International Journal of Modern Physics A

The sinh–Gordon model with integrable boundary conditions is considered in low order perturbation theory. It is pointed out that results obtained by Ghoshal for the sine–Gordon breather reflection factors suggest an interesting dual relationship between models with different boundary conditions. Ghoshal's formula for the lightest breather is checked perturbatively to O(β²) in the special set of cases in which the ϕ→-ϕ symmetry is maintained. It is noted that the parametrization of the boundary potential which is natural for the semiclassical approximation also provides a good parametrizaiton at the "free-fermion" point.

We study the conformal properties of the multiconstraint KP hierarchy and its non-standard partner by covariantizing their corresponding Lax operators. The associated second Hamiltonian structures turn out to be nonlocal extensions of W_n algebra by some integer or half-integer spin fields depending on the order of the Lax operators. In particular, we show that the complicated second Hamiltonian structure of the nonstandard multiconstraint KP hierarchy can be simplified by factorizing its Lax operator to multiplication form. We then diagonalize this simplified Poisson matrix and obtain the free field realizations of its associated nonlocal algebras.

A class of finite GUT's in curved space–time is considered in connection with the cosmological inflation scenario. It is confirmed that the use of the running scalar-gravitational coupling constant in these models helps realizing a successful chaotic inflation. The analyses are made for some different sets of the models.

We construct integrals of motion (IM) for the sine–Gordon model with boundary at the free fermion (β²=4π) which correctly determine the boundary S matrix. The algebra of these IM ("boundary quantum group" at q=1) is a one-parameter family of infinite-dimensional subalgebras of twisted . We also propose the structure of the fractional-spin IM away from the free fermion point (β²≠4π).

We consider the possibility that neutrinos (but no other light fermions) are coupled very weakly to an extremely light scalar boson. We first analyze the simple problem of one generation of neutrino and show that, for ranges of parameters that are allowed by existing data, such a system can have serious consequences for the evolution of stars and could impact precision laboratory measurements. We discuss the extension to more generations and show that the general conclusion remains viable. Finally, we note that, should such a scalar field be present, experiments give information about effective masses, not the masses that arise in unified field theories.

After a summary of a recently proposed new type of instant form of dynamics (the Wigner-covariant rest-frame instant form), the reduced Hamilton equations in the covariant rest-frame Coulomb gauge for the isolated system of N scalar particles with pseudoclassical Grassmann-valued electric charges plus the electromagnetic field are studied. The Lienard–Wiechert potentials of the particles are evaluated and it is shown how the causality problems of the Abraham–Lorentz–Dirac equation are solved at the pseudoclassical level. Then, the covariant rest-frame description of scalar electrodynamics is given. Applying to it the Feshbach–Villars formalism, the connection with the particle plus electromagnetic field system is found.

Based on the technique of derivation of a theory, presented in out recent paper,¹ we investigated the properties of the derived quantum system. We show that the derived quantum system possesses the (nonanomalous) symmetries of the original one, and prove that the exact Green functions of the derived theory are expressed in terms of the semiclassically approximated Green functions of the original theory.

We consider an application of the overlap formalism to supersymmetric Yang–Mills theory in three dimensions. We extend the overlap formalism for 3D Dirac fermion to Majorana fermion and show that the parity invariance is exactly preserved, which ensures that the continuum limit is supersymmetric without fine tuning. For SU(N) gauge group, N must be taken to be even in order to make the theory free from global gauge anomaly. We also discuss how to obtain two-dimensional super Yang–Mills theory from the 3D theory through dimensional reduction on the lattice.

We discuss ε-expansion in curved space–time for asymptotically free and asymptotically nonfree theories. The existence of stable and unstable fixed points is investigated for fϕ⁴ theory and SU(2) gauge theory. It is shown that ε-expansion maybe compatible with aysmptotic freedom on special solutions of the RG equations in a special ase (supersymmetric theory). Using ε-expansion RG technique, the effective Lagrangian for covariantly constant gauge SU(2) field and effective potential for gauged NJL model are found in (4-ε)-dimensional curved space (in linear curvature approximation). The curvature-induced phase transitions from symmetric phase to asymmetric phase (chromomagnetic vacuum and chiral symmetry broken phase, respectively) are discussed for the above two models.

The deep inelastic scattering of neutrinos on unpolarized nucleons is considered in a generalized parton model which takes into account quark-clustering effects, modeled by diquarks. The diquark contributions are expected to be significant at small Q² values and to vanish asymptotically, and describe phenomenologically higher twist corrections. The most general case is studied, which includes both scalar and pseudovector diquarks inside the nucleons, as well as the contribution of scalar–vector and vector–scalar transitions. The resulting scaling violations are briefly discussed.