John R. Klauder
Proposal for Divergence-Free Quantization of Covariant Scalar Fields
Preprint series: ESI preprints

MSC:

81T15 Perturbative methods of renormalization

81T70 Quantization in field theory; cohomological methods, See also {58F06}

PACS: 03.65.Db,11.10.-z,11.10.Kk
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 $\hbar$ 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 $n=2,3$.