Ap. Balachandran et P. Teotoniosobrinho, VERTEX OPERATORS FOR THE BF SYSTEM AND ITS SPIN STATISTICS THEOREMS, International journal of modern physics A, 9(10), 1994, pp. 1569-1629
Let B and F = 1/2F(munu)dx(mu) AND dx(nu) be two-forms, F(munu) being
the field strength of an Abelian connection A. The topological BF syst
em is given by the integral of B AND F. With ''kinetic energy'' terms
added for B and A, it generates a mass for A, thereby suggesting an al
ternative to the Higgs mechanism, and also gives the London equations.
The BF action, being the large length and time scale limit of this au
gmented action, is thus of physical interest. In earlier work, it has
been studied on spatial manifolds SIGMA with boundaries partial deriva
tive SIGMA, and the existence of edge states localized at partial deri
vative SIGMA has been established. They are analogous to the conformal
family of edge states to be found in a Chern-Simons theory in a disc.
Here we introduce charges and vortices (thin flux tubes) as sources i
n the BF system and show that they acquire an infinite number of spin
excitations due to renormalization, just as a charge coupled to a Cher
n-Simons potential acquires a conformal family of spin excitations. Fo
r a vortex, these spins are transverse and attached to each of its poi
nts, so that it resembles a ribbon. Vertex operators for the creation
of these sources are constructed and interpreted in terms of a Wilson
integral involving A and a similar integral involving B. The standard
spin-statistics theorem is proved for these sources. A new spin-statis
tics theorem, showing the equality of the ''interchange'' of two ident
ical vortex loops and 2pi rotation of the transverse spins of a consti
tuent vortex, is established. Aharonov-Bohm interactions of charges an
d vortices are studied. The existence of topologically nontrivial vort
ex spins is pointed out and their vertex operators are also discussed.