In this paper, a rigorous construction of the S^1 -equivariant Dirac operator (i.e., Dirac– Ramond operator) on the space of (mean zero) loops in R^d is given and its equivariant L^2 - index computed. Essential use is made of infinite tensor product representations of the canonical anticommutation relations algebra.
Spera, M., Wurzbacher, T., The Dirac-Ramond operator on loops in flat space, <<JOURNAL OF FUNCTIONAL ANALYSIS>>, N/A; 197 (N/A): 110-139. [doi:10.1016/S0022-1236(02)00178-7] [http://hdl.handle.net/10807/35686]
The Dirac-Ramond operator on loops in flat space
Spera, Mauro;
2003
Abstract
In this paper, a rigorous construction of the S^1 -equivariant Dirac operator (i.e., Dirac– Ramond operator) on the space of (mean zero) loops in R^d is given and its equivariant L^2 - index computed. Essential use is made of infinite tensor product representations of the canonical anticommutation relations algebra.
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