Abstract
A self-contained, genuinely three-dimensional, monodromy-matrix based, nonperturbative, covariant path-integral approach to polynomial invariants of knots and links in the framework of (topological) quantum Chern–Simons field theory is proposed. The idea of ‘‘physical’’ observables represented by an auxiliary topological quantum-mechanical model in an external gauge field is introduced as a replacement for the limited notion of the Wilson loop. The possibility of using various generalizations of the Chern–Simons action (also higher-dimensional ones) as well as a purely functional language thereby arises. The theory is quantized in the framework of the antibracket-antifield formalism of Batalin and Vilkovisky, which is well adapted to this case. Using Stokes’s theorem and formal translational invariance of the path-integral measure we derive a monodromy matrix corresponding to an arbitrary pair of irreducible representations of an arbitrary semisimple Lie group.
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