The action tag has no wiki summary.
1
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1answer
78 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:
$$S = \int dt \int ...
3
votes
3answers
1k views
Derivation of Maxwell's equations from field tensor lagrangian
I've started reading Peskin and Schroeder on my own time, and I'm a bit confused about how to obtain Maxwell's equations from the (source-free) lagrangian density $L = ...
1
vote
1answer
51 views
Why vary the action with respect to the inverse metric?
Whenever I have read texts which employ actions that contain metric tensors, such as the Nambu-Goto, Polyakov or Einstein-Hilbert action, the equations of motion are derived by varying with respect to ...
0
votes
1answer
45 views
if i want action to be positive number then it require that $\tau_i$ be bigger than $\tau_f$, isn't it true? [closed]
the action is the length of the geodesic
$S=-E_o\int_i^f d\tau$
we get an action that is minimised for the correct path.
if i want action to be positive number then it require that $\tau_i$ be ...
1
vote
1answer
97 views
Discretization of action in path integral
I am reading Peskin and Schroeder (path integrals) and it states that discretising the classical action gives:
$$S~=~\int \left(\frac{m}{2}\dot{x}^{2}-V(x)\right)
dt ~\rightarrow~ \sum ...
4
votes
2answers
272 views
Action for a point particle in a curved spacetime
Is this action for a point particle in a curved spacetime correct?
$$\mathcal S =-Mc \int ds = -Mc \int_{\xi_0}^{\xi_1}\sqrt{g_{\mu\nu}(x)\frac{dx^\mu(\xi)}{d\xi} \frac{dx^\nu(\xi)}{d\xi}} \ \ d\xi$$
4
votes
1answer
85 views
What is the action for an electromagnetic field if including magnetic charge
Recently, I try to write an action of an electromagnetic field with magnetic charge and quantize it. But it seems not as easy as it seems to be. Does anyone know anything or think of anything like ...
1
vote
2answers
119 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 ...
2
votes
3answers
216 views
Noether's current expression in Peskin and Schroeder
In the second chapter of Peskin and Schroeder, An Introduction to Quantum Field Theory, it is said that the action is invariant if the Lagrangian density changes by a four-divergence.
But if we ...
5
votes
1answer
86 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
73 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
$$S~=~\int d^{4}x \frac{a^{2}(t)}{2}(\dot{h}^{2}-(\nabla h)^2).$$
...
2
votes
1answer
170 views
Polyakov action: difference induced metric and dynamical metric
The Polyakov action is given by:
$$
S_p ~=~ -\frac{T}{2}\int d^2\sigma \sqrt{-g}g^{\alpha\beta}\partial_{\alpha}X^{\mu}\partial_{\beta}X^{\nu}\eta_{\mu\nu} ~=~ -\frac{T}{2}\int d^2\sigma ...
3
votes
2answers
362 views
Conversion of the Nambo-Goto action into the Polyakov action?
I`ve read that the Nambo-Goto action containing the induced metric $\gamma_{\alpha\beta}$
$$\tag{1} S_{NG} ~=~ -T\int_{\tau_i}^{\tau_f} d\tau \int_0^{\ell} d\sigma \sqrt{-\gamma}$$
can be converted ...
1
vote
0answers
68 views
Solving the path integral for $(ax)^4-(bx)^2$ potential
I need help in solving the path integral of potential given by the form
$(ax)^4-(bx)^2$
This potential is maybe known as Ginzberg Landau potential
I tried using the approximation in which the ...
5
votes
3answers
545 views
Entropy and the principle of least action
Is there any link between the law of maximum entropy and the principle of least action. Is it possible to derive one from the other ?
2
votes
1answer
84 views
Calculating the (on-shell) action of a free particle
I am having difficulty with the first problem from Feynman and Hibbs' book.
For a free particle $L = (m/2)\dot{x}^2$. Show that the (on-shell) action $S_{cl}$ corresponding to the classical ...
1
vote
2answers
189 views
Why lagrangian is negative number?
In the special relativistic action for a massive point particle,
$$\int_{t_i}^{t_f}\mathcal {L}dt,$$
why is the Lagrangian
$$\mathcal {L}=-E_o\gamma^{-1}$$
a negative number?
11
votes
1answer
204 views
Lagrangian for Euler Equations in general relativity
The stress energy tensor for relativistic dust
$$
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 ...
7
votes
1answer
303 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 ...
3
votes
3answers
116 views
What is the meaning of the word “Principle” in Physics?
What is the meaning of the word principle in Physics?
For example in the "action principle". Is it an action law, an action equation, or an unproved assumption? (I have an idea what an action is).
...
0
votes
0answers
54 views
path integrals: how/why can the phase be identified with the action?
In Peskin & Schroeder, chapter 9 introduces the functional methods.
The idea, to recall, is simply to sum over all the possible paths:
$U(x_a,x_b;T) = \sum_{\text{all paths}} e^{i . ...
7
votes
1answer
175 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 ...
11
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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 ...
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votes
2answers
75 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 ...
2
votes
1answer
203 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 ...
2
votes
3answers
145 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
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 ...
0
votes
0answers
42 views
Help identifying an expression for the action
I found the following expression for the action of a (free, I think) relativistic particle in my notes but I can't remember from what it came from:
$$ S = \int_{0}^{N} \left [ ...
4
votes
2answers
301 views
How to apply Noether's theorem
Say I have a point transformation:
$$x' ~=~ (1 +\epsilon)x,$$
$$t' ~=~ (1 +\epsilon)^2t,$$
and Lagrangian
$$ L ~=~ \frac{1}{2}m\dot{x}^2 - \frac{\alpha}{x^2}.$$
How do I go out about showing ...
1
vote
1answer
152 views
What's the motivation behind the action principle? [closed]
What's the motivation behind the action principle?
Why does the action principle lead to Newtonian law?
If Newton's law of motion is more fundamental so why doesn't one derive Lagrangians and ...
3
votes
2answers
124 views
Could we get rid of explicit fields derivatives in Quantum Field Theories?
For instance, if we choose the following scalar field Lagrangian, which is (I hope) Lorentz-invariant, where $l$ is a a length scale, and with a $(-1,1,1,1)$ metric:
$$ \mathfrak{L}(x) \sim ...
2
votes
2answers
197 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 ...
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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 ...
4
votes
2answers
261 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
0answers
101 views
Dirac action and conventions
I have a (possibly) fundamental question, which is driving me crazy.
Notation
When considering the Dirac action (say reading Peskin's book), one have
$\int ...
3
votes
4answers
379 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 ...
14
votes
4answers
454 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 ...
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 ...
4
votes
1answer
363 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 ...
1
vote
1answer
111 views
What do I call the inverse of a propagator?
Let's suppose I have a theory described by a Lagrangian as follows:
$ \mathcal{L} = A_\mu \underbrace{\left( \partial^2 g^{\mu\nu} - \partial^\mu \partial^\nu + m^2 g^{\mu \nu} \right)}_{K^{\mu \nu}} ...
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
484 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 ...
2
votes
2answers
206 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?
2
votes
0answers
69 views
Is there some connection between the Virial theorem and a least action principle?
Both involve some 'averaging' over energies (kinetic and potential) and make some prediction about their mean values. As far as the least action principles, one could think of them as saying that the ...
5
votes
2answers
615 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 ...
3
votes
3answers
389 views
$\hbar$, the angular momentum and the action
Is there anything interesting to say about the fact that $\hbar$, the angular momentum and the action have the same units or is it a pure coincidence?
5
votes
2answers
281 views
Is it circular reasoning to derive Newton's laws from action minimization?
Usually, a typical example of the use of the action principle that
I've read a lot is the derivation of Newton's equation (generalized to
coordinate $q(t)$). However, in the classical mechanics ...
5
votes
4answers
725 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
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3answers
285 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
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 ...
