Quantization of Scalar Fields in Curved Background and Quantum Algebras
Abstract
We show that a suitable deformation of the algebra hk(1) of the creation and annihilation operators for a complex scalar field, initially quantized in Minkowski space--time, induces the canonical quantization of the same field in a generic gravitational background. This discloses the physical meaning of the deformation parameter q which turns out to be related to the gravitational field. The thermal properties are re-obtained in this formalism, and the application to Schwarzschild and Rindler space-times are carried out.
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