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Proca action
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Proca action : ウィキペディア英語版
Proca action

In physics, specifically field theory and particle physics, the Proca action describes a massive spin-1 field of mass ''m'' in Minkowski spacetime. The corresponding equation is a relativistic wave equation called the Proca equation.〔Particle Physics (2nd Edition), B.R. Martin, G. Shaw, Manchester Physics, John Wiley & Sons, 2008, ISBN 978-0-470-03294-7〕 The Proca action and equation are named after Romanian physicist Alexandru Proca.
This article uses the (+−−−) metric signature and tensor index notation in the language of 4-vectors.
==Lagrangian density==

The field involved is the 4-potential ''A''μ = (φ/''c'', A), where φ is the electric potential and A is the magnetic potential. The Lagrangian density is given by:
:\mathcal=-\frac(\partial^\mu A^\nu-\partial^\nu A^\mu)(\partial_\mu A_\nu-\partial_\nu A_\mu)+\fracA^\nu A_\nu.
where ''c'' is the speed of light, ''ħ'' is the reduced Planck constant, and ∂μ is the 4-gradient.

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