A quantum field theoretical approach to the P vs. NP problem via the sign of the fermionic Quantum Monte Carlo Andrei T. Patrascu1 1University College London, Department of Physics and Astronomy, London, WC1E 6BT, UK 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 sector leads to the implementation of a Kahler structure over the field space. The discrete symmetry appears to be induced by the Hodge-* operator. The particular extension of the field space presented here makes the operators of the de-Rham cohomology manifest. This method implies the identification of the (anti)-BRST and dual-(anti)-BRST operators with the exterior derivative and its dual in the context of the complex de-Rham cohomology. The novelty of this method relies on the fact that the field structure is doubled two times in order to make use of a supplemental symmetry prescribed by algebraic geometry. This leads to a generalization of Kramers theorem that avoids the Quantum Monte Carlo phase sign problem without any apparent increase in complexity. arxiv.org/pdf/1403.2067v1.pdf
Posted on: Sat, 15 Mar 2014 20:15:13 +0000
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