Linked Questions

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2answers
152 views

Classical trajectories that are not a minimum of the action [duplicate]

Are there physically realizable dynamical systems where the true trajectory is not a minumum action trajectory? Formally, Lagrangian mechanics only requires that the trajectory be an extremum (or ...
2
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0answers
89 views

Principle of Most Action? [duplicate]

In Landau-Lifshitz - Vol 1. Mechanics, right after the introduction of the principle of leas action, there is the following comment: It should be mentioned that this formulation ($S = \int\limits_{...
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0answers
35 views

Extremum of the action functional [duplicate]

Is there an example where a classical particle follows a path of maximal action rather than that of minimum action?
1
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0answers
23 views

example from physics where the action of the physical trajectory has a saddlepoint? [duplicate]

It's a well established concept in various fields of physics that the action of the field / trajectory that becomes physically real, minimizes / maximizes the action functional. For the calculations, ...
6
votes
2answers
2k views

When is the principle of stationary action not the principle of least action?

I've only had a very brief introduction to Lagrangian mechanics. In a physics course I took last year, we briefly covered the principle of stationary action --- we looked at it, derived some equations ...
8
votes
2answers
1k views

Sign in front of QFT kinetic terms

I'd like to know if the sign in front of a kinetic term in QFT important. For the scalar field we conventionally write (in the $ + --- $ metric), \begin{equation} {\cal L} _{ kin} = \frac{1}{2} \...
4
votes
2answers
700 views

Action max, min, or saddle?

It is well known that $\delta S = 0$ lays the foundation for variational mechanics. But I am confused as to whether or not this S is a minimum, a maximum, or a saddle point. Some books address this ...
6
votes
1answer
386 views

Lack of Maslov index in the path integral formalism

Introduction Consider Feynman's famous path integral formula \begin{equation} K(x_a,x_b) = \int \mathcal{D}[x(t)] \exp \left[ \frac{i}{\hbar} \int_{t_a}^{t_b} dt \, \mathcal{L}(x(t),\dot{x}(t),t) \...
5
votes
2answers
142 views

Is Action Always “Locally” Least?

In general, I know it's true that the Principle of Least Action is more properly called the Principle of "Stationary" Action. However, there are results which seem to suggest that for sufficiently ...
2
votes
1answer
495 views

Why does overall action need to have an extremum?

Quoting from Landau's and Lifshitz' Mechanics : The integral ${\int\limits_{t_1}^{t_2}}L(q, \dot{q},t)\,dt$ for the entire path must have an extremum, but not necessarily a minimum. This, however,...
4
votes
1answer
99 views

Is action for free particle really minimal?

On my mechanics classes I have a problem: show, that the action for free non-relativistic particle $$S=\int\limits_{t_i}^{t_f}\frac{m\dot{x}^2}{2}dt\tag{1}$$ is really the least (but not maximal). ...
2
votes
1answer
239 views

Principle of Stationary Action and Euler-Lagrange Equation

Principle of Stationary Action: Given a mechanical system, there exists an action $S$ such that it is extremitized, or $\delta S=0$, for the actual motion of the system. $$S = \int_{t_1}^{...
0
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0answers
360 views

Is the principle of least action fully equivalent to the Euler-Lagrange equations?

I am citing from Landau and Lifschitz, this statement that will seem to you well-known, trivial, etc: "Between these positions, (i.e. $q_1$ and $q_2$) the system moves then in such a way that the ...
2
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0answers
42 views

Max & inflection point in the principle of least action [duplicate]

Short question: What is the physics interpretation of max & inflection points in the principle of least action? Long question: If $$L(q_1,q_2;t)=K-V$$ then let $$S = \int^{t_1}_{t_2} L(q_1,...