I'm learning ray optics and feeling so confused by the definition of "Hamiltonian of light".(adsbygoogle = window.adsbygoogle || []).push({});

What I learned was that the "Hamiltonian of light" defined by [itex]H = n-|\vec{p}| = 0[/itex] indicates the momentum conservation, where [itex]n[/itex] is refractive index and [itex]\vec{p}[/itex] here is the canonical momentum. The canonical momentum is defined by [itex]\vec{p}=\frac{dL}{d\vec{r}'}=\frac{dL}{d(\frac{d\vec{r}}{ds})}[/itex] where [itex]\vec{r}[/itex] is the position vector, [itex]s[/itex] is the path length and [itex]L = n*|\vec{r}'| [/itex] is the Lagrangian.

My questions are

1. [itex]H[/itex] of light is conserved, but is momentum of light conversed? If so how is it indicated in the equations?

2. [itex]H[/itex] of classical mechanics is [itex]K+V[/itex]=kinective energy+potential energy, this is a clear physical meaning, but what does [itex]H[/itex] of light mean?

(Sorry for the long definition statement, I wanna make sure that people hold the same definition of things otherwise they can point out where I went wrong)

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# Relation between Hamiltonian of light ray and that of mechanics

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