2024/05/26 by Jonathan Weitsman, Weitsman, Jonathan
Mathematics · Medicine · #Advanced Operator Algebra Research #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Medical Imaging Techniques and Applications #Quantum Algebra (math.QA) #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2405.16569
openalex publication_date 2024/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We use recent progress on Chern-Simons gauge theory in three dimensions [18] to give explicit, closed form formulas for the star product on some functions on the affine space \mathcal A(Σ) of (smooth) connections on the trivialized principal G-bundle on a compact, oriented two manifold Σ. These formulas give a close relation between knot invariants, such as the Kauffman bracket polynomial, and the Jones and HOMFLY polynomials, arising in Chern Simons gauge theory, and deformation quantization of \mathcal A(Σ). This relation echoes the relation between the manifold invariants of Witten [20] and Reshetikhin-Turaev [16] and \em geometric quantization of this space (or its symplectic quotient by the action of the gauge group). In our case this relation arises from explicit algebraic formulas arising from the (mathematically well-defined) functional integrals of [18].