Andreev hidden spinor coordinates: Standard Model, gravity and $^3$He

Abstract

This paper is prepared for a special memorial issue of J. Low Temp. Phys. dedicated to memory of Alexander Andreev. I discuss his ideas devoted to the fundamental problem in modern physics -- the origin and validity of the superselection rule, which forbids the superposition of a fermion and a boson state. Andreev suggested extra spin degrees of freedom, due to which the $2\pi$ rotation does not change the sign of the fermionic wave function, and as a result the fermion-boson transmutations becomes possible. Although his approach looks somewhat contradictory from the point of view of the present physics, in principle his ideas can be realized on the more fundamental trans-Planckian level leading to new physics. Different scenarios of the extension of the internal spinor space are considered.