Proposal for Divergence-Free Quantization of Covariant Scalar Fields

          @misc{ pirsa_PIRSA:10100049,
            doi = {10.48660/10100049},
            url = {https://pirsa.org/10100049},
            author = {Klauder, John},
            keywords = {Quantum Gravity},
            language = {en},
            title = {Proposal for Divergence-Free Quantization of Covariant Scalar Fields},
            publisher = {Perimeter Institute},
            year = {2010},
            month = {oct},
            note = {PIRSA:10100049 see, \url{https://pirsa.org}}
          }
          

Abstract

Guided by idealized but soluble nonrenormalizable models, a nontraditional proposal for the quantization of covariant scalar field theories is advanced, which achieves a term-by-term, divergence-free perturbation analysis of interacting models expanded about a suitable pseudofree theory [differing from a free theory by an $O(\hbar^2)$ term]. This procedure not only provides acceptable solutions for models for which no acceptable solution currently exists, e.g., $\varphi^4_n$, for spacetime dimension $n\ge4$, but offers a new, divergence-free solution, for less-singular models as well, e.g., $\varphi^4_n$, for $n=2,3$.