A remark on different lattice approximations and continuum limits for φ 4 2-fields

Sergio Albeverio; Song Liang

doi:10.1163/1569397042722346

A remark on different lattice approximations and continuum limits for φ ⁴ ₂-fields

Sergio Albeverio^*, Song Liang

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

Consider the lattice approximation of a φ ⁴ ₂-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→0 a′| log a| ^5/4 < ∞ and it coincides with the original φ ⁴ ₂-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.

Original language	English
Pages (from-to)	313-318
Number of pages	6
Journal	Random Operators and Stochastic Equations
Volume	12
Issue number	4
DOIs	https://doi.org/10.1163/1569397042722346
Publication status	Published - 2004
Externally published	Yes

Keywords

Continuum limits
Inequalities
Lattice approximation
Quantum fields
φ -model

ASJC Scopus subject areas

Analysis
Statistics and Probability

Access to Document

10.1163/1569397042722346

Cite this

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abstract = "Consider the lattice approximation of a φ 4 2-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→0 a′| log a| 5/4 < ∞ and it coincides with the original φ 4 2-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.",

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AU - Liang, Song

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AB - Consider the lattice approximation of a φ 4 2-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→0 a′| log a| 5/4 < ∞ and it coincides with the original φ 4 2-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.

KW - Continuum limits

KW - Inequalities

KW - Lattice approximation

KW - Quantum fields

KW - φ -model

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