International Journal of Modern Physics A

We study the problem of string propagation in a general instanton background for the case of the complete heterotic superstring. We define the concept of generalized hyper-Kähler manifolds and we relate it to (4,4) superconformal theories. We propose a generalized h-map construction that predicts a universal SU(6) symmetry for the modes of the string excitations moving in an instanton background. We also discuss the role of abstract N = 4 moduli and, applying it to the particular limit case of the solvable SU(2) × R instanton found by Callan et al., we show that it admits deformations and corresponds to a point in a 16-dimensional moduli space. The geometrical characterization of the other spaces in the same moduli space remains an open problem.

The path-integral quantization of chiral gravity is considered and the complete set of anomalies arising from both matter and ghost integrations is calculated. The effects of background charge are included and the results are related to the operator quantization. For those matter theories with exact quantum symmetry, the ghost contributions precisely cancel the matter-dependent anomalies. The results are extended to nonchiral gravity.

A method whereby the integral of a holomorphic projective twistor one-form may be re-expressed as the integral of an associated holomorphic projective twistor three-form is suggested. This method is used to represent the Penrose universal contour integral formulas for spinning zero-rest-mass free fields in terms of twistor diagrams.

Relativistic theory for the family of the principal meson trajectories was constructed. In the framework of relativistic quantum mechanics the coordinates of quarks should be noncommutative, which leads to a set of consistency conditions. Exploiting the geometrical basis of our model, we have obtained relativistic analogs of orbital and spin momenta and construct the gauge-invariant coordinates of physical particles. It makes possible to introduce the interaction terms in a simple geometrical way.

By considering corrections to the asymptotic scaling functions of the photon and electron in quantum electrodynamics with N_f flavors, we solve the skeleton Dyson equations at O(1/N_f) in the large N_f expansion at the d-dimensional critical point of the theory and deduce the critical exponent β′(g_c), in arbitrary dimensions, and subsequently present a method for computing higher order corrections to β(g).

A relativistic spin 1/2 particle quantum dynamics on the total space P of principle bundle, which is commonly attributed to Dirac monopole, is described. This dynamics is completely characterized with the help of additional U(1)-bundle P* which turned out to be connected with scattering problem. We formulate the representation in which the Hamiltonian has the most simple form. Lift of the Lorentz group to the total space is constructed.

We give the expressions for the energy of the nondispersive scalar and electromagnetic waves and the conditions that energy is finite.