Nonclassical analogs of solitons in quantum field theory
type: Item
instance of: scholarly article
title: Nonclassical analogs of solitons in quantum field theory
zbMATH Open document ID: 0802.58033
DOI: 10.1007/BF01016990
author: K. Sveshnikov
published in: Theoretical and Mathematical Physics
publication date: 1994-07-13T00:00:00Z
review text: A long-standing problem is whether solitons, i.e. particle-like solutions of classical nonlinear field equations, have quantum analogues, at least in a two-dimensional spacetime. Starting from a Lagrangian density \({1 \over 2} (\partial \varphi)^ 2 - \lambda^{-2} V (\lambda \varphi)\) and canonical commutation relations, the author shows by a scaling argument that \(\gamma = \lambda^ 2\) acts like an effective Planck constant. He then explores the semiclassical regime (expansion in \(\lambda)\) and finds a discrete series ``quantum solitons'', characterized by an integer \(N\). These states disappear when \(\lambda \to 0\): they have total energy \(O(\lambda)\). Still, they cannot be shown to exist in a rigorous sense for the quantum regime. The author also provides calculations of the profile functions and masses, and investigates the stability of these states in the \(\varphi^ 4\) model.
Mathematics Subject Classification ID: 37J35
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 81T40
Mathematics Subject Classification ID: 81Q20
Mathematics Subject Classification ID: 35Q51
zbMATH DE Number: 589557
zbMATH Keywords: quantum theory
zbMATH Keywords: semiclassical approximation
zbMATH Keywords: solitons
reviewed by: Gert Roepstorff
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf01016990
OpenAlex ID: W2077657708
description: scientific article; zbMATH DE number 589557