Soliton quantization in lattice field theories

Abstract

Quantization of solitons in terms of Euclidean region functional integrals is developed, and Osterwalder-Schrader reconstruction is extended to theories with topological solitons. The quantization method is applied to several lattice field theories with solitons, and the particle structure in the soliton sectors of such theories is analyzed. A construction of magnetic monopoles in the fourdimensional, compact t/(l)-model, in the QED phase, is indicated as well.

A disorder analysis of the Ising model

“…In a few models the transformation to the dual is known analytically (the Ising model, the U(1) model with Villain action [3], the 3d XY model). In other theories duality is expected to be at work, but its presence has only been tested numerically [4][5][6][7][8][9].…”

String representation of Abelian Higgs theory and Aharonov-Bohm effect on the lattice

“…The gauge invariant operator Φ c (x) creates a scalar charged particle at point x, together with the photon cloud surrounding it. Our construction of string creation operators [11] is based on the same idea, and is quite similar to the construction of soliton creation operators suggested by Fröhlich and Marchetti [12]. It is convenient to consider the model dual to the original one (1).…”

Understanding Color Confinement

“…This is what happens in many models of statistical mechanics, like the 2d Ising model [3], the 3d X − Y model [4], the lattice U(1) gauge theory [5] [6]. The nature of the excitations is determined by the dimensions of space.…”