# All Questions

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### Effect of Co-ordinate Change on Euler-Lagrange Equations for Scalar Fields

Consider a single scalar field $\phi$ on a manifold $\mathcal{M}$. Suppose in $\{x^\mu\}$ co-ordinates, the Lagrangian density is $\mathcal{L}(\phi, \frac{\partial \phi}{\partial x^\mu})$. This means ...
2answers
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1answer
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### What's the Lagrangian density means?

I remember from my classical mechanics class the Lagrangian function, but I don´t understand what's the meanning of the lagrangian density in General Relativity. What's the difference between one and ...
0answers
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### Showing path integral formalism is Lorentz-invariant without resorting to Hamiltonian formalism

I think people typically say that path integral formalism is manifestly Lorentz-invariant, because Lagrangian density is Lorentz-invariant. However, path formalism is typically defined with time ...
1answer
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2answers
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### With respect to what quantities do I vary Lagrangians in field theory?

I have recently been wondering, with respect to which quantities (covariant or contravariant) one should vary QFT Lagrangians and whether there is some rule regarding this. Let me give an example ...