Supersymmetry and Homotopy
| dc.creator | Maumary, Serge | |
| dc.creator | Ojima, Izumi | |
| dc.date | 2000-05-26 | |
| dc.date.accessioned | 2026-07-07T04:27:49Z | |
| dc.date.available | 2026-07-07T04:27:49Z | |
| dc.description | The homotopical information hidden in a supersymmetric structure is revealed by considering deformations of a configuration manifold. This is in sharp contrast to the usual standpoints such as Connes' programme where a geometrical structure is rigidly fixed. For instance, we can relate supersymmetries of types N=2n and N=(n, n) in spite of their gap due to distinction between $\Bbb{Z}_2$(even-odd)- and integer-gradings. Our approach goes beyond the theory of real homotopy due to Quillen, Sullivan and Tanré developed, respectively, in the 60's, 70's and 80's, which exhibits real homotopy of a 1-connected space out of its de Rham-Fock complex with supersymmetry. Our main new step is based upon the Taylor (super-)expansion and locality, which links differential geometry with homotopy without the restriction of 1-connectedness. While the homotopy invariants treated so far in relation with supersymmetry are those depending only on $\Bbb{Z}_2$-grading like the index, here we can detect new $\Bbb{N}$-graded homotopy invariants. While our setup adopted here is (graded) commutative, it can be extended also to the non-commutative cases in use of state germs (Haag-Ojima) corresponding to a Taylor expansion. | |
| dc.identifier | https://arxiv.org/abs/math-ph/0005027 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0005027 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/56560 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Algebraic Topology | |
| dc.title | Supersymmetry and Homotopy | |
| dc.type | text |