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equations:proca_equation

# Proca Equation

$$m^2 A^\rho = \partial_\sigma ( \partial^\sigma A^\rho - \partial^\rho A^\sigma) \quad \text { or } \quad m^2 A^\rho = \partial_\sigma F^{\sigma \rho}$$
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: $F^{\sigma \rho} \equiv \partial^\sigma A^\rho - \partial^\rho A^\sigma$.

## Why is it interesting?

The Proca equation is a generalization of the 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.

## Layman

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.

## Student

In this section things should be explained by analogy and with pictures and, if necessary, some formulas.

## Researcher

The motto in this section is: the higher the level of abstraction, the better.

Example1
Example2:

## History

Contributing authors: