| Lattice Approximation in the Stochastic Quantization of (04)2 Fields (2007) | |||||||||||
Abstract | |||||||||||
| The Parisi-Wu program of stochastic quantization [8] involves construction of a stochastic process which has a prescribed Euclidean quantum field measure as its invariant measure. This program was rigorously carried out for a finite volume (phi superscript 4) sub 2 measure by G. Jona-Lasinio and P. K. Mitter in [6]. These results were extended in [2], which also proves a finite to infinite volume limit theorem. The aim of this note is to prove a related limit theorem, viz., that of the finite dimensional processes obtained by stochastic quantization of the lattice (phi superscript 4) sub 2 fields to their continuum limit, i.e., the (phi superscript 4) sub 2 process of [2], [6]. The proof imitates that of the limit theorem of [2] in broad terms, though the technical details differ. Note that this limit theorem can also be construed as an alternative construction of the (phi superscript 4)sub 2 process - in finite volume. - The next section recalls the finite volume (phi superscript 4)sub 2 process. Section III summarizes the relevant facts about the lattice approximation to the (phi superscript 4)sub 2 field from Sections 9.5 and 9.6 of [4]. Section IV proves the limit theorem.. Sponsored in part by the Air Force Office of Scientific Research. Presented at the Meeting on Stochastic Partial Differential Equations and Applications II, held in Trento, Italy in Feb 1988. To appear in the Proceedings of Meeting on Stochastic Partial Differential Equations and Applications II, Feb 1988. | |||||||||||
Publication details | |||||||||||
| |||||||||||