A note on the renormalized square of free quantum fields in space-time dimension d ≥ 4

Sergio Albeverio; Song Liang

doi:10.1016/j.bulsci.2006.02.004

A note on the renormalized square of free quantum fields in space-time dimension d ≥ 4

Sergio Albeverio, Song Liang

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

1 Citation (Scopus)

Abstract

We consider the renormalized or Wick square of the free quantum field, which is well-defined as a Hida distribution. It is known that this is a random variable for space-time dimension d ≤ 3. In this report, by considering the characteristic function, we show that this Wick square is not a random variable in dimension d ≥ 4.

Original language	English
Pages (from-to)	1-11
Number of pages	11
Journal	Bulletin des Sciences Mathematiques
Volume	131
Issue number	1
DOIs	https://doi.org/10.1016/j.bulsci.2006.02.004
Publication status	Published - 2007 Jan
Externally published	Yes

Keywords

Free field model
Hida distribution
Lévy-Khinchine representation
Quantum fields
Wick powers

ASJC Scopus subject areas

Mathematics(all)

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10.1016/j.bulsci.2006.02.004

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title = "A note on the renormalized square of free quantum fields in space-time dimension d ≥ 4",

abstract = "We consider the renormalized or Wick square of the free quantum field, which is well-defined as a Hida distribution. It is known that this is a random variable for space-time dimension d ≤ 3. In this report, by considering the characteristic function, we show that this Wick square is not a random variable in dimension d ≥ 4.",

keywords = "Free field model, Hida distribution, L{\'e}vy-Khinchine representation, Quantum fields, Wick powers",

author = "Sergio Albeverio and Song Liang",

note = "Funding Information: * Corresponding author. Contacting address: Song Liang, Graduate School of Information Sciences, Tohoku University, Aramaki Aza Aoba 09, Aoba-ku, Sendai 980-8579, Japan. E-mail address: liang@math.is.tohoku.ac.jp (S. Liang). 1 Financially 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 = "2007",

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doi = "10.1016/j.bulsci.2006.02.004",

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AU - Albeverio, Sergio

AU - Liang, Song

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N2 - We consider the renormalized or Wick square of the free quantum field, which is well-defined as a Hida distribution. It is known that this is a random variable for space-time dimension d ≤ 3. In this report, by considering the characteristic function, we show that this Wick square is not a random variable in dimension d ≥ 4.

AB - We consider the renormalized or Wick square of the free quantum field, which is well-defined as a Hida distribution. It is known that this is a random variable for space-time dimension d ≤ 3. In this report, by considering the characteristic function, we show that this Wick square is not a random variable in dimension d ≥ 4.

KW - Free field model

KW - Hida distribution

KW - Lévy-Khinchine representation

KW - Quantum fields

KW - Wick powers

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A note on the renormalized square of free quantum fields in space-time dimension d ≥ 4

Abstract

Keywords

ASJC Scopus subject areas

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