Critical notes about Noether's theorem (Part I)

  • David CARFI’ University of California Riverside, USA


In this brief critical notes, we state and prove the classic Noether's theorem, in a language and in the mood of modern Differential Geometry. This modern approach, on one hand, wants to stimulate a dialogue between the classic Noether's theorem version users and the modern differential geometry developers, on the other hand, it opens the way for some extensions of the theorem, with possible physical insights about the matter.


[1] Arnold, V. I. (1989). Mathematical Methods of Classical Mechanics. Springer-Verlag. Second Edition.
[2] Carfì, D. (1989). Force fields and relativistic kinetic energy. Researchgate Paper, 1-6.
[3] Carfì, D. (2000). A new kind of infinite-dimensional differentiable manifolds. Researchgate Paper, 1-15.
[4] Carfì, D. (2001a). On some second order properties of torse forming vector fields. Differential Geometry - Dynamical Systems 3 (2), 7-12.
[5] Carfì, D. (2001b). SL-ultradifferentiable Manifolds. Analele Universitatii Bucuresti - Seria Informatica 50, 21-31. Proceedings of the Centellian of Vranceanu.
[6] Carfì, D. (2002). On some Types of Vector Fields on Manifolds with Levi-Civita structure. AAPP | Physical, Mathematical, and Natural Sciences 80 (1), 67-73.
[7] Carfì, D. (2003a). New frameworks for the one consumer model: exterior differential calculus. Researchgate Paper, 1-11.
[8] Carfì, D. (2003b). S-Differential Calculus for Microeconomics. Researchgate Paper, 1-13.
[9] Carfì, D. (2004). Tangent spaces on S-manifolds. Differential Geometry Dynamical Systems 6, 1-13.
[10] Carfì, D. (2008). Structures on the space of financial events. AAPP | Physical, Mathematical, and Natural Sciences 86 (2), 1-13.
[11] Carfì, D. (2009a). Fibrations for financial dynamical systems. Researchgate Paper, 1-23.
[12] Carfì, D. (2009b). Fibrations of financial events. Proceedings of the International Geometry Center - International Conference “Geometry in Odessa 2009", 25-30 May 2009, Odessa, Ukraine - 2 (3), 7-18. Available as MPRA Paper at
[13] Carfì, D. (2009c). Fibrations on the financial events plane. Researchgate Paper, 1-20.
[14] Carfì, D. (2011a). Fibred spaces and financial structures. Researchgate Paper, 1-31.
[15] Carfì, D. (2011b). Financial Lie groups. In Proceedings of the International Conference RIGA 2011. Bucharest University, Bucharest. Also available as Researchgate Paper pp. 1-18, at
[16] Carfì, D. (2011c). Lie group structures for financial evolutions. Researchgate Paper, 1-12.
[17] Carfì, D. (2017). Differential Geometry and Relativity Theories vol 1. – Tangent vectors, derivatives, paths, 1-forms, vector fields. Lambert Academic Publishing. ISBN: 978-3-330-02885-2.
[18] Carfì, D. and K. Cvetko-Vah (2011). Skew lattice structures on the financial events plane. Applied Sciences 13, 9-20.
[19] Curtis, W. and F. Miller (1985). Differential Manifolds and Theoretical Physics. Academic Press, Inc.
How to Cite
CARFI’, David. Critical notes about Noether's theorem (Part I). Journal of Mathematical Economics and Finance, [S.l.], v. 4, n. 2, p. 69-78, dec. 2018. ISSN 2458-0813. Available at: <>. Date accessed: 21 mar. 2019. doi: