A General Theory of Wightman Functions
| dc.creator | Ritter, William Gordon | |
| dc.date | 2004-04-08 | |
| dc.date | 2004-05-18 | |
| dc.date.accessioned | 2026-07-07T04:31:06Z | |
| dc.date.available | 2026-07-07T04:31:06Z | |
| dc.description | One of the main open problems of mathematical physics is to consistently quantize Yang-Mills gauge theory. If such a consistent quantization were to exist, it is reasonable to expect a ``Wightman reconstruction theorem,'' by which a Hilbert space and quantum field operators are recovered from n-point functions. However, the original version of the Wightman theorem is not equipped to deal with gauge fields or fields taking values in a noncommutative space. This paper explores a generalization of the Wightman construction which allows the fundamental fields to take values in an arbitrary topological *-algebra. In particular, the construction applies to fields valued in a Lie algebra representation, of the type required by Yang-Mills theory. This appears to be the correct framework for a generalized reconstruction theorem amenable to modern quantum theories such as gauge theories and matrix models. We obtain the interesting result that a large class of quantum theories are expected to arise as limits of matrix models, which may be related to the well-known conjecture of Kazakov. Further, by considering deformations of the associative algebra structure in the noncommutative target space, we define certain one-parameter families of quantum field theories and conjecture a relationship with deformation quantization. | |
| dc.identifier | https://arxiv.org/abs/math-ph/0404027 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0404027 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/57699 | |
| dc.subject | Mathematical Physics | |
| dc.subject | 81T05 | |
| dc.title | A General Theory of Wightman Functions | |
| dc.type | text |