This work addresses a specific technical question of relevance to canonical quantization of gravity using the so-called new variables and loop-based techniques of Ashtekar, Rovelli, and Smolin. In particular, certain ‘superselection laws’ that arise in current applications of these techniques to solving the diffeomorphism constraint are considered. Their status is elucidated by studying an anal...

We give a new proof of von Neumann's theorem, which states that the Schrödinger representation of the canonical commutation relations is (up to unitary equivalence) the only one, in the case of a finite number of canonical variables.

Using the previous construction of the geometrical representation (GR) of the centerless 1D, N = 4 extended Super Virasoro algebra, we construct the corresponding Short Distance Operation Product Expansions for the deformed version of the algebra. This algebra differs from the regular algebra by the addition of terms containing the Levi-Civita tensor. How this addition changes the super-commuta...