@article{e3ab522140d14774a675d053d8d79573,
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. Funding Information: The second author gratefully acknowledges financial support by the Alexander von Humboldt Stiftung. The warm hospitality of Prof. Luciano Tubaro and the Mathematics Department of the University of Trento, where part of this work was done, is also gratefully acknowledged.",
year = "2007",
month = jan,
doi = "10.1016/j.bulsci.2006.02.004",
language = "English",
volume = "131",
pages = "1--11",
journal = "Bulletin des Sciences Mathematiques",
issn = "0007-4497",
publisher = "Elsevier Masson SAS",
number = "1",
}