Proca action

From Wikipedia, the free encyclopedia

In physics, in the area of field theory, the Proca action describes a massive spin-1 field of mass m in Minkowski spacetime. The field involved is a real vector field A. The Lagrangian density is given by:

\mathcal{L}=-\frac{1}{4}(\partial^\mu A^\nu-\partial^\nu A^\mu)(\partial_\mu A_\nu-\partial_\nu A_\mu)+\frac{m^2 c^2}{2 \hbar^2}A^\mu A_\mu

The above presumes the metric signature (+---). Here, c is the speed of light and \hbar is Planck's constant. In the dimensionless units commonly employed in theoretical physics, these may both be taken to be one.

The Euler-Lagrange equation of motion is

\partial_\mu(\partial^\mu A^\nu - \partial^\nu A^\mu)+ \left(\frac{mc}{\hbar}\right)^2 A^\nu=0

which is equivalent to the conjunction of

\left(\partial_\mu \partial^\mu+ \left(\frac{mc}{\hbar}\right)^2\right)A_\nu=0

with

\partial_\mu A^\mu=0 \!

which is the Lorenz gauge condition.

The Proca action is the gauge-fixed version of the Stückelberg action via the Higgs mechanism.

Quantizing the Proca action requires the use of second class constraints.

 This quantum mechanics-related article is a stub. You can help Wikipedia by expanding it.
Retrieved from "http://en.wikipedia.org../../../p/r/o/Proca_action.html"