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Advances in High Energy Physics
Volume 2012 (2012), Article ID 415634, 33 pages
Research Article

DeWitt-Virasoro Construction in Tensor Representations

The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600113, India

Received 5 June 2012; Accepted 17 August 2012

Academic Editor: Richard J. Szabo

Copyright © 2012 Partha Mukhopadhyay. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We generalize the DeWitt-Virasoro (DWV) construction of arXiv:0912.3987 [hep-th] to tensor representations of higher ranks. A rank- tensor state, which is by itself coordinate invariant, is expanded in terms of position eigenstates that transform as tensors of the same rank. The representation of the momentum operator in these basis states is then obtained by generalizing DeWitt's argument (1952). Such a representation is written in terms of certain bivector of parallel displacement and its covariant derivatives. With this machinery at hand we find tensor representations of the DWV generators defined in the previous work. The results differ from those in spin-zero representation by additional terms involving the spin connection. However, we show that the DWV algebra found earlier as a scalar expectation value remains the same, as required by consistency, as all the additional contributions conspire to cancel in various ways. In particular, vanishing of the anomaly term requires the same condition of Ricci-flatness for the background.