Can I say that the conjugate momentum defined by p_\phi \equiv \frac{\partial L}{\partial \dot{\phi}} is a covariant quantity?

[latex]p_{\phi} \equiv \frac{\partial L}{\partial \dot{\phi}}[/latex]

 

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[_latex]p_{\phi} \equiv \frac{\partial L}{\partial \dot{\phi}}[_/latex]

 

NB

CapnR - noparse tags still not working

What is [math]\phi[/math]? Is it a field or a coordinate? Also, what do you mean by "covariant?" Covariant in the sense that it's a covector, or in the sense that you want it to transform like a tensor? If [math]\phi[/math] is a coordinate then obviously [math]p_\phi[/math] doesn't transform like a tensor because it's just a component of [math]p_\mu[/math]. If [math]\phi[/math] is a field then there's an associated conjugate momentum field [math]\pi (\mathbf{x}) = \frac{\partial \mathcal{L}}{\partial \dot{\phi}(\mathbf{x})}[/math] where [math]\mathcal{L}[/math] is the Lagrangian density of the field.