Tagged Questions
1
vote
1answer
81 views
Retrieving Maxwell's equations from the minimum action principle
I'm currently working at the start of Alexei Tsvelik's book Quantum Field Theory in Condensed Matter Physics. I'm kinda stumped on a few essential steps.
Starting with the action:
$$S = \int dt \int ...
1
vote
2answers
121 views
How the boundary term in the variation of the action vanishes
Can someone explain a little more that why the last term in equation (1.5) vanishes?
Reference:
David Tong, Quantum Field Theory: University of Cambridge Part III Mathematical Tripos, Lecture ...
5
votes
1answer
87 views
Does anybody know of any good sources that explain (generically) how we form Lagrangians/Actions/Superpotentials for different field content?
I regularly find that I'll understand where the field content in a particular physics paper comes from, but then a Lagrangian or action or superpotential is stated and I don't know how it's derived. ...
2
votes
1answer
76 views
Varying an action (cosmological perturbation theory)
I am stuck varying an action, trying to get an equation of motion. (Going from eq. 91 to eq. 92 in the image.)
This is the action
$$S~=~\int d^{4}x \frac{a^{2}(t)}{2}(\dot{h}^{2}-(\nabla h)^2).$$
...
0
votes
1answer
45 views
if i want action to be positive number then it require that $\tau_i$ be bigger than $\tau_f$, isn't it true? [closed]
the action is the length of the geodesic
$S=-E_o\int_i^f d\tau$
we get an action that is minimised for the correct path.
if i want action to be positive number then it require that $\tau_i$ be ...
2
votes
1answer
85 views
Calculating the (on-shell) action of a free particle
I am having difficulty with the first problem from Feynman and Hibbs' book.
For a free particle $L = (m/2)\dot{x}^2$. Show that the (on-shell) action $S_{cl}$ corresponding to the classical ...
1
vote
2answers
192 views
Why lagrangian is negative number?
In the special relativistic action for a massive point particle,
$$\int_{t_i}^{t_f}\mathcal {L}dt,$$
why is the Lagrangian
$$\mathcal {L}=-E_o\gamma^{-1}$$
a negative number?
7
votes
1answer
306 views
Do an action and its Euler-Lagrange equations have the same symmetries?
Assume a certain action $S$ with certain symmetries, from which according to the Lagrangian formalism, the equations of motion (EOM) of the system are the corresponding Euler-Lagrange equations.
Can ...
2
votes
3answers
146 views
Is the path of stationary action unique? What are the physical implications of $L_{\dot{x}}=L_x$
Below, for any function $Q$ the notation $Q_x$ means $\frac{\partial Q}{\partial x}$, and $Q_{xx}$ means $\frac{\partial^2 Q}{\partial x^2}$.
In physics, the trajectory of a particle is given by the ...
1
vote
1answer
153 views
What's the motivation behind the action principle? [closed]
What's the motivation behind the action principle?
Why does the action principle lead to Newtonian law?
If Newton's law of motion is more fundamental so why doesn't one derive Lagrangians and ...
1
vote
2answers
155 views
What is the relativistic action of a massive particle?
all Lorentz observers watching a particle move will compute the same value for the quantity
$$ds^2 = -(c \, dt)^2 + dx^2 + dy^2 + dz^2,$$
$$ds^2 = g_{\mu\nu}dx^{\mu}dx^{\nu},$$
and ''ds/c'' is then ...
4
votes
2answers
306 views
How to apply Noether's theorem
Say I have a point transformation:
$$x' ~=~ (1 +\epsilon)x,$$
$$t' ~=~ (1 +\epsilon)^2t,$$
and Lagrangian
$$ L ~=~ \frac{1}{2}m\dot{x}^2 - \frac{\alpha}{x^2}.$$
How do I go out about showing ...
3
votes
4answers
390 views
Physical meaning of action in Lagrangian mechanics
Action is defined as $S = \int_{t_1}^{t_2}L \, dt$ where $L$ is Lagrangian.
I know that using Euler-Lagrange equation, all sorts of formula can be derived, but I remain unsure of the physical meaning ...
4
votes
2answers
264 views
Gauge fixing and equations of motion
Consider an action that is gauge invariant. Do we obtain the same information from the following:
Find the equations of motion, and then fix the gauge?
Fix the gauge in the action, and then find the ...
3
votes
3answers
200 views
Is the Lagrangian “math” or “science”?
I've seen in class that we can get from Lagrangian to derive equations of motion (I know its used elsewhere in physics, but I haven't seen it yet). It's not clear to me whether the Lagrangian itself ...
14
votes
4answers
458 views
Is the principle of least action a boundary value or initial condition problem?
