Path integrals with generalized Grassmann variables

1995/04/22 by Масуд Чайчиан, M. Chaichian, Andrey Demichev +1
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #hep-th #math.QA #q-alg

paper · pdf · doi:10.1016/0375-9601(95)00649-n

9 pages, LaTeX

arxiv created 1995/04/22 · openalex publication_date 1995/10/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct path integral representations for the evolution operator of q-oscillators with root of unity values of q-parameter using Bargmann-Fock representations with commuting and non-commuting variables, the differential calculi being q-deformed in both cases. For q²=-1 we obtain a new form of Grassmann-like path integral.

Citations

• Particle spin dynamics as the grassmann variant of classical mechanics
• On Quantum Field Theory with Nonzero Minimal Uncertainties in Positions and Momenta