Abstract
I would like to explain what I mean by non-Lagrangian theories. There are two kinds of non-Lagragian theories. One is a non-Lagrangian theory with Lagrangians and the other a non-Lagrangian theory without Lagragians. The former theories do not make use of a Lagrangian explicitly, although the existence of a Lagrangian is assumed. The latter on the other hand do not even assume the existence of a Lagrangian. In the physics of high-energy particles, the non-Lagrangian theories without Lagrangian are becoming popular and I myself tried to formulate such a non-Lagrangian theory without success. The reason why non-Lagrangian theories are so difficult is that conservation laws do not follow from invariance. Let me give you an example. Take a coupled oscillator in one dimension.
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References
D. Lurié, Y. Takahshi, and H. Umezawa “Generalized Ward Identity and Unified Treatment of Conservation Laws,” J. Math. Phys. 7: 1478 (1966).
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© 1968 Springer Science+Business Media New York
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Takahashi, Y. (1968). Non-Lagrange Theories and Generalized Conservation Laws. In: Ramakrishnan, A. (eds) Symposia on Theoretical Physics and Mathematics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-5424-4_9
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DOI: https://doi.org/10.1007/978-1-4899-5424-4_9
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