Related papers: An Alternative to Collective Coordinates
Collective coordinate methods are frequently applied to study dynamical properties of solitons. These methods simplify the field equations - typically partial differential equations - to ordinary differential equations for selected…
The introduction and quantization of a center-of-mass coordinate is demonstrated for the one-soliton sector of nonlinear field theories in (1+1) dimensions. The present approach strongly emphazises the gauge and BRST-symmetry aspects of…
Recently a linearized perturbation theory has been formulated for soliton sectors of quantum field theories. While it is more economical than alternative formalisms, such as collective coordinates, it is currently limited to solitons which…
An interferometer in which all of its components are treated as quantum bodies is examined with the standard interpretation and with a model in which its uncoupled spatially separated components act collectively. These models utilize…
We develop a consistent relativistic generalization of collective coordinate quantization of field theory solitons. Our principle of introducing collective coordinates is that the equations of motion of the collective coordinates ensure…
A field theoretical perturbation theory in inverse powers of coupling constant is developed which is manifestly covariant in every order of the expansion. A dilatation operator serves as an evolution dynamical one in a scale non-invariant…
In classical Lorentz-invariant field theories, localized soliton solutions necessarily break translation symmetry. In the corresponding quantum field theories, the position is quantized and, if the theory is not compactified, they have…
The emergence of violations of conformal invariance in the form of non-local operators in the two-dimensional action describing solitons inevitably leads to the introduction of collective coordinates as two dimensional ``wormhole…
A collective coordinate theory is develop for soliton ratchets in the damped discrete sine-Gordon model driven by a biharmonic force. An ansatz with two collective coordinates, namely the center and the width of the soliton, is assumed as…
Recently we have introduced a lightweight, perturbative approach to quantum solitons. Thus far, our approach has been largely limited to configurations consisting of a single soliton plus a finite number of mesons, whose classical limit is…
Various soliton-obstruction systems have been studied from analytical perspective. We have used collective coordinate to approach the dynamics of solitons as they meet a potential obstruction in a form of square barriers and holes for three…
We consider constructing the relativistic system of collective coordinates of a field theory soliton on the basis of a simple principle: The collective coordinates must be introduced into the static solution in such a way that the equation…
Noncommutative solitons are easier to find in a noncommutative field theory. Similarly, the one-loop quantum corrections to the mass of a noncommutative soliton are easier to compute, in a real scalar theory in 2+1 dimensions. We carry out…
We generalize effective energy variational techniques to study appropriately quantized solitonic field configurations. Our approach rests on collective quantization ideas and is specifically designed for the numerical evaluation of soliton…
The appearance of noncommuting spatial coordinates is studied in quantum systems containing a magnetic monopole and under the influence of a radial potential. We derive expressions for the commutators of the coordinates that have been…
The intuitive classical space-time picture breaks down in quantum gravity, which makes a comparison and the development of semiclassical techniques quite complicated. Using ingredients of the group averaging method to solve constraints one…
The forced soliton equation is the starting point for semiclassical computations with solitons away from the small momentum transfer regime. This paper develops necessary analytical and numerical tools for analyzing solutions to the forced…
In this series of lectures a method is developed to compute one-loop shifts to classical masses of kinks, multi-component kinks, and self-dual vortices. Canonical quantization is used to show that the mass shift induced by one-loop quantum…
We construct a modified non-BPS sine-Gordon theory which supports stable static kinks of arbitrary topological degree $N$. We use this toy model to study problems which are interesting for higher-dimensional soliton theories supporting…
We give a pedagogical introduction to Linearized Soliton Perturbation Theory (LSPT), a new and efficient tool for calculations involving quantum solitons. It is a Hamiltonian approach with a focus on explicitly constructing the soliton…