“Loop the loop”

The applicability of the collective coordinate method (saddle-point approximation) for large-N planar models is discussed. Some unstated assumptions are clarified. Statements that Wilson loops form a complete set of gauge invariant operators are also examined and a set of generalized algebraic Mandelstam relations among Wilson loops is presented. The inclusion of loops that wind around themselves and cross many times, as independent variables, is stressed.     

“Almost direct” photons

Quantum chromodynamics has intensified the interest and enhanced the importance of measuring the production of direct photons in hadron collisions. We point out that lepton pairs of low invariant mass (m² < m²_ψ) provide an equally good probe for testing Q.C.D. Their experimental observation is not only easier, the relevant data may already exist.     

On “diagonal” Bianchi cosmologies

A list of the possible “diagonal” Bianchi cosmologies is given, with a proof that it is complete.     

Deformed “commutative” Chern–Simons’ system

Noncommutative Chern–Simons’ system is non-perturbatively investigated at a full deformed level. A deformed “commutative” phase space is found by a non-canonical change between two sets of deformed variables of noncommutative space. It is explored that in the “commutative” phase space all calculations are similar to the case in commutative space. Spectra of its energy and angular momentum of the Chern–Simons’ system are obtained at the full deformed level. The noncommutative–commutative correspondence is clearly showed. Formalism for the general dynamical system is briefly presented. Some subtle points are clarified.