Infinite-Dimensional and Colored Supermanifolds

DOI

10.1142/S140292511000088XHow to use a DOI?

Keywords

Infinite-dimensional supermanifolds; Topos theory; glutosers

Abstract

Here the theory of finite-dimensional supermanifolds is generalized in two directions.

First, we introduce infinite-dimensional supermanifolds “locally isomorphic” to arbitrary Banach (or, more generally, locally convex) superspaces. This is achieved by considering supermanifolds as functors (equipped with some additional structure) from the category of finite-dimensional Grassmann superalgebras into the category of the corresponding smooth manifolds (Banach or locally convex).

Selected examples: flag supermanifolds of Banach superspaces as well as unitary supergroups of Hilbert superspaces.

Second, we define “generalized” supermanifolds, “locally isomorphic” to 𝕑2k -graded Banach (or, more generally, locally convex) spaces. These generalized supermanifolds are referred to in what follows (super)^k-manifolds, or colored manifolds). The corresponding superfields (i.e., morphisms into “coordinate ring”) describing, hopefully, particles with more general statistics than Bose + Fermi, turn out to have, in general, an infinite number of components.

Copyright

© 2010 The Authors. Published by Atlantis Press and Taylor & Francis

Open Access

This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Vladimir Molotkov
PY  - 2021
DA  - 2021/01/07
TI  - Infinite-Dimensional and Colored Supermanifolds
JO  - Journal of Nonlinear Mathematical Physics
SP  - 375
EP  - 446
VL  - 17
IS  - Supplement 1
SN  - 1776-0852
UR  - https://doi.org/10.1142/S140292511000088X
DO  - 10.1142/S140292511000088X
ID  - Molotkov2021
ER  -