✎ Proca Equation [The Physics Travel Guide]

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====== Proca Equation ======

<note tip> $$ m^2 A^\rho =    \partial_\sigma ( \partial^\sigma A^\rho -  \partial^\rho  A^\sigma) \quad  \text { or } \quad  m^2 A^\rho =    \partial_\sigma F^{\sigma  \rho}  $$

-->Definitions#

* $\partial_{\sigma} $ denotes the partial derivative,
  * $m$ denotes the mass of the particle,
  * $A^\rho$ is either the wave function of the spin $1$ particle if we use the Proca equation in a particle theory, or describes the spin $1$ field if we work in a field theory. 
  * $F^{\sigma  \rho}$ is the electromagnetic field tensor: $F^{\sigma  \rho} \equiv \partial^\sigma A^\rho -  \partial^\rho  A^\sigma$.

<--

</note>

The Proca equation is a generalization of the [[equations:maxwell_equations|Maxwell equation]] for massive spin $1$ particles. Formulated differently, the Maxwell equation is only a special case of the Proca equation for massless particles/fields.

The Proca equation is important because it correctly describes massive spin $1$ particles/fields.

<note tip>
Explanations in this section should contain no formulas, but instead colloquial things like you would hear them during a coffee break or at a cocktail party.
</note>
  
<tabbox Student>

<note tip>
In this section things should be explained by analogy and with pictures and, if necessary, some formulas.
</note>
 
<tabbox Researcher>

<note tip>
The motto in this section is: //the higher the level of abstraction, the better//.
</note>

--> Example1#

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--> Example2:#

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</tabbox>

Please solve the following equation to prove you're human. 183 -13 = Please keep this field empty:

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