Harry Lehmann

Chiral invariance and effective range expansion for pion pion scattering

Abstract The well-known low-energy theorems for the scattering of massless pions are extended to terms which are of fourth order in the pion momenta.

On the superpropagator of fields with exponential coupling

We define the vacuum expectation value of the time-ordered product of two exponentials of free fields as a distribution using minimal singularity as a criterion. The implication of this definition for an exponentially self-coupled scalar field is studied in second order of a perturbation expansion.

On the high-energy limit of ordinary dispersion relations

Abstract The connection between the high-energy behaviour of real and imaginary parts of scattering amplitudes is studied on the basis of dispersion relations for fixed momentum transfer.

Second-order effects in chiral-invariant pion lagrangians and the use of superpropagators

Abstract We examine the second-order corrections to the scattering amplitude and to the vector currents for chiral-invariant Lagrangians of massless pions. Standard renormalization theory leads to three undetermined parameters. We discuss the possibility of choosing definite values for these parameters by applying the technique of superpropagators. In an appendix we investigate the restrictions which follow if localizability of the perturbation expansion in powers of the interaction Lagrangian is required. It is shown that this condition determines the pion-field coordinates uniquely.

Classical models of confinement

Abstract We investigate the structure of classical models of confinement by analytic methods. The models considered involve just one abelian gauge field and can be viewed as non-linear versions of Maxwells theory. We study in detail the case of two opposite static point charges. A scaling law is found for small separations of the charges, while a perturbation treatment is developed for large separations. The results obtained for large separations include an exact evaluation of the first correction term to the linear potential and a classification of the asymptotic field configurations.

A new variant of symmetry breaking for quark mass matrices

Abstract We propose a definite pattern for the breaking of a discrete flavor symmetry of the quark mass matrices which is caused by the masses of the first two generations of quarks. We discuss the consequences of this proposal for the KM matrix.

Mikheyev–Smirnov–Wolfenstein Effect¶for Linear Electron Density

Abstract: When the electron density is a linear function of distance, it is known that the MSW equations for two neutrino species can be solved in terms of known functions. It is shown here that more generally, for any number of neutrino species, these MSW equations can be solved exactly in terms of single integrals. While these integrals cannot be expressed in terms of known functions, some of their simple properties are obtained. Application to the solar neutrino problem is briefly discussed.

A class of field theories in two-dimensional space-time with aU1×U1 symmetry

The derivative coupling of massless pseudoscalar neutral particles with a charged spinor field in two-dimensional space-time is reduced to a self-interacting spinor field and a free pseudoscalar field.More generally, it is shown that any given local field theory with a conserved vector current and without massless particles can be extended to a local theory with an additional pseudoscalar field and with aU1×U1 symmetry.