Proca action

Proca action

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}{16pi}(partial^mu A^ u-partial^ u A^mu)(partial_mu A_ u-partial_ u A_mu)+frac{m^2 c^2}{8pi hbar^2}A^ u A_ u.

The above presumes the metric signature (+---). Here, "c" is the speed of light and hbar is Dirac'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 (this is also called the Proca equation):

:partial_mu(partial^mu A^ u - partial^ u A^mu)+left(frac{mc}{hbar} ight)^2 A^ u=0

which is equivalent to the conjunction of

:left(partial_mu partial^mu+left(frac{mc}{hbar} ight)^2 ight)A_ u=0


:partial_mu A^mu=0 !

which is the Lorenz gauge condition. The Proca equation is closely related to the Klein-Gordon equation.

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.

Wikimedia Foundation. 2010.

Look at other dictionaries:

  • Stueckelberg action — In field theory, the Stueckelberg action (named after Ernst Stueckelberg) describes a massive spin 1 field as a R (the real numbers are the Lie algebra of U(1)) Yang Mills theory coupled to a real scalar field φ which takes on values in a real 1D …   Wikipedia

  • Variable speed of light — The variable speed of light (VSL) concept states that the speed of light in a vacuum, usually denoted by c , may not be constant in some cases. In most situations in condensed matter physics when light is traveling through a medium, it… …   Wikipedia

  • Second class constraints — In a constrained Hamiltonian system, a dynamical quantity is second class if its Poisson bracket with at least one constraint is nonvanishing. A constraint that has a nonzero Poisson bracket with at least one other constraint, then, is a second… …   Wikipedia

  • Covariant formulation of classical electromagnetism — Electromagnetism Electricity · …   Wikipedia

  • Noether's theorem — This article discusses Emmy Noether s first theorem, which derives conserved quantities from symmetries. For her related theorem on infinite dimensional Lie algebras and differential equations, see Noether s second theorem. For her unrelated… …   Wikipedia

  • Théorie de jauge sur réseau — Traduction à relire Lattice gauge theory → …   Wikipédia en Français

  • Romania — This article is about the modern country. For other uses, see Romania (disambiguation). Romania România …   Wikipedia

  • Louis de Broglie — Born 15 August 1892(1892 08 15) Dieppe, France …   Wikipedia

  • Klein–Gordon equation — Quantum mechanics Uncertainty principle …   Wikipedia

  • Janus — For other uses, see Janus (disambiguation). Bifrons redirects here. For other uses, see Bifrons (disambiguation). A statue representing Janus Bifrons in the Vatican Museums In ancient Roman religion and mythology, Janus is the god of beginnings… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”