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Questions tagged [action]

The action is the integral of the Lagrangian over time, or the integral of the Lagrangian Density over both time and space.

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Action principle and Functional derivative in CM

I want to extremize this well known action. $$S[\phi]=\int \mathcal{L}(\phi(t),\dot{\phi}(t)) dt$$ The result is also well known. It turns out to be E-L equation. The Action principle states that the ...
86 views

Stability of Schwarzschild and Reissner-Nordstrom spacetimes

I am interested to know what is the best we can say about stability of Schwarzschild and Reissner-Nordstrom black holes. I found some who study the behavior of perturbations that satisfy the ...
42 views

Convergence Property of Path-Integral

Let the action be $$S= \int \bigg\{ \frac{1}{2} \big(\frac{dX}{dt}\big)^2 - V(X) \bigg\} d\tau$$ and the corresponding Path-Integral $$Z= \int DX(t) e^{iS}.$$ Since the convergence is not clear we ...
57 views

Grassmann-even action

I am currently studying supersymmetric quantum mechanics with the help of the book Mirror Symmetry by Kentaro Hori (and others). On page 155 where they introduce Grassmann variables they say that the ...
31 views

How principle of least action? [duplicate]

I had learned the principle of least action.But I didn't get the motive behind taking the least action. Or why should the particle follow a path where it have a least action?
112 views

Derivation of Hamilton-Jacobi equation

I am trying my own way of deriving the Hamilton Jacobi equation $$\frac{\partial S}{\partial t} = -H \tag{1}$$ through direct variation. I think the difficulty of doing this is that the upper limit ...
63 views

Taylor expansion in derivation of Noether-theorem

In my classical mechanics lecture we derived the Noether-theorem for a coordinate transformation given by: $$q_i(t) \rightarrow q^{'}_i(t)=q_i(t) + \delta q_i(t) = q_i(t) + \lambda I_i(q,\dot q,t).$$...
327 views

Show two Lagrangians are equivalent

I need to show that these two Lagrangians are equivalent: \begin{align} L(\dot{x},\dot{y},x,y)&=\dot x^2+\dot y + x^2-y ,\\ \tilde{L}(\dot x, \dot y, x, y)&=\dot x^2+\dot y -2y^3. \end{align} ...