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

learn more… | top users | synonyms

3
votes
2answers
108 views

What exactly is the Action? (Learning lagrangian)

I have been trying to wrap my head around lagrangian mechanics but I find some parts confusing. For example, what exactly is action and why is it defined by the Kinetic energy minus the potential ...
5
votes
2answers
496 views

Why don't all free particles lose their kinetic energy?

I'm currently studying Action. I've been reading about how a particle has particular probabilities of ending at an infinite number of events. Say I have a free particle that isn't experiencing any ...
0
votes
1answer
53 views

On the connection between forces and the principle of stationary action

Feynman tries to account for the relation between the principle of stationary action, which is a statement about the whole path of a particle, and Newton's second law, which is a statement about the ...
0
votes
1answer
63 views

Finding the action of a discretized Lagrangian

I am trying to find the action associated with the Lagrangian density $$ \mathcal{L} = \frac{1}{2}\left( \frac{\partial\phi}{\partial x} \right)^2 + \frac{1}{2}m^2\phi^2. \tag{1} $$ I am supposed to ...
0
votes
1answer
39 views

Physical significance of omitting a purely time dependent term from a Lagrangian

For a simple pendulum whose point of support moves on a vertical circle of radius $a$ with constant frequency $\gamma$, you can write the Lagrangian down. The potential energy can be written as ...
0
votes
1answer
41 views

3-cylinder surface element (Poisson's “A Relativist's Toolkit”)

From Poisson's "A Relativist's Toolkit": he introduces the non-dynamical term $$ S_0=\frac{1}{8\pi}\int_{\partial\Omega}\epsilon K\sqrt{\lvert h\rvert}d^3x $$ in the GR action, where $h$ is the ...
1
vote
3answers
82 views

The Nambu-Goto action how do we know the Hamilton's principle applies?

I am reading 'A first course in string theory' by Barton Zwiebach (2ed) on page 112 he comes up (after a small derivation) the action formula: $$S=-\frac{T_0}{c} \int d\tau d \sigma \sqrt{-\gamma}.$$ ...
4
votes
2answers
215 views

Why does the non-linearity of the string action prohibit stretching due to strong excitations?

From 't Hooft's String Theory lecture notes on page 8 (paraphrased): To understand hadronic particles as excited states of strings, we have to study the dynamical properties of these strings, and ...
-3
votes
0answers
48 views

How to write the Lagrangian for a body that exhibits gravitation?

Can anyone tell me how one actually goes about writing the Lagrangian for a mass that exhibits gravity? If I wanted to write the Lagrangian for, say, a spherical mass in space that curves the ...
2
votes
0answers
35 views

Help me calculate the Euclidean action of a gravitating system!

I recently read Gibbons and Hawking's paper Action integrals and partition functions in quantum gravity, Phys. Rev. D 15 (1977) 2752. I am interested in repeating their calculations. It is fairly ...
0
votes
1answer
36 views

Reversing time for a closed system of particles

For a closed system of particles, the lagrangian in classical mechanics is $$L=\sum \frac{1}{2}mv_a^2 - U(\mathbf{r_1},\mathbf{r_2}, \cdots)$$ For an arbitrary position function $x(t)$, to see the ...
10
votes
6answers
2k views

Entropy and the principle of least action

Is there any link between the law of maximum entropy and the principle of least action. Is it possible to derive one from the other ?
1
vote
2answers
75 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 ...
4
votes
4answers
309 views

Geodesic Equation from variation: Is the squared lagrangian equivalent?

It is well known that geodesics on some manifold $M$, covered by some coordinates ${x_\mu}$, say with a Riemannian metric can be obtained by an action principle . Let $C$ be curve $\mathbb{R} \to M$, ...
11
votes
1answer
909 views

Do an action and its Euler-Lagrange equations have the same symmetries?

Assume a certain action $S$ with certain symmetries, from which according to the Lagrangian formalism, the equations of motion (EOM) of the system are the corresponding Euler-Lagrange equations. Can ...
1
vote
1answer
54 views

Derivation of an ordinary, Lagrangian/Hamiltonian and action formulation

I am confused as to how the different formulations in physics are derived. In many fields of physics, we usually begin with an ordinary formulation (e.g Newton's Laws in classical mechanics), and ...
18
votes
3answers
4k views

Deriving the Lagrangian for a free particle

I'm a newbie in physics. Sorry, if the following questions are dumb. I began reading "Mechanics" by Landau and Lifshitz recently and hit a few roadblocks right away. Proving that a free particle ...
2
votes
3answers
73 views

Hamilton's Principle - achieving Hamilton equations

Consider the action function: $$\mathcal{S}(t)=\int_{t_1}^{t_2}\mathcal{L}(q_i,\dot{q_i},t) dt$$ where $\mathcal{L}$ is the Lagrangian of the system. The Hamiltonian is defined by the following ...
4
votes
1answer
724 views

Conversion of the Polyakov action into the Nambo-Goto action?

