Questions tagged [action]

Question 1

Consider a dynamical system with Lagrangian $L$ and configuration space $X$, we are interested in trajectories of this system over a time interval $q:[t_0,t_1]\rightarrow X$. When one has the ...

Question 2

In nonrelativistic mechanics, the action for a particle of mass $m$ moving in a potential $V(\mathbf{x})$ is $$ S_{\text{classical}} = \int \left(\frac{1}{2} m \mathbf{v}^2 - V(\mathbf{x}) \right) dt.\...

Question 3

I am computing the EOM of the Nambu-Goto action $$S[X] = -T\int d^2 \sigma \sqrt{-\det{(\partial_a X^\mu \partial_b X_\mu)}}$$ and I want to write this in a specific form using the second fundamental ...

Question 4

Given a particle in space, the EL equations give us a differential equation for determining how the partilce will move as time evolves. I am comfortable deriving a least action principle which ...

Question 5

The way I usually see the Hamilton-Jacobi equation derived goes like this. Start with an action principle $$ \mathcal{S}[q]=\int L(q,\dot{q})dt.$$ Evaluate this action on a solution to the Euler-...

Question 6

There is a lot of setup needed to ask this question, and numerous steps of which I'm not 100% sure, but my main question is contained in the last paragraph. Consider an antiferromagnetic quantum spin ...

Question 7

In some cases of motion, the action is not minimized, but only stationary. Is there an example of a system described by general relativity - thus by the Einstein-Hilbert action and thus the Einstein ...

Question 8

Why is the action of a quantum anharmonic oscillator equal to $$S = \int_{-\infty}^{\infty}m\frac{\dot{x}(t)^2}{2}-k\frac{x(t)^2}{2}-λ\frac{x(t)^4}{4!}dt$$ rather than $$S = \int_{-\infty}^{\infty}\...

Question 9

Kislev developed black hole metric in quintessence field by considering $T^t_t=T^r_r$ for energy momentum tesor corresponding to quintessence. Is there any action for the quintessence fild that gives ...

Question 10

I read that symmetry breaking is an indication that the solution of the equation of motion, the state, does not possess the same symmetry the action enjoys. Does this mean that in some physical ...

Question 11

A colleague once told me that measurements of action $A$ follow $$ \Delta A \geq \hbar/2 $$ Is this correct? In other words: Is measured action uncertain? Note that the question differs from the ...

Question 12

Consider the following $1D$ action of a particle $$S = \int dt ~t(\dot{x}-x)$$ The Euler-Lagrange equation to the above leads to $$\frac{d}{dt}\left(\frac{\partial L}{\partial \dot{x}}\right)-\frac{\...

Question 13

Can the Herglotz's variational principle be used to derive the fundamental thermodynamic relation? Or in general, does there exist some functional $\mathcal F[u]$ for which the variation set to zero: $...

Question 14

While exploring connections between quantum and cosmological scales, I found an exact numerical identity that seems surprisingly physical, not just coincidental. The ground state energy of the ...

Question 15

In this article by physicist Andrei Linde about quantum cosmology and inflation, when talking about constructing multiverse models, he indicates that cellular automata are not described by action ...

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Questions tagged [action]

Is there a version of Hamilton's Principle of Stationary Action when only initial conditions are known and the final end state is unknown? [duplicate]

How does the relativistic action logically follow from the nonrelativistic action, and why is proper time involved? [closed]

EOM of Nambu-Goto in second fundamental form

Reasoning for fixed endpoints when constructing the action from the EL equations

Hamilton-Jacobi confusion: What is the coordinate dependence of the Hamilton principal function?

The continuum limit of antiferromagnetic magnons

In general relativity can the Einstein-Hilbert action ever be stationary but not least, i.e. a saddle?

What is the correct action for an anharmonic oscillator?

Action for quintessence

The difference in the number of symmetries an action has and those that the on-shell action has (when the system is a manifold with a boundary)

Is there an uncertainty principle for action $A$ of the form $\Delta A ≥ \hbar/2$? [closed]

Equation of motion has no solution

Herglotz's variational principle in thermodynamics

$ ( \text{Hydrogen Ground State Energy} ) \times (\text{Age of Oldest Known Star}) = 1 \text{ Js}$ [closed]

Can Cellular Automata models be described by Lagrangians?

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