Remark on the integration by parts formula for the φ 3 4-quantum field model

Sergio Albeverio; Song Liang; Boguslav Zegarlinski

doi:10.1142/S0219025706002275

Remark on the integration by parts formula for the φ ₃ ⁴-quantum field model

Sergio Albeverio, Song Liang, Boguslav Zegarlinski

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

6 Citations (Scopus)

Abstract

An integration by parts formula for the measure μ of the Euclidean φ ₃ ⁴-quantum field model is proven. It is also proven that the regularized logarithmic derivative of μ when the regularization is removed does not converge in L ²(μ).

Original language	English
Pages (from-to)	149-154
Number of pages	6
Journal	Infinite Dimensional Analysis, Quantum Probability and Related Topics
Volume	9
Issue number	1
DOIs	https://doi.org/10.1142/S0219025706002275
Publication status	Published - 2006 Mar
Externally published	Yes

Keywords

Continuum limits
Integration by parts formula
Quantum fields
φ -model

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Statistics and Probability
Mathematical Physics
Applied Mathematics

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title = "Remark on the integration by parts formula for the φ 3 4-quantum field model",

abstract = "An integration by parts formula for the measure μ of the Euclidean φ 3 4-quantum field model is proven. It is also proven that the regularized logarithmic derivative of μ when the regularization is removed does not converge in L 2(μ).",

keywords = "Continuum limits, Integration by parts formula, Quantum fields, φ -model",

author = "Sergio Albeverio and Song Liang and Boguslav Zegarlinski",

note = "Funding Information: We are very grateful to Professor Michael R{\"o}ckner for stimulating discussions. S. Liang was supported in part by Alexander von Humboldt Foundation, Germany and Grant-in-Aid for the Encouragement of Young Scientists (No. 15740057), Japan Society for the Promotion of Science.",

year = "2006",

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doi = "10.1142/S0219025706002275",

language = "English",

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T1 - Remark on the integration by parts formula for the φ 3 4-quantum field model

AU - Albeverio, Sergio

AU - Liang, Song

AU - Zegarlinski, Boguslav

N1 - Funding Information: We are very grateful to Professor Michael Röckner for stimulating discussions. S. Liang was supported in part by Alexander von Humboldt Foundation, Germany and Grant-in-Aid for the Encouragement of Young Scientists (No. 15740057), Japan Society for the Promotion of Science.

PY - 2006/3

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N2 - An integration by parts formula for the measure μ of the Euclidean φ 3 4-quantum field model is proven. It is also proven that the regularized logarithmic derivative of μ when the regularization is removed does not converge in L 2(μ).

AB - An integration by parts formula for the measure μ of the Euclidean φ 3 4-quantum field model is proven. It is also proven that the regularized logarithmic derivative of μ when the regularization is removed does not converge in L 2(μ).

KW - Continuum limits

KW - Integration by parts formula

KW - Quantum fields

KW - φ -model

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