Grassmann phase space theory for fermions

Phase-Space Methods for Fermions

Phase-space representations first arose from the attempt to describe quantum mechanics in terms of distributions over classical variables [1]. For example, Wigner introduced a function of phase-space variables W(x, p) that would classically correspond to a joint-probability distribution: an integration over x gives the marginal distribution for p and vice-versa. However in quantum mechanics, su...

Non - Grassmann Formulation of Regularized Gauge Theory with Fermions 1

Regularized continuum gauge theory coupled to quadratic matter simplifies significantly on integration of the matter fields. As an illustration, we discuss in some detail the resulting non-Grassmann formulation of regularized gauge theory with Dirac fermions.

Gaussian phase-space representations for fermions

We introduce a positive phase-space representation for fermions, using the most general possible multimode Gaussian operator basis. The representation generalizes previous bosonic quantum phase-space methods to Fermi systems. We derive equivalences between quantum and stochastic moments, as well as operator correspondences that map quantum operator evolution onto stochastic processes in phase s...

Space Forms of Grassmann Manifolds

Quantum phase-space simulations of fermions and bosons

We introduce a unified Gaussian quantum operator representation for fermions and bosons. The representation extends existing phase-space methods to Fermi systems as well as the important case of Fermi–Bose mixtures. It enables simulations of the dynamics and thermal equilibrium states of many-body quantum systems from first principles. As an example, we numerically calculate finite-temperature ...