Quantum kink model and SU(2) symmetry: Spin interpretation and T-violation

In this paper we consider the class of exact solutions of the Schröedinger equation with the Razavi potential. By means of this we obtain some wavefunctions and mass spectra of the relativistic scalar field model with spontaneously broken symmetry near the static kink solution. Appearance of the bosons, which have two different spins, will be shown in the theory, thereby the additional breaking of discrete symmetry between the quantum mechanical kink particles with the opposite spins (i.e. the T -violation) takes place. PACS numbers: 02.20.Sv, 11.15.Ex, 11.27.+d At present, quantum field theories, having topologically non-trivial solutions are being intensively developed. Mass spectra of particles, which are predicted by such theories, can be received by means of the effective action formalism [1], which describes the low-energy dynamics of stable solutions taking into account small quantum oscillations. In particular, [2] was devoted to one such theory, namely, the d = 1 + 1 relativistic model φ with spontaneously broken symmetry. In that paper the nonperturbative quantum scalar field theory near the static kink solution, which can be interpreted as a quantum mechanical heavy particle, was considered. As a result of quantization of the kink’s internal degrees of freedom, the Schröedinger equation was received in terms of the raising and lowering operators. It was noted that, dependent on what ordering procedure for the operators was chosen, unitary non-equivalent theories take place. Regrettably, important aspects of the physical sense of such theories, as well as the question of obtaining exact solutions and mass spectra, remain open. In this paper we try to resolve these problems in particular. It became possible owning to the analogies found between the key equations of [2] and the wide class of the Schröedinger equations with the double-well potentials related to SU(2) symmetry [4, 5, 6], in particular, the Razavi potentials [7, 8, 9]. We start from the action S[φ] = ∫ dx    1 2 ∂φ ∂xi ∂φ ∂xi − 1 4 g [ φ − ( m g )2]2    (1) where φ(x, t) is the dimensionless scalar field, m and g are real parameters. The corresponding equations of motion have the kink solution [3] φc(x) = m g tanh mx √ 2 (2)