A Field-Theoretical Approach to the P vs. NP Problem via the Phase Sign of Quantum Monte Carlo

I present here a new method that allows the introduction of a discrete auxiliary symmetry in a theory in such a way that the eigenvalue spectrum of the fermion functional determinant is made up of complex conjugated pairs. The method implies a particular way of introducing and integrating over auxiliary fields related to a set of artificial shift symmetries. Gauge fixing the artificial continuous shift symmetries in the direct and dual sectors leads to the appearance of direct and dual Becchi–Rouet–Stora–Tyutin (BRST)-type global symmetries and of a symplectic structure over the field space. Such a method may allow the extension of the applicability of quantum Monte Carlo methods to some problems plagued by the fermionic sign problem.