Relation Between Topological Field Theory and Quantum Field Theory
Abstract: Mathematical and
physical sciences are very interconnected in many problems of research. Usually
the mathematical science is a tool in physics research. However, certain case
of two space and one time dimensions of topology field theory such as Jones and
HOMFLY polynomials, can be computed by using quantum field theory method. In
this paper, first, we investigate polynomial invariants of SO(3) group case by
using braiding group concept. By using group concept, this polynomial has an
exact solution. Next, its solution will be compared by using calculation of
vacuum expectation value (VEV) of unknotted Wilson loop operators in 2+1 Chern-Simons-Witten (CSW) theory with the
same group. The above VEV is computed by quantum field theory method that has convergent series solution form as
function of coupling constant order. The computation result, up to third order shows
that the VEV of SO(3) group is identical to the polynomial invariants in the
same group.
Author: Asep Yoyo Wardaya,
Freddy Permana Zen, Jusak Sali Kosasih and Triyanta
Journl Code: jpmatematikagg120004
