Abstract
One of the biggest challenges in physics is to understand the dynamics of systems characterized by a very large number of degrees of freedom. The prototypical example is the thermodynamics of a classical fluid, whose microscopics is described by roughly \(N_A\sim 10^{23}\) point-like interacting particles. A somewhat similar situation arises in the context of Quantum Field Theories (QFTs), where the fundamental degrees of freedom are represented by quantum fluctuations about the vacuum of the theory at any point in space-time.
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Notes
- 1.
In a square lattice, \(\xi \) is of the order of a few lattice spacing a, while it is usually associated to the inverse mass of the lightest particle of the theory m in the QFT context. At short distances \(p\gg m\) the dynamics of the theory will be dominated by massless excitations, while at long distances \(p\ll \xi \) many degrees of freedom will be effectively non-propagating.
- 2.
E.g. theories with spectrum bounded from below.
- 3.
Here we are specifically using the standard RG terminology.
- 4.
Note that “small” deformations of the critical point are in principle determined in terms of the data of the undeformed theory.
- 5.
- 6.
Incidentally, conformal symmetry is the only known bosonic extension of the Poincarè group not leading to trivial QFTs [6].
- 7.
- 8.
From the RG analysis, there is no reason to expect isolated critical points, in general. However “ordinary” CFTs are often isolated. Is this “selection” due to additional constraints?
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Lauria, E. (2019). Preamble. In: Points, Lines, and Surfaces at Criticality. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-030-25730-9_1
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DOI: https://doi.org/10.1007/978-3-030-25730-9_1
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