A geometric approach to the Lagrangian and Hamiltonian formalism of electrodynamics

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

doi:10.1117/12.2267944

14 April 2017 A geometric approach to the Lagrangian and Hamiltonian formalism of electrodynamics

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

Proceedings Volume 10337, Saratov Fall Meeting 2016: Laser Physics and Photonics XVII; and Computational Biophysics and Analysis of Biomedical Data III; 103370M (2017) https://doi.org/10.1117/12.2267944
Event: Saratov Fall Meeting 2016: Fourth International Symposium on Optics and Biophotonics, 2016, Saratov, Russian Federation

Abstract

In solving field problems, for example problems of electrodynamics, we commonly use the Lagrangian and Hamiltonian formalisms. Hamiltonian formalism of field theory has the advantage over the Lagrangian, which inherently contains a gauge condition. While the gauge condition is introduced ad hoc from some external reasons in the Lagrangian formalism. However, the use of the Hamiltonian formalism in the field theory is difficult due to the non-regularity of the field Lagrangian. We must use such variant of the Lagrangian and the Hamiltonian formalism, which would allow us to work with the field models, in particular, to solve the problem of electrodynamics. We suggest to use the modern differential geometry and the algebraic topology, in particular the theory of fiber bundles, as a mathematical apparatus. This apparatus leads to greater clarity in the understanding of mathematical structures, associated with physical and technical models. The usage the fiber bundles theory allows us to deepen and expand both the Lagrangian and the Hamiltonian formalism. We can detect a wide range of these formalisms. Also we can select the most appropriate formalism. Actually just using the fiber bundles formalism we can adequately solve the problems of the field theory, in particular the problems of electrodynamics.

Citation Download Citation

D. S. Kulyabov, A. V. Korolkova, L. A. Sevastianov, E. G. Eferina, and T. R. Velieva "A geometric approach to the Lagrangian and Hamiltonian formalism of electrodynamics", Proc. SPIE 10337, Saratov Fall Meeting 2016: Laser Physics and Photonics XVII; and Computational Biophysics and Analysis of Biomedical Data III, 103370M (14 April 2017); https://doi.org/10.1117/12.2267944

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available