I've read that the Polyakov action using an intrinsic metric $h_{\alpha\beta}$ $$\tag{1} S_P ~=~ -\frac{T}{2}\int d^2 \sigma \sqrt{-h}h^{\alpha\beta} \partial_{\alpha}X^{\mu}\partial_{\beta}X^{\nu} ...
0
votes
0answers
36 views

Does the principle of stationary action always work? [duplicate]

Give some Lagrangian we use the principle of stationary action to find the desired euqations of motion for something (e.g. a field). A lot of modern physics seems to be based on the principle of ...
2
votes
1answer
116 views

Does Conformal Invariance of the Polyakov Action in Conformal Gauge imply Conformal Invariance of the Pre-gauge-fixed Polyakov Action?

In bosonic string theory the Polyakov action can be put in into conformal gauge. It is then possible to show that the resulting gauge fixed action is conformally invariant. Actually it's shown that ...
4
votes
1answer
109 views

How does one express a Lagrangian and Action in the language of forms?

In Lipschitzs Classical Mechanics a Lagrangian is defined as: $L(q,q',t)$ for some trajectory $q(t)$ of a particle And the action is defined as: $S:=\int^a_b L(q,q',t) dt$ How does one ...
2
votes
1answer
60 views

Proving independence of the lagrangian on position of a free particle using the euler-lagrange equation

I asked a similar question some time back but am trying to work this from another angle. In deriving the lagrangian of a free particle, we use the homogeneity of space to conclude that the lagrangian ...
1
vote
1answer
62 views

Equation of motion of an auxiliary field

I'm a newbie in the field of QFT and SUSY, so I'm warning you: this might be a stupid question. I'm working with auxiliary fields to describe supersymmetric models and I understand that upon ...
0
votes
1answer
53 views

Deriving lagrangian of a free particle - How do you arrive at Lagrangian independency conclusions

I guess this question has been asked before, but I'm looking at a slightly different aspect. I'm reading Landau's book on classical mechanics. In deriving the lagrangian for a free particle, I ...
2
votes
0answers
59 views

Decoupling of generalized coordinates in lagrangian

Say you have a lagrangian $L$ for a system of 2 degrees of freedom. The action, S is: $S[y,z] = \int_{t_1}^{t_2} L(t,y,y',z,z')\,dt \tag{1}$ If $y$ and $z$ are associated with two parts of the ...
1
vote
2answers
39 views

If I flex my arm, where is the “equal and opposite” reaction?

In my sight, nothing happens at all. Is the opposite reaction pressure applied to my bones? It certainly seems so; however, since I flex my arms in a curve, shouldn't the opposite reaction direction ...
0
votes
1answer
45 views

Information contained in Lagrangians and actions [duplicate]

I've been looking into analytical mechanics with the intention of finding out more about Lagrangians and actions. As far as I currently understand it, the Lagrangian is formed with positions and ...
4
votes
3answers
398 views

Calculating the (on-shell) action of a free particle

I am having difficulty with the first problem from Feynman and Hibbs' book. For a free particle $L = (m/2)\dot{x}^2$. Show that the (on-shell) action $S_{cl}$ corresponding to the classical ...
1
vote
1answer
59 views

Formulating a symplectic integrator for a non-local Hamiltonian

I recently asked two questions, Q. [1] and Q. [2], regarding reformulating non-local Lagrangians as Hamiltonians. In these questions, the Hamiltonian is formulated as an integral because of it's ...
4
votes
1answer
144 views

Legendre transform for non-local Lagrangians, or Hamiltonian of non-local Lagrangian and their properties

This is sort of a multi-part question, mostly dealing with how to treat non-local Hamiltonians and how the corresponding properties of Hamiltonians work in a non-local framework. I proposed an example ...
1
vote
2answers
129 views

An inconsistency in Hamiltonian formulation for non-local Lagrangian: what am I doing wrong?

