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Laine, M. and Vuorinen, A. (2016) Basics of Thermal Field Theory. Lecture Notes in Physics, Vol. 925, Springer, Berlin.
https://doi.org/10.1007/978-3-319-31933-9

has been cited by the following article:

• TITLE: Broken Charges Associated with Classical Spacetime Symmetries under Canonical Transformation in Real Scalar Field Theory

  AUTHORS: Susobhan Mandal

  KEYWORDS: Noether’s Theorem, Killing Vector Field, Einstein’s Equivalence, Broken Charges

  JOURNAL NAME: Journal of High Energy Physics, Gravitation and Cosmology, Vol.5 No.1, December 20, 2018

  ABSTRACT: We know from Noether’s theorem that there is a conserved charge for every continuous symmetry. In General Relativity, Killing vectors describe the spacetime symmetries and to each such Killing vector field, we can associate conserved charge through stress-energy tensor of matter which is mentioned in the article. In this article, I show that under simple set of canonical transformation of most general class of Bogoliubov transformation between creation, annihilation operators, those charges associated with spacetime symmetries are broken. To do that, I look at stress-energy tensor of real scalar field theory (as an example) in curved spacetime and show how it changes under simple canonical transformation which is enough to justify our claim. Since doing Bogoliubov transformation is equivalent to coordinate transformation which according to Einstein’s equivalence principle is equivalent to turn on effect of gravity, therefore, we can say that under the effect of gravity those charges are broken.