Lattice Approximation in the Stochastic Quantization of (04)2 Fields
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1988
- Accession Number
- ADA459749
Entities
People
- Sanjoy K. Mitter
- Vivek S. Borkar
Organizations
- Tata Institute of Fundamental Research