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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2020, Volume 310, Pages 107–118
DOI: https://doi.org/10.4213/tm4109 (Mi tm4109) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Quantum Anomalies via Differential Properties of Lebesgue–Feynman Generalized Measures

John E. Gougha, Tudor S. Ratiubcd, Oleg G. Smolyanovef

a Institute of Mathematics, Physics and Computer Science, Aberystwyth University, Penglais, Aberystwyth, Ceredigion, SY23 3BZ, UK
b School of Mathematical Sciences, Shanghai Jiao Tong University, 800 Dongchuan Road, Minhang District, Shanghai, 200240, China
c Section de Mathématiques, Université de Genève, 2-4 rue du Lièvre, Case postale 64, 1211 Genève 4, Switzerland
d École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
e Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, 119991 Russia
f Moscow Institute of Physics and Technology (National Research University), Institutskii per. 9, Dolgoprudnyi, Moscow oblast, 141701 Russia
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DOI: https://doi.org/10.4213/tm4109
Abstract: We address the problem concerning the origin of quantum anomalies, which has been the source of disagreement in the literature. Our approach is novel as it is based on the differentiability properties of families of generalized measures. To this end, we introduce a space of test functions over a locally convex topological vector space, and define the concept of logarithmic derivatives of the corresponding generalized measures. In particular, we show that quantum anomalies are readily understood in terms of the differential properties of the Lebesgue–Feynman generalized measures (equivalently, of the Feynman path integrals). We formulate a precise definition for quantum anomalies in these terms.
Funding agency Grant number
National Natural Science Foundation of China 11871334
Swiss National Science Foundation NCCR SwissMAP
Lomonosov Moscow State University "Фундаментальные проблемы математики и механики"
Ministry of Education and Science of the Russian Federation 5-100
T. S. Ratiu was partially supported by the National Natural Science Foundation of China (grant no. 11871334) and the NCCR SwissMAP grant of the Swiss National Science Foundation. O. G. Smolyanov was supported by the Lomonosov Moscow State University (grant “Fundamental problems of mathematics and mechanics”) and by the Moscow Institute of Physics and Technology within the Russian Academic Excellence Project “5-100.”
Received: January 23, 2020
Revised: January 23, 2020
Accepted: June 16, 2020
English version:
Proceedings of the Steklov Institute of Mathematics, 2020, Volume 310, Pages 98–107
DOI: https://doi.org/10.1134/S0081543820050077
Bibliographic databases:
Document Type: Article
UDC: 517.1
Language: Russian
Citation: John E. Gough, Tudor S. Ratiu, Oleg G. Smolyanov, “Quantum Anomalies via Differential Properties of Lebesgue–Feynman Generalized Measures”, Selected issues of mathematics and mechanics, Collected papers. On the occasion of the 70th birthday of Academician Valery Vasil'evich Kozlov, Trudy Mat. Inst. Steklova, 310, Steklov Math. Inst., Moscow, 2020, 107–118; Proc. Steklov Inst. Math., 310 (2020), 98–107
Citation in format AMSBIB
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\bookinfo Collected papers. On the occasion of the 70th birthday of Academician Valery Vasil'evich Kozlov
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\pages 107--118
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    • This publication is cited in the following 1 articles:
    1. M. G. Shelakov, “Extension of the generalized Lebesgue–Feynman–Smolyanov measure on a Hilbert space”, Russ. J. Math. Phys., 30:1 (2023), 114  crossref  mathscinet
    Citing articles in Google Scholar: Russian citations, English citations
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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