- Tytuł:
- Some applications of Noether’s theorem
- Autorzy:
-
Montiel-Pérez, J. Yaljá
López-Bonilla, J.
López-Vázquez, R.
Vidal-Beltrán, S. - Tematy:
-
Complex Riemann-Silberstein vector
Duality rotations
Ignorable variable
Invariance of the action
Lanczos variational method
Linear differential equation of second order
Maxwell equations
Noether’s theorem
Variation of parameters
Variational symmetry - Pokaż więcej
- Wydawca:
- Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
- Powiązania:
- https://bibliotekanauki.pl/articles/1166045.pdf Link otwiera się w nowym oknie
- Opis:
- If the action S= ∫_(t_1)^(t_2)▒〖L(q,〗 (q,) ̇t) dt is invariant under the infinitesimal transformation t ̃=t+ε τ(q,t), q ̃_r= q_r+ε ξ_r (q,t),r=1,… ,n, with ε=constant ≪1, then the Noether’s theorem permits to construct the corresponding conserved quantity. The Lanczos approach employs to ε= q_(n+1) as a new degree of freedom, thus the Euler-Lagrange equation for this new variable gives the Noether’s constant of motion. Torres del Castillo and Rubalcava-García showed that each variational symmetry implies the existence of an ignorable coordinate; here we apply the Lanczos approach to the Noether’s theorem to motivate the principal relations of these authors. The Maxwell equations without sources are invariant under duality rotations, then we show that this invariance implies, via the Noether’s theorem, the continuity equation for the electromagnetic energy. Besides, we demonstrate that if we know one solution of p(x)y''+q(x)y'+r(x)y=0, then this Lanczos technique allows obtain the other solution of this homogeneous linear differential equation.
- Dostawca treści:
- Biblioteka Nauki
Artykuł