| DATE: |
2005-09-22 15:00 - |
| PLACE: |
Hon-kan Rm. 220 |
| TITLE: |
Describing Curved Spaces by Matrices |
| CONTACT: |
Tango |
| SPEAKER: |
Prof. Hikaru Kawai (Department of physics, Kyoto University) |
| LANGUAGE: |
Japanese |
| ABSTRACT: |
It is shown that a covariant derivative on any d-dimensional manifold
M can be mapped to a set of d operators acting on the space of
functions on the principal Spin(d)-bundle over M. In other words, any
d-dimensional manifold can be described in terms of d operators acting
on an infinite dimensional space. Therefore it is natural to introduce a
new interpretation of matrix models in which matrices represent such
operators. In this interpretation the diffeomorphism, local Lorentz
symmetry and their higher-spin analogues are included in the unitary
symmetry of the matrix model. Furthermore the Einstein equation is
obtained from the equation of motion, if we take the standard form of
the action S=-tr([A_{a},A_{b}][A^{a},A^{b}]).
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