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1. On the Unruh effect and the Thermofield Double State: The goal of this document is to present a pedagogical development of the Unruh effect and the Thermofield Double State. In section 2, we construct the Rindler spacetime and analyze the observer’s perspective under constant acceleration in Minkowski, which motivates relating the Fourier modes in both geometries using the Bogoliubov-Valatin transformations. In section 3, we examine the physics involved, which leads us to the Unruh effect. Finally, in section 4, we obtain the Thermofield Double State by performing a Euclidean analysis of the field and geometry.
2. Path integral derivation of the thermofield double state in causal diamonds: In this article, we follow the framework given in the article {\it Physica A}, \textbf{158}, pg 58-63 (1989) by R. Laflamme to derive the thermofield double state for a causal diamond using the Euclidean path integral formalism, and subsequently derive the causal diamond temperature. The interpretation of the physical and fictitious system in the thermofield double state arises naturally from the boundary conditions of the fields defined on the Euclidean sections of the cylindrical background geometry $S^{1}{\beta}\times \mathbb{R}$, where $\beta$ defines the periodicity of the Euclidean time coordinate and $S^{1}{\beta}$ is a circumference of length $\beta$. The temperature detected by a static diamond observer at $x=0$ matches with the thermofield double temperature derived via this path integral procedure.