Thank you for your comments. I had a look to Eq. (13) in http://de.arxiv.org/abs/hep-th/0202204 and this (the result of (13) shouldn't be $$ i \chi(x)/\sqrt(g_{00})$$ ?) just confirms that the formulation of the equal time commutation relations depends on the choice of $$ \Sigma $$. Even if one...
I have a question regarding the covariance of the equal time commutation relations in relativistic quantum field theory. In the case of a scalar field one has that the commutator is (see Peskin, pag. 28 eq. (2.53) )
$ [\phi(0), \phi(y)] = D(-y) - D(y) $
is an invariant function, which is zero...