We discuss various aspects of resummed chiral perturbation theory, which was developed recently in order to consistently include the possibility of large vacuum fluctuations of the s̄s-pairs and the scenario with smaller value of the q̄q condensate for Nf = 3. The subtleties of this approach are illustrated using a concrete example of observables connected with πη scattering. This process seems t...

We generalize the analysis of [12] and develop a singular pseudodifferential calculus. The symbols that we consider do not satisfy the standard decay with respect to the frequency variables. We thus adopt a strategy based on the Calderón-Vaillancourt Theorem. The remainders in the symbolic calculus are bounded operators on L, whose norm is measured with respect to some small parameter. Our main...

This paper is example 5 in chapter 5. Let H be an n-cycle. A permutation s is H-admissible if Hs = H' where H' is an n-cycle. Here we define a 19 X 19 matrix, M, in the following way: We obtain the remainders modulo 100 of each of the smallest 342 odd primes. we obtain the remainders modulo 100 of each of the primes. They are placed in M according to the original value of each prime. Thus their...