Maxwell’s equations instantaneous Hamiltonian

D. S. Kulyabov; A. V. Korolkova; L. A. Sevastianov; E. G. Eferina; T. R. Velieva; I. S. Zaryadov

doi:10.1117/12.2267938

14 April 2017 Maxwell’s equations instantaneous Hamiltonian

D. S. Kulyabov, A. V. Korolkova, L. A. Sevastianov, E. G. Eferina, T. R. Velieva, I. S. Zaryadov

Proceedings Volume 10337, Saratov Fall Meeting 2016: Laser Physics and Photonics XVII; and Computational Biophysics and Analysis of Biomedical Data III; 103370L (2017) https://doi.org/10.1117/12.2267938
Event: Saratov Fall Meeting 2016: Fourth International Symposium on Optics and Biophotonics, 2016, Saratov, Russian Federation

Abstract

The Hamiltonian formalism is extremely elegant and convenient to mechanics problems. However, its application to the classical field theories is a difficult task. In fact, you can set one to one correspondence between the Lagrangian and Hamiltonian in the case of hyperregular Lagrangian. It is impossible to do the same in field theories. In the case of irregular Lagrangian the Dirac–Bergman Hamiltonian formalism with constraints is usually used, and this leads to a number of certain difficulties. The paper proposes a reformulation of the problem to the case of a field without sources. This allows to use a instantaneous (symplectic) Hamiltonian formalism.

Citation Download Citation

D. S. Kulyabov, A. V. Korolkova, L. A. Sevastianov, E. G. Eferina, T. R. Velieva, and I. S. Zaryadov "Maxwell’s equations instantaneous Hamiltonian", Proc. SPIE 10337, Saratov Fall Meeting 2016: Laser Physics and Photonics XVII; and Computational Biophysics and Analysis of Biomedical Data III, 103370L (14 April 2017); https://doi.org/10.1117/12.2267938

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