# Construction of Kink Sectors for Two-Dimensional Quantum Field Theory Models. An Algebraic Approach

February 24, 1999

Several two-dimensional quantum field theory models have more than one vacuum
state. Familiar examples are the Sine-Gordon and the $\phi^4_2$-model. It is
known that in these models there are also states, called kink states, which
interpolate different vacua. A general construction scheme for kink states in
the framework of algebraic quantum field theory is developed in a previous
paper. However, for the application of this method, the crucial condition is
the split property for wedge algebras in the vacuum representations of the
considered models. It is believed that the vacuum representations of
$P(\phi)_2$-models fulfill this condition, but a rigorous proof is only known
for the massive free scalar field. Therefore, we investigate in a construction
of kink states which can directly be applied to a large class of quantum field
theory models, by making use of the properties of the dynamics of a $P(\phi)_2$
and Yukawa$_2$ models.

open access link

Rev.Math.Phys. 10 (1998) 851-891

Keywords:

kink states, interacting models, two-dimensional models