Geodesic
Quantum Anomalies via Differential Properties of Lebesgue--Feynman Generalized Measures
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Selected issues of mathematics and mechanics, Tome 310 (2020), pp. 107-118

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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. 
@article{TM_2020_310_a6,
     author = {John E. Gough and Tudor S. Ratiu and Oleg G. Smolyanov},
     title = {Quantum {Anomalies} via {Differential} {Properties} of {Lebesgue--Feynman} {Generalized} {Measures}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {107--118},
     publisher = {mathdoc},
     volume = {310},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2020_310_a6/}
}
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John E. Gough; Tudor S. Ratiu; Oleg G. Smolyanov. Quantum Anomalies via Differential Properties of Lebesgue--Feynman Generalized Measures. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Selected issues of mathematics and mechanics, Tome 310 (2020), pp. 107-118. http://geodesic.mathdoc.fr/item/TM_2020_310_a6/