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Results tagged with physics
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user 766
For questions about mathematical problems arising from physics, the natural science studying general properties of matter, radiation and energy.
9
votes
Maxwell equations as Euler-Lagrange equation without electromagnetic potential
The nature of the Maxwell equations (including their Lagrangian aspects) can be clarified by viewing these equations as part of a larger family of classical field theories in physics. … Because of this gauge invariance, it is initially tempting in all four cases to try to ignore the primary field as much as possible and try to formulate the physics in terms of the secondary fields (which …
- 114k
10
votes
Maxwell equations as Euler-Lagrange equation without electromagnetic potential
There is a trivial sense in which the answer is "yes": the solutions to the Maxwell equations are (formally, at least) the global minimisers to the functional
$$ \int\int |\mathrm{div} E|^2 + |\mathrm …
- 114k
17
votes
Accepted
Cone shaped solutions to wave equation
At human scales, the wavelength of visible light is so tiny (or equivalently, the frequency is so high) that the wave equation can be modeled by geometric optics (this is the high frequency limit of t …
- 114k