Quantum field theory in curved spacetime

Quantum field theory in curved spacetime describes quantum fields on a classical curved spacetime background. It accounts for matter’s quantum behavior while treating gravity and geometry as nonquantized.

Quantum field: A field whose observables obey quantum principles and whose excitations are interpreted as particles. The theory applies quantum fields to a spacetime whose geometry is curved.
General relativity: A theory of gravity in which spacetime geometry is dynamical and responds to energy and momentum. Its spacetime solutions provide the backgrounds on which quantum fields are studied.
Semiclassical gravity: A framework in which classical spacetime responds to the expectation value of quantum matter’s stress-energy tensor. It feeds quantum-field effects back into the gravitational background without quantizing gravity.
Quantum gravity: A proposed framework in which gravitational degrees of freedom themselves obey quantum principles. Unlike this framework, quantum gravity does not hold spacetime geometry fixed as a classical background.
Quantum vacuum: A lowest-energy state of a quantum field, defined relative to a choice of time evolution. Curved or time-dependent geometry can make vacuum definitions observer-dependent.
Lorentzian manifold: A smooth manifold equipped with a metric of Lorentzian signature, encoding causal and temporal structure. It supplies the geometric arena for field propagation and causal relations.
Hawking temperature: The temperature associated with the thermal spectrum predicted for radiation from a black hole. It quantifies the thermal consequence of quantum fields near a black-hole horizon.
Quantum field theory in flat spacetime: Quantum field theory formulated on Minkowski spacetime with its fixed, flat geometry. Curvature removes some global structures, including a generally unique vacuum and particle definition.
Bogoliubov transformation: A linear transformation mixing creation and annihilation operators while preserving their commutation relations. It relates particle definitions associated with different observers or spacetime eras.
Klein–Gordon equation: A relativistic wave equation describing free scalar fields, with a mass-dependent term. Its curved-spacetime form is a standard model for quantum field dynamics.

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