We investigate classical strings defined by the Nambu-Goto action with the boundary term added. We demonstrate that the latter term has a significant bearing on the string dynamics. It is confirmed that new action terms that depend on higher order derivatives of string coordinates cannot be considered as continuous perturbations from the starting string functional. In the case the boundary term reduces to the Gauss-Bonnet term, a stability analysis is performed on the rotating rigid string solution. We determine the most generic solution that the fluctuations grow to. Longitudinal string excitations are found. The Regge trajectories are nonlinear.

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We present the study of parametric resonance in a one-dimensional cavity based on the analysis of classical optical paths. The recursive formulas for field energy are given. We separate the mechanism of particle production and the resonance amplification of radiation. The production of photons is a purely quantum effect described in terms of quantum anomalies in recursive formulas. The resonance enhancement is a classical phenomenon of focusing and amplifying beams of photons due to Döppler effect.

The problem of meson bound states with N f massive fermions in two dimensional quantum electrodynamics is discussed. We speculate about the spectrum of the lightest particles by means of the effective semiclassical description. In particular, the systems of fundamental fermions with SU (2) and SU (3) flavour symmetries broken by massive terms are investigated.

For one-dimensional vibrating cavity systems appearing in the standard illustration of the dynamical Casimir effect, we propose an approach to the construction of exact closed-form solutions. As new results, we obtain solutions that are given for arbitrary frequencies, amplitudes and time regions. In a broad range of parameters, a vibrating cavity model exhibits the general property of exponential instability. Marginal behaviour of the system manifests in a powerlike growth of radiated energy.