Here is a question that's been bothering me since I was a sophomore in university, and should have probably asked before graduating:
In analytic (Lagrangian) mechanics, the derivation of the ...
4
votes
1answer
368 views
Deriving the action and the Lagrangian for a free particle in Relativistic mechanics
My question relates to
Landau, Classical Theory of Field, Chapter 2 - Relativistic Mechanics, paragraph 8 - The principle of least action.
As stated there, To determine the action integral for a ...
2
votes
2answers
207 views
What is the significance of action?
What is the physical interpretation of
$$ \int_{t_1}^{t_2} (T -V) dt $$
where, $T$ is Kinetic Energy and $V$ is potential energy.
How does it give trajectory?
5
votes
2answers
621 views
Hamilton-Jacobi Equation
In the Hamilton-Jacobi equation, we take the partial time derivative of the action. But the action comes from integrating the Lagrangian over time, so time seems to just be a dummy variable here and ...
11
votes
2answers
1k views
Deriving the Lagrangian for a free particle
I'm a newbie in physics. Sorry, if the following questions are dumb. I began reading "Mechanics" by Landau and Lifshitz recently and hit a few roadblocks right away.
Proving that a free particle ...
5
votes
4answers
728 views
Why can't any term which is added to the Lagrangian be written as a total derivative (or divergence)?
All right, I know there must be an elementary proof of this, but I am not sure why I never came across it before.
Adding a total time derivative to the Lagrangian (or a 4D divergence of some 4 ...
3
votes
3answers
289 views
Calculating lagrangian density from first principle
In most of the field theory text they will start with lagrangian density for spin 1 and spin 1/2 particles. But i could find any text where this lagrangian density is derived from first principle.
2
votes
2answers
198 views
How do I show that there exists variational/action principle for a given classical system?
We see variational principles coming into play in different places such as Classical Mechanics (Hamilton's principle which gives rise to the Euler-Lagrange equations), Optics (in the form of Fermat's ...
2
votes
1answer
148 views
Differentiation of the action functional
In the QFT book by Itzykson and Zuber, the variation of the action functional $I=\int_{t_1}^{t_2}dtL$ is written as:
$$\delta I=\int_{t_1}^{t_2}dt\frac{\delta I}{\delta q(t)}\delta q(t)$$
How is ...
11
votes
1answer
205 views
Lagrangian for Euler Equations in general relativity
The stress energy tensor for relativistic dust
$$
T_{\mu\nu} = \rho v_\mu v_\nu
$$
follows from the action
$$
S_M = -\int \rho c \sqrt{v_\mu v^\mu} \sqrt{ -g } d^4 x
= -\int c \sqrt{p_\mu ...
8
votes
2answers
76 views
More general invariance of the action functional
I will formulate my question in the classical case, where things are simplest.
Usually when one discusses a continuous symmetry of a theory, one means a one-parameter group of diffeomorphisms of the ...
3
votes
2answers
366 views
Conversion of the Nambo-Goto action into the Polyakov action?
I`ve read that the Nambo-Goto action containing the induced metric $\gamma_{\alpha\beta}$
$$\tag{1} S_{NG} ~=~ -T\int_{\tau_i}^{\tau_f} d\tau \int_0^{\ell} d\sigma \sqrt{-\gamma}$$
can be converted ...
12
votes
6answers
2k views
Why the Principle of Least Action?
I'll be generous and say it might be reasonable to assume that nature would tend to minimize, or maybe even maximize, the integral over time of $T-V$. Okay, fine. You write down the action ...
2
votes
1answer
206 views
What variables does the action $S$ depend on?
Action is defined as,
$$S ~=~ \int L(q, q', t) dt,$$
but my question is what variables does $S$ depend on?
Is $S = S(q, t)$ or $S = S(q, q', t)$ where $q' := \frac{dq}{dt}$?
In ...
7
votes
1answer
176 views
To construct an action from a given two-point function
This is really a basic question whose answer I guess may have to do with the way we construct Feynman rules and diagrams. The question is: Suppose I have been given a two-point function (found in some ...
2
votes
1answer
485 views
Does Action in Classical Mechanics have a Interpretation? [duplicate]
Possible Duplicate:
Hamilton's Principle
The Lagrangian formulation of Classical Mechanics seem to suggest strongly that "action" is more than a mathematical trick. I suspect strongly ...
3
votes
3answers
1k views
Derivation of Maxwell's equations from field tensor lagrangian
I've started reading Peskin and Schroeder on my own time, and I'm a bit confused about how to obtain Maxwell's equations from the (source-free) lagrangian density $L = ...
22
votes
5answers
1k views
Hamilton's Principle
Hamilton's principle states that a dynamic system always follows a path such that its action integral is stationary (that is, maximum or minimum).
Why should the action integral be stationary? On ...
