Fermions and the Calculus for Grassmann Variables

Bryan J. Dalton, John Jeffers, Stephen Mark Barnett

R A Ramirez, G. L. Rossini, D. C. Cabra +1 more

We describe coherent states and associated generalized Grassmann variables for a system of m independent q -boson modes. A resolution of unity in terms of generalized Berezin integrals leads to generalized Grassmann symbolic calculus. Formulae for operator traces are given and the thermodynamic partition function for a system of q -boson oscillators is discussed.

Ramírez, Romina Andrea, G. L. Rossini, D. C. Cabra +1 more

We describe coherent states and associated generalized Grassmann variables for a system of m independent q-boson modes. A resolution of unity in terms of generalized Berezin integrals leads to generalized Grassmann symbolic calculus. Formulae for operator traces are given and the thermodynamic partition function for a system of q-boson oscillators is discussed.

Bryan J. Dalton, John Jeffers, Stephen Mark Barnett

A phase space theory for fermions has been developed using Grassmann phase space variables which can be used in numerical calculations for cold Fermi gases and for large fermion numbers. Numerical calculations are feasible because Grassmann stochastic variables at later times are related linearly to such variables at earlier times via c‐number stochastic quantities. A Grassmann field version has been developed making large fermion number applications possible. Applications are shown for few mode and field theory cases.