| DATE: |
2006-11-22 13:30 - 14:30 |
| PLACE: |
Kenkyu Honkan 2F RM 220 |
| TITLE: |
Noncommutative geometry in condensed-matter physics |
| CONTACT: |
tsuda |
| SPEAKER: |
Naoyuki Sugimoto (Department of Applied Physics, University of Tokyo) |
| LANGUAGE: |
Japanese |
| ABSTRACT: |
Generally, the physical laws are required to satisfy the following two conditions. (1) The products appearing in the equations have the associative property. (2) The equations are gauge-covariant. In quantum mechanics, the noncommutativity of operators plays the crucial role, which can be translated into that of the products appearing in the equations. Therefore it is of vital importance to develop a formalism of gauge covariant noncommutative product describing the commutators between x and p, and also between different components of $\pi$. ($\pi=p-e A$ is the gauge covariant momentum).
In this talk, I will describe the formalism of gauge-covariant Wigner representation by introducing the star product taking into account this noncommutativity. This is achieved by using the deformational quantization method. We apply this result to Keldysh formalism, and show some examples of the problems in condensed matter physics on which this formalism has been successfully applied.
This work has been done in collaboration with Shigeki Onoda and Naoto Nagaosa.
Ref: N. Sugimoto, S. Onoda and N. Nagaosa, cond-mat/0611142 |
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