# Can anybody identify these two equations for me? [closed]

I am trying to identify these two equations:

$$S=\int L\ \gamma \ d\tau \quad \tag{1}$$

$$\quad \frac{\partial L}{\partial \phi}-\partial_\mu\left[\frac{\partial L}{\partial(\partial_\mu \phi)}\right]=0\quad \tag{2}$$

They are probably from quantum mechanics or relativity, but I'm stuck.

• See this. – G. Smith Sep 6 '19 at 20:54
• In the absence of any existing comment indicating why a post might be downvoted, it's best to give some indication in a comment. A first time poster needs some indication of the problem. – StephenG Sep 6 '19 at 21:11
• @StephenG But for your edit to the question is it not $\left[...\right]$? Why for the 2nd equation is there these brackets? – Sebastiano Sep 6 '19 at 22:10

$$S$$ is the action and $$L$$ the Lagrangian describing some system.
The $$\gamma d\tau$$ seems to indicate that a single relativistic particle is being considered. (The $$\gamma$$ is its Lorentz factor and $$\tau$$ is its proper time.) More generally, there would just be a $$dt$$.
Requiring that the action be stationary ($$\delta S=0$$) under small variations of the dynamical variables in the Lagrangian leads to the Euler-Lagrange equations.
Your second equation is an example of such when the dynamical variable is a scalar field $$\phi(\mathbf{x},t)$$. In that case, the Lagrangian is a spatial integral over some Lagrangian density that depends on $$\phi$$ and its spatial and temporal derivatives.