Abstract
In this section, we briefly summarize our basic knowledge of quantum field theories, required for the investigation of equilibrium (and eventually nonequilibrium) features of quantum systems with a very large (infinite) number of degrees of freedom. The best representation of the dynamical variables are fields with a Lagrangian describing local interactions among them. The thus defined field theory can then be quantized and eventually put in a heat bath.
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Notes
- 1.
We remark that in (2 + 1)-dimensional field theories, there is a possibility to define particles with any α with unit length. These are called anyons.
- 2.
This vacuum contribution used to be attributed to the Casimir effect, where we measure the energy difference arising when the volume of the quantization space is changed. It is also worth noting that fermions and bosons contribute with opposite signs, which means that in supersymmetric models, the net zero-point contribution is zero.
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Jakovác, A., Patkós, A. (2016). Finite Temperature Field Theories: Review. In: Resummation and Renormalization in Effective Theories of Particle Physics. Lecture Notes in Physics, vol 912. Springer, Cham. https://doi.org/10.1007/978-3-319-22620-0_2
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DOI: https://doi.org/10.1007/978-3-319-22620-0_2
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