## Supersymmetric-time evolution.(English)Zbl 0943.58004

Cerdonio, M. (ed.) et al., General relativity and gravitational physics. Proceedings of the 10th Italian conference, Bardonecchia, Italy, September 1-5, 1992. Singapore: World Scientific. 467-471 (1994).
From the introduction: “We consider the supersymmetric $$(1,1)$$ evolution parameter (time). The generator of this evolution is the supersymmetric derivative $$D_t= \left({\partial\over\partial\theta}+ \theta{\partial\over\partial x}\right)$$ for the real case and $$\partial_t= \left({\partial\over\partial\theta}- i\theta{\partial\over\partial x}\right)$$ for the complex case, where $$\theta$$ is odd and $$x$$ is even. These operators are the generators of real and complex supersymmetric transformations.
Differential equations with supersymmetric $$(1,1)$$ time play an important role in applications to supersymmetric quantum mechanics”.
For the entire collection see [Zbl 0936.00049].

### MSC:

 58C50 Analysis on supermanifolds or graded manifolds 35Q99 Partial differential equations of mathematical physics and other areas of application 58A50 Supermanifolds and graded manifolds

### Keywords:

supersymmetric-time evolution