This question is based on a previous question I asked, Q. [1] In this question, I proposed an example of a non-local Lagrangian (functional), I'm revisiting it here: $$\mathbb{L}=\frac{1}{2}\int^t_0 ...
6
votes
1answer
297 views

How do you determine the Lagrangian? [duplicate]

I have always been puzzled by how do you arrive at Lagrangians? That is, how do you know that the functional you need to get Newton's equations is $$L = T-V(x)~?$$ Do you derive the Lagrangian ...
0
votes
0answers
66 views

The principle of least action [duplicate]

I have read about the principle of least action. This principle suggests that nature would allow a particle to travel in a path along which the integral of the difference between kinetic energy and ...
2
votes
2answers
168 views

Chern Simons action in 4 dimensions

I can not understand why we do not have a Chern-Cimons action for 4 or even forms? And why it not good theory for (3+1) dim?
0
votes
1answer
98 views

Euclidean classical action

This is the Euclidean classical action $S_{cl}[\phi]=\int d^{4}x\ (\frac{1}{2}(\partial_{\mu}\phi)^{2}+U(\phi))$. It would be nice if somebody could explain the structure of the potential. I don't ...
1
vote
1answer
90 views

Hamilton-Jacobi theory and initial value problem?

Having read through some recent posts regarding the Lagrangian formulation being interpreted into an initial value problem rather than the familiar boundary condition problem we are familiar with, I ...
2
votes
3answers
105 views

Time dependence of the Lagrangian of a free particle?

I am working through Landau's book on Classical Mechanics. I understand the logic and physics of isotropy and homogeneity of space-time behind the derivation of the Lagrangian for a free particle, but ...
1
vote
4answers
247 views

Help understanding what the Hamiltonian signifies for the action compared with the Euler-Lagrange equations for the Lagrangian?

Consider the Lagrangian for a simple harmonic oscillator \begin{equation} L (x,\dot{x}) = \frac{1}{2}m\dot{x}^2 - \frac{1}{2}kx^2 \end{equation} Obviously we have \begin{align} \frac{\partial ...
4
votes
1answer
167 views

Can we derive most fundamental laws from the Action Principle? [duplicate]

It is said in the book Fearful Symmetry - The Search for Beauty in Modern Physics that we can derive all basic laws in physics from a simple principle called Least Action Principle (although it may be ...
0
votes
1answer
103 views

The einbein in the action of a relativistic massive point particles [closed]

The action of a relativistic massive point particle moving in space-time is $$S=-m\int d\tau \sqrt{g _{\nu \rho}\frac{dx^{\nu}}{d\tau}\frac{dx^{\rho}}{d\tau}}$$ [with Minkowski sign convention ...
1
vote
0answers
40 views

Alternative formulations of Lagrangians and Hamiltonian? [closed]

We have the Hamiltonian, a concept that was based on trajectories being used extensively in General Relativity, Electromagnetism, Quantum Mechanics, Classical Physics and lot more. Where we use the ...
4
votes
1answer
112 views

Does a symmetry necessarily leave the action invariant?

A symmetry maps a configuration with stationary action to another configuration with stationary action. However, does it necessarily preserve the value of the action exactly? It seems that it should ...
1
vote
1answer
87 views

Does an on-shell symmetry necessarily change the Lagrangian by a total derivative?

This is a follow-up question to: Does a symmetry necessarily leave the action invariant? Qmechanic writes here: Here the word off-shell means that the Lagrangian eqs. of motion are not assumed to ...
7
votes
1answer
134 views

Is it possible to derive the brane action in pure supergravity?

The branes that source the RR fields of supergravity are described by the DBI action plus a CS term. I know this only from superstring considerations. Is there a way to find this result without ...
2
votes
1answer
292 views

Derivation of the supergravity action in 11D

The Einstein-Hilbert action of general relativity is uniquely determined by general covariance and the requirement that only second derivatives in the metric appear. Yang-Mills theory can be motivated ...
1
vote
2answers
83 views

How to calculate the classical on-shell action for a harmonic oscillator? [closed]

So, short and sweet, I've been reading the path integrals book by Feynman and Hibbs, and one of the elementary problems they ask is to calculate the classical on-shell$^1$ action of a harmonic ...
2
votes
2answers
87 views

“Find the Lagrangian of the theory”

I've heard a few of my professors throw around the term "finding the Lagrangian of a theory". What exactly is this referring to. From what I understand it seems that you determine invariances ...
4
votes
1answer
169 views

Boundary term in Einstein-Hilbert action

Why is the boundary term in the Einstein-Hilbert action, the Gibbons-Hawking-York term, generally "missing" in General Relativity courses, IMPORTANT from the variational viewpoint, geometrical setting ...
0
votes
2answers
84 views

Trying to understand relativistic action of a massive point particle

I got badly lost in derivation of relativistic formulas for energy and momentum. I stumbled upon relativistic action as follows (which should explain relativistic motion of a classical particle): $$ ...