The discussion centers on the role of the time operator in the covariant quantization of string theory, as outlined in David Tong's paper (arXiv:0908.0333). The time operator is identified as a local field operator on the world sheet but is not considered an observable due to its dependence on unphysical local symmetries and constraints. Despite this limitation, it functions as an operator within an extended unconstrained space that includes the physical constrained space as a subset. For further insights, applications of this concept can be found in another referenced paper (arXiv:hep-th/0702060), particularly in Section 5.2.
PREREQUISITESThe discussion is beneficial for theoretical physicists, string theorists, and researchers interested in the foundations of quantum mechanics and the implications of time operators in advanced physics models.
But it is still an operator on an extended unconstrained space, containing the physical constrained space as a subspace.tom.stoer said: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.