Quantum field theory on timelike hypersurfaces in Rindler space

TL;DR

This paper applies the general boundary formulation of quantum field theory to a scalar field in Rindler space, demonstrating the equivalence of different quantization schemes and boundary conditions.

Contribution

It constructs an isomorphism between Hilbert spaces in different spacetime regions, showing the equivalence of S-matrices in these settings.

Findings

Hilbert space isomorphism preserves quantum probabilities

S-matrices are equivalent in different boundary conditions

Quantization schemes yield consistent results

Abstract

The general boundary formulation of quantum field theory is applied to a massive scalar field in two dimensional Rindler space. The field is quantized according to both the Schr\"odinger-Feynman quantization prescription and the holomorphic one in two different spacetime regions: a region bounded by two Cauchy surfaces and a region bounded by one timelike curve. An isomorphism is constructed between the Hilbert spaces associated with these two boundaries. This isomorphism preserves the probabilities that can be extracted from the free and the interacting quantum field theories, proving the equivalence of the S-matrices defined in the two settings, when both apply.