Talk:Gupta–Bleuler formalism

The external link at the bottom of the page (http://daarb.narod.ru/qed-eng.html) appears to be a link to original research and not particularly relevant to the page. I'll remove it. K igor k (talk) 07:06, 2 December 2008 (UTC)[reply]

What is this in math

If we include gauge covariance, we realize a photon can have three possible polarizations (two transverse and one longitudinal (i.e. parallel to the 4-momentum)). This is given by the restriction $k\cdot \epsilon =0$ . However, the longitudinal component is merely unphysical gauge. While it would be nice to define a stricter restriction than the one given above which only leaves the two transverse components, it is easy to check that this can't be defined in a Lorentz covariant manner because what is transverse in one frame of reference isn't transverse anymore in another.

To resolve this difficulty, first look at the subspace with three polarizations. The sesquilinear form restricted to it is merely semidefinite, which is better than indefinite. In addition, the subspace with zero norm turns out to be none other than the gauge degrees of freedom. So, define the physical Hilbert space to be the quotient space of the three polarization subspace by its zero norm subspace. This space has a positive definite form, making it a true Hilbert space.

What is this in math? I can't understand it when it is expressed in everyday casual English without symbols or full description. The way it's written, it's more an evaluative summary for experts. 84.226.185.221 (talk) 13:29, 30 September 2015 (UTC)[reply]