No abstract

We prove that any gauged WZNW model has a Lax pair representation, and give explicitly the general solution of the classical equations of motion of the SL(2,R)/U(1) theory. We calculate the symplectic structure of this solution by solving a differential equation of the Gelfand-Dikii type with initial state conditions at infinity, and transform the canonical physical fields non-locally onto canonical free fields. The results will, finally, be collected in a local Bäcklund transformation. These calculations prepare the theory for an exact canonical quantization.God does not care about our mathematical difficulties. He integrates empirically.Albert Einstein

Gauged WZNW models are integrable conformal field theories. We integrate the classical SL(2,R)/U(1) theory with periodic boundary conditions, which describes closed strings moving in a curved targetspace geometry. We calculate its Poisson bracket structure by solving an initial state problem. The results differ from previous fieldtheoretic calculations due to zero modes. For a future exact canonical quantization the physical fields are (non-locally) transformed onto canonical free fields.

We establish a novel representation of arbitrary Euler-Zagier sums in terms of weighted vacuum graphs. This representation uses a toy quantum field theory with infinitely many propagators and interaction vertices. The propagators involve Bernoulli polynomials and Clausen functions to arbitrary orders. The Feynman integrals of this model can be decomposed in terms of a vertex algebra whose structure we investigate. We derive a large class of relations between multiple zeta values, of arbitrary lengths and weights, using only a certain set of graphical manipulations on Feynman diagrams. Further uses and possible generalizations of the model are pointed out.

826WAVELENGTH DEPENDENCE OF REFLECTIVITY (tan OB) 2 dependence of the reflectivity which holds for the kinematical limit is also satisfied in the range of the vibration amplitudes above the value Uo*. This is in agreement with our theoretical prediction based on (18).The authors are grateful to Dr R. Michalec for kindly lending the quartz crystals and to Mr A. Dvorak for his help with the preparation of the manuscript. Concluding remarksWe have investigated the dependence on the neutron wavelength of the integrated reflectivity of perfect and nearly perfect vibrating crystals in symmetrical diffraction geometries, the vibration vector u being always parallel to the diffraction vector h. We have verified the predictions of the wave-optical theory developed for the Bragg case and which is valid for any value of the vibration amplitude, from the perfect crystal to the kinematical limit. In the Laue case, our measurements could be used to discuss the rather large range of validity of (18)