On the Unruh effect and the thermofield double state

TL;DR

This review pedagogically explains the Unruh effect and thermofield double state, detailing their theoretical foundations, physical implications, and connections to black hole thermodynamics, with derivations and analogies.

Contribution

It provides a comprehensive, pedagogical derivation of the Unruh effect and thermofield double state, linking quantum field theory in curved spacetime with black hole physics.

Findings

Derivation of Rindler spacetime and Bogoliubov transformations

Analysis of the Unruh effect and its thermal nature

Construction of the thermofield double state from Euclidean methods

Abstract

The purpose of this review is to provide a pedagogical development of the Unruh effect and the thermofield double state. In Section 2, we construct Rindler spacetime and analyze the perspective of an observer undergoing constant acceleration in Minkowski spacetime, which motivates the establishment of the relationship between the Fourier modes in both geometries using the Bogoliubov-Valatin transformation. In Section 3, we explore the underlying physics leading to the Unruh effect, its analogy with the thermal radiation observed around a Schwarzschild black hole, and its manifestation through the coupling of a particle detector to the scalar field. Finally, in Section 4, we derive the thermofield double state by conducting a Euclidean analysis of the field and geometry.