|
| related topics |
| {equation, function, exp} |
| {group, space, representation} |
| {phase, path, phys} |
| {operator, operators, space} |
| {let, theorem, proof} |
| {energy, gaussian, time} |
| {measurement, state, measurements} |
| {field, particle, equation} |
| {vol, operators, histories} |
| {key, protocol, security} |
|
Supersymmetry and Brownian motion on supermanifolds
Alice Rogers
abstract: An anticommuting analogue of Brownian motion, corresponding to fermionic
quantum mechanics, is developed, and combined with classical Brownian motion to
give a generalised Feynman-Kac-It\^o formula for paths in geometric
supermanifolds. This formula is applied to give a rigorous version of the
proofs of the Atiyah-Singer index theorem based on supersymmetric quantum
mechanics. It is also shown how superpaths, parametrised by a commuting and an
anticommuting time variable, lead to a manifestly supersymmetric approach to
the index of the Dirac operator. After a discussion of the BFV approach to the
quantization of theories with symmetry, it is shown how the quantization of the
topological particle leads to the supersymmetric model introduced by Witten in
his study of Morse theory.
- oai_identifier:
- oai:arXiv.org:quant-ph/0201006
- categories:
- quant-ph
- comments:
- 49 pages
- arxiv_id:
- quant-ph/0201006
- report_no:
- KCL-MTH-01-50
- created:
- 2002-01-03
Full article ▸
|
|
| related documents |
| 9905002v1 |
| 0111034v1 |
| 9809047v2 |
| 9602012v1 |
| 0211168v5 |
| 9712039v2 |
| 9902057v2 |
| 0004065v2 |
| 0201021v1 |
| 0609213v1 |
| 0009108v5 |
| 9707025v1 |
| 0302107v1 |
| 0106110v1 |
| 0604167v1 |
| 9505012v2 |
| 9910114v1 |
| 0404102v1 |
| 0601195v1 |
| 0303154v1 |
| 0301138v2 |
| 0509135v2 |
| 0211112v2 |
| 0612217v1 |
| 0602058v1 |
|