The fluctuations of scalar fields, that are invariant under rotations of the worldvolume, in Euclidian signature, can be described by a system of Langevin equations. These equations can be understood as defining a change of variables in the functional integral for the noise, with which the physical degrees of freedom are in equilibrium. The absolute value of the Jacobian of this change of variables therefore repackages the fluctuations. This provides a new way of relating the number and properties of scalar fields with the consistent and complete description of their fluctuations and is another way of understanding the relevance of supersymmetry, which, in this way, determines the minimal number of real scalar fields (e.g. two in two dimensions, four in three dimensions and eight in four dimensions), in order for the system to be consistently closed.
Journal of Physics Conference Series
- Pub Date:
- November 2021
- High Energy Physics - Theory;
- Condensed Matter - Statistical Mechanics
- 9 pages LaTeX, uses utphys for the references. Written contribution to the talk at the "38th Conference on Recent Developments in High Energy Physics and Cosmology" of the Hellenic Society for the Study of High Energy Physics (16-19 June 2021, Thessaloniki, Greece)