# Tagged Questions

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### Actions that are not integrals

So far every action I've seen in physics has been an integral of a Lagrangian, be it a point particle: $$S = \int dt\ L$$ or fields (relativistic or not): $$S = \int d^4x\ \mathcal{L}$$ and so ...
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### Extrinsic Curvature variation

I have seen the post Explicit Variation of Gibbons-Hawking-York Boundary Term on variation of Gibbons-Hawking term, that was really helpful, however, I have problem evaluating $\delta K$ and getting ...
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### Are the partial derivatives of Lagrangian in the varied action functional derivatives?

In particle mechanics Lagrangian $L$ depends upon position, velocity (and may be explicitly on time), whereas in field theory the Lagrangian density ${\cal L}$ similarly (or analogously) depends upon ...
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### Why we do calculus of variation instead of finding maxima or miniama of function? [closed]

Why we do calculus of variation instead of finding maxima or minima of function? What is the difference between finding maxima or mimima i.e. critical point of a function and calculus of variation?
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### When is numerical value of Lagrangian evaluated on-shell a full differential?

I noticed recently that for many field equations, Lagrangian evaluated on-shell (i.e. using equations of motions) is a full derivative- a divergence or something, or in other words a boundary term. ...
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### Euler-Lagrange Equation with logarithmic potential

A particle moving towards the origin has initial conditions $x(t=0) = 1$ and $\dot{x}(t=0)=0$. If the Lagrangian is $$L:=\frac{m}{2}\dot{x}^2 -\frac{m}{2}\ln|x|$$ This should satisfy Euler ...
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### shape formed by a stiff string with ends pinched together [closed]

Suppose I have a string of length $L$ with a bending energy given by $$E=\frac{1}{2}\epsilon \int_0^L ds\, (\mathbf{R}''(s))^2$$ Let's say I form a bight with it by pinching the ends together, ...
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### Variational proof of the Hellmann-Feynman theorem

I use the following notation and definition for the (first) variation of some functional $E[\psi]$: \delta E[\psi][\delta\psi] := \lim_{\varepsilon \rightarrow 0} \frac{E[\psi + \...
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### Euler-Lagrange for simple scalar field (Peskin & Shroeder)

I'm reading Peskin & Schroeder and they give as a simple example the Lagrangian $$\mathcal{L} = \frac{1}{2} (\partial_\mu \phi)^2$$ First of all, I'm guessing that $(\partial_\mu \phi)^2$ is ...
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### Deriving Maxwell's equation from the Lagrangian of an electromagnetic field with a charge density $\rho$

I want to derive Maxwell's equation from the Lagrangian of an electromagnetic field with a charge density of $\rho$ The Lagrangian is given by L={1\over2}(\epsilon_0E^2-{1\over\mu}B^2)-\rho\phi+\...
I don't understand here what does the book mean by expanding in terms of $\delta{q}$ and $\delta{\dot{q}}$ can someone explain that part.