- #1

- 165

- 1

Also, could you give a concise explanation of light-cone variables?

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter Demon117
- Start date

- #1

- 165

- 1

Also, could you give a concise explanation of light-cone variables?

- #2

Nugatory

Mentor

- 13,318

- 6,250

- #3

tom.stoer

Science Advisor

- 5,766

- 162

There are two key-ideas:

- the light-cone frame does is some sense correspond to the infinite momentum frame

- on the light-cone the dispersion relation becomes trivial

However the light-cone frame is singular, and afaik there is no fully consistent quantization.

- #4

- 5,830

- 1,136

One of the most important features of the Light Cone of an event is that it invariantly encodes the Causal Relations of that event with other events, which [in my opinion] is the most important feature of Einsteinian relativity (which was first put into this spacetime framework by Minkowski). For example, look at the diagrams on p. 89 of Geroch's "General Relativity from A to B" books.google.com/books?id=rwPDssnbHPEC&lpg=PP1&pg=PA89#v=onepage&q=light-cone&f=false

Light-Cone variables are associated with a non-rectangular coordinate system, where the coordinate axes are along the light cone. In 1+1 spacetime, instead of (t,x), we have instead (u,v) where u=t+x and v=t-x [in my signature convention and my choice of scale-factor (some use, e.g. , (t+x)/2 or (t+x)/sqrt(2) )]. One key feature of these axes is that they are eigenvectors of the Lorentz Boost. The Lorentz Boost looks very simple in Light-Cone variables.... it is diagonal... and the two entries (i.e. the eigenvalues) are reciprocals of each other [since the boost has determinant 1]. (The eigenvalues are the Doppler factors.)

The wave-operator in 1+1 spacetime in light-cone variables immediately gives http://mathworld.wolfram.com/dAlembertsSolution.html .

My avatar is a ticking light-clock. The future-light-cone of tick 1 intersects and reflects off the worldtube of a inertial circular light-clock and refocuses back to tick 2 (along the past-light-cone of tick 2).

Share: