Classical BV cohomology of the N=1 spinning particle

2025/10/01 by Eugenia Boffo, Boffo, Eugenia, Martin Cederwall +1
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2510.00655

openalex publication_date 2025/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the classical Batalin--Vilkovisky cohomology at negative ghost number of the spinning particle, observed in ref. arXiv:1511.02135, is removed by a Koszul--Tate resolution involving saturation of Grassmann odd variables. The model thus satisfies the axioms of Felder and Kazhdan. The AKSZ formulation of the resolved model is described. We reveal partial information on the resolution of the constrained phase space, which involves resolving the parity-shifted tangent sheaf of the light-cône. Specialising to dimension one, we describe the full resolution.

Citations

• Reframing classical mechanics: An AKSZ sigma model perspective
• Canonical supermultiplets and their Koszul duals
• Spinning Particles in Quantum Mechanics and Quantum Field Theory
• New Geometrical Approach to Superstrings
• Quantization of Gauge Systems
• Ueber die Theorie der algebraischen Formen

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