Bosonization and even Grassmann variables

ar X iv : h ep - t h / 96 07 16 0 v 1 1 8 Ju l 1 99 6 Bosonization and even Grassmann variables

We test a new approach to bosonization in relativistic field theories and many-body systems, based on the use of fermionic composites as integration variables in the Berezin integral defining the partition function of the system. The method appears promising since at zeroth order it correctly describes the propagators of the composites, which can be evaluated in a number of significant cases. S...

Supersymmetry without Grassmann variables

Supersymmetry transformations may be represented by unitary operators in a formulation of supersymmetry without numbers that anti-commute. The physical relevance of this formulation hinges on whether or not one may add states of even and odd fermion number, a question which soon may be settled by experiment.

Supersymmetry without Grassmann variables

Use of even Grassmann variables to construct effective actions for mesons

In the framework of an approach to bosonization based on the use of fermionic composites as fundamental variables, a quadratic action in even Grassmann variables with the quantum numbers of the pions has been constructed. It includes the σ-field in order to be invariant under [SU(2)]L ⊗ [SU(2)]R transformations over the quarks. This action exhibits the Goldstone phenomenon reducing its symmetry...

Grassmann Variables and the Jaynes-cummings Model

1 0.1 Abstract The Jaynes-Cummings model of a two-level atom in a single mode cavity is of fundamental importance both in quantum optics and in quantum physics generally , involving the interaction of two simple quantum systems-one fermionic system (the TLA), the other bosonic (the cavity mode). Depending on the initial conditions a variety of interesting effects occur, ranging from ongoing osc...