In 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: Field theory (mathematics), the theory of the algebraic concept of field. ... Mass is a property of physical objects that, roughly speaking, measures the amount of matter they contain. ... Spin has several meanings, including those primarily discussed as spinning: For spin in sub-atomic physics, see spin (physics) For the periodical, see Spin Magazine Computer: For unproductive repetition in a computer program, see spin (software) For finding bugs in multi-threaded code, see SPIN model checker For the computer... A field is an open land area, used for growing agricultural crops. ... In physics and mathematics, Minkowski space (or Minkowski spacetime) is the mathematical setting in which Einsteins theory of special relativity is most conveniently formulated. ... Vector field given by vectors of the form (-y, x) In mathematics a vector field is a construction in vector calculus which associates a vector to every point in Euclidean space. ... A Lagrangian of a dynamical system, named after Joseph Louis Lagrange, is a functional of the dynamical variables which concisely describes the equations of motion of the system. ...

(+---) signature The signature of a metric tensor (or more generally a nondegenerate symmetric bilinear form, thought of as quadratic form) is the number of positive and negative eigenvalues of the metric. ...

The Euler-Lagrange equation is In physics, the action principle is an assertion about the nature of motion from which the trajectory of an object subject to forces can be determined. ...

which is equivalent to

and

The Proca action is the gauge-fixed version of the Stückelberg action via the Higgs mechanism. The Higgs mechanism, originally discovered by the British physicist Peter Higgs (building on a previous suggestion by Philip Anderson in condensed matter physics), is the mechanism that gives masses to all elementary particles in particle physics. ...