Time operator in string theory

[atyy]

In covariant quantization of the string, say as in David Tong's http://arxiv.org/abs/0908.0333 (p28), time is an operator.

Is the time operator Hermitian, and does it correspond to an observable?

 

[tom.stoer]

This time operator is something like a local field operator defined on the world sheet. It can't be an observable b/c it's subject to (unphysical) local symmetries and related constraints.

 

[Demystifier]

This time operator is something like a local field operator defined on the world sheet. It can't be an observable b/c it's subject to (unphysical) local symmetries and related constraints.

But it is still an operator on an extended unconstrained space, containing the physical constrained space as a subspace.

For some applications of this idea see e.g.
http://arxiv.org/abs/hep-th/0702060
especially Sec. 5.2.