QUANTIZATION OF NONLINEAR FIELD-THEORIES

We examine the problem of the center-of-mass motion in nonlinear field theories that support classical static solutions. As a concrete example we consider the model of Goldstone and Jackiw. The total Hamiltonian is separated into three terms: one describing a free kink (baryon) moving with constant arbitrary (not necessarily small) velocity, a second term describing free fluctuations (mesons), and a third term describing the baryon-meson interaction. Total momentum conservation is ensured and the treatment is relativistically covariant. We present the classical theory and also a method which allows the construction of a quantized Hamiltonian and of asymptotic states consisting of one baryon and many mesons. The formalism can then be used for the calculation of S-matrix elements. The passage from the classical to the quantum theory requires the introduction of unphysical (ghost) states. The principles of the method can be applied to theories in higher space-time dimensions. © 1990 The American Physical Society.