Using perturbative methods we derive new results for the spectrum and correlation functions of the general Z Z 3 -chiral Potts quantum chain in the massive low-temperature phase. Explicit calculations of the ground state energy and the first excitations in the zero momentum sector give excellent approximations and confirm the general statement that the spectrum in the low-temperature phase of general Z Z n -spin quantum chains is identical to one in the high-temperature phase where the rôle of charge and boundary conditions are interchanged. Using a perturbative expansion of the ground state for the Z Z 3 model we are able to gain some insight in correlation functions. We argue that they might be oscillating and give estimates for the oscillation length as well as the correlation length.

The model of the bosonic string with the Nambu-Goto action extended by the term proportional to the external curvature of the world sheet is explored. The external curvature of the world sheet is determined by the second order derivatives of the string coordinates. Thus, a modified Lagrangian is the singular Lagrangian of second order. The canonical variables for this theory are introduced, constraints are found and the Hamiltonian formulation of the classical dynamics in this theory is constructed. The transition to the quantum theory is briefly discussed.

The derivation of the Glauber type representation for the high energy scattering amplitude of particles of spin 1/2 is given within the framework of the Dirac equation in the Foldy Wouthuysen (FW) representation and two-component formalism. The differential cross sections on the Yukawa and Gaussian potentials are also considered and discussed.Comment: 16 pages, 4 figure

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