The Polymer representation for the scalar field: A Wigner functional approach

Abstract: In this paper, we analyze the polymer representation of the real-valued scalar field theory within the deformation quantization formalism. Specifically, we obtain the polymer Wigner functional by taking the limit of Gaussian measures in the Schodinger representation. The limiting functional corresponds to the polymer representation derived by using algebraic methods such as the GNS construction, and the Fock quantization procedure.