# Proca Definition and 13 Threads

Proca can be:

Alexandru Proca, Romanian physicist
Proca action, in physics, named after Alexandru Proca
Eugeniu Gh. Proca, Romanian physician
Nicolae Proca, Romanian footballer
Zeno Proca (1906–1936), Romanian chess player

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8. ### Tensor indices (proving Lorentz covariance)

Homework Statement [/B] So, I need to show Lorentz covariance of a Proca field E-L equation, conceptually I have no problems with this, I just have to make one final step that I cannot really justify. Homework Equations "Proca" (quotation marks because of the minus next to the mass part, I...
9. ### What are the Equations of Motion for a Proca Gauge Field in AdS Space?

Homework Statement Consider a massivegauge field in AdS_{d+1} space given by the action S=\int_{AdS} d^{d+1}x\sqrt{g}\left(\frac{1}{4}F_{\mu\nu}F^{\mu \nu}+\frac{m^2}{2}A_\mu A^\mu \right) a) Derive the equations of motion for A_\mu in the Poincaré patch of AdS_{d+1}. The metric is...
10. ### Proca Lagrangian (Math troubles with four vectors)

I'm reading Griffith's Elementary particles and I'm stuck on the math for one of the examples, could anyone show me what I'm missing or point me in the right direction? I attached a pdf (of the word doc I was using) that shows what I did so far since I'm really bad with LaTeX and it would've...
11. ### Derivation of the Proca equation from the Proca Lagrangian

How to show the Proca equation by using the given Proca Lagrangian? Surely, I know the Euler-Lagrange equation, but I can't solve this differentiation!(TT) The given Proca lagrangian is, \mathcal{L}=...
12. ### Deriving the EOM for Proca Lagrangian

Homework Statement Consider the Proca Lagrangian L=-\frac{1}{16\pi}F^2-\frac{1}{c}J_{\mu}A^{\mu}+\frac{M^2}{8\pi}A_{\mu}A^{\mu} in the Lorentz gauge \partial_{\mu}A^{\mu}=0 Find the equation of motion. Homework Equations F^2=F_{\mu\nu}F^{\mu\nu} The Attempt at a...
13. ### How Do You Derive the Propagator for the Proca Action?

Hi all, I'm stuck with this following problem: Homework Statement Consider the Proca action, S[A_\mu] = \int \, \mathrm d^4x \left[ - \frac14 F_{\mu\nu} F^{\mu\nu} + \frac12 m^2 A_\mu A^\mu \right] where F_{\mu\nu} = 2 \partial_{[\mu} A_{\nu]} is the anti-symmetric electromagnetic...