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Sergio Albeverio, Song Liang

A Remark on different lattice approximations and continuum limits for -fields

Keywords: Lattice approximation, quantum fields, -model, , inequalities, continuum limits

Consider the lattice approximation of a -quantum field model with different lattice cutoffs a′ and a in the free and interacting parts, respectively. In [1] it was shown that the corresponding continuum limit measure exists if lim_a→0a′| log a|^5/4 < ∞ and it coincides with the original - field measure if lim_a→0 a′| log a|² < ∞. In this paper, a result is given indicating that the new continuum limit measure might be different from the original one if a′ is too big compared with a.

Random Operators and Stochastic Equations, Walter de Gruyter

Print ISSN: 0926-6364
Volume: 12, 12/2004
Pages: 313 - 318

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