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equations:proca_equation
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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.
Examples
- Example1
- Example2:
FAQ
History
equations/proca_equation.1520936877.txt.gz · Last modified: 2018/03/13 10:27 (external edit)
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