a Download a PDF of the paper titled Quantum Field Theory in Curved Spacetime, by Robert M.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |