Spin in the path integral: anti-commuting versus commuting variables

Abstract

We discuss the equivalence between the path integral representations of spin dynamics for anti-commuting (Grassmann) and commuting variables and establish a bosonization dictionary for both generators of spin and single fermion operators. The content of this construction in terms of the representations of the spin algebra is discussed in the path integral setting. Finally it is shown how a `free field realization' (Dyson mapping) can be constructed in the path integral.

9 pages, Latex

References in corpus (1)

• Nonabelian Bosonization as Duality

Cited by in corpus (4)

• BRST Cohomology and Hilbert Spaces of Non-Abelian Models in the Decoupled Path Integral Formulation
• Mapping between the classical and pseudoclassical models of a relativistic spinning particle in external bosonic and fermionic fields. I
• Bosonization in d=2 from finite chiral determinants with a Gauss decomposition
• Mapping between the classical and pseudoclassical models of a relativistic spinning particle in external bosonic and fermionic fields. II