This is a review I did for the Phys 400 - Special Problems in Physics course at the Middle East Technical University.  The thermofield double (TFD) state has been an important tool in statistical physics since its construction by Takahashi and Umezawa. Defined as the purification of the thermal Gibbs state, it has been used in thermal field theories, black hole physics, and quantum gravity research. In this project, we present a review of the TFD states and apply it to the case of an accelerated observer in the Minkowski vacuum to derive the Unruh effect. 

Below, you can find the report paper I have written for the project as well as the poster and the presentation slides.

Here are the references I used that did not fit in the poster:

[1] Yasushi Takahashi and Hiroomi Umezawa. “Thermo field dynamics”. In: International Journal of Modern Physics B 10.13n14 (1996), pp. 1755–1805.

[2] Jürgen Audretsch. Entangled systems: new directions in quantum physics. eng. Weinheim: Wiley-VCH, 2007. ISBN: 978-3-527-40684-5.

[3] William Cottrell et al. “How to Build the Thermofield Double State”. In: Journal of High Energy Physics 2019.2 (Feb. 2019), p. 58. ISSN: 1029-8479. doi:10.1007/JHEP02(2019)058.

[4] Xiao-Kan Guo. “Thermofield double states in group field theory”. In: International Journal of Modern Physics A 36.02 (2021), p. 2150008.

[5] W. Israel. “Thermo-field dynamics of black holes”. en. In: Physics Letters A 57.2 (May 1976), 107–110. ISSN: 03759601.                                                        doi: 10.1016/0375-9601(76)90178-X.

[6] Juan Maldacena. “Eternal black holes in anti-de Sitter”. In: Journal of High Energy Physics 2003.04 (2003), p. 021.

[7] Gustavo Valdivia-Mera. “On the Unruh effect and the Thermofield Double State”. In: arXiv:2001.09869 (Sept. 2024). arXiv:2001.09869 [hep-th].          url: http://arxiv.org/abs/2001.09869.