Classification of integration patterns on R1|1

✍ Scribed by O.A. Sánchez-Valenzuela; C. Victoria-Monge

• Book ID: 104358097
• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 238 KB
• Volume: 13
• Category: Article
• ISSN: 0926-2245
• DOI: 10.1016/s0926-2245(00)00032-2

✦ Synopsis

The indefinite integration problem in R 1|1 is approached by looking at those derivations on this graded manifold that admit a right inverse. The integration formulae that arise this way are classified in terms of the action of the diffeomorphism group of R 1|1 . The Berezin integral, and other integral formulae proposed in the literature for graded manifolds, arise as examples of right inverses for specific derivations. A thorough analysis of the Berezin integral is made for (1, 1)-dimensional smooth and holomorphic graded manifolds. It is proved that a SUSY-curve carries a canonical indefinite integration defined on its Berezinian sheaf which is not given by the Berezin integral. Finally, the variational calculus is applied to the integrals here classified, and their corresponding Euler-Lagrange equations are given.