# Tagged Questions

The action tag has no wiki summary.

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 ...
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 = ...
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 ...
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 ...
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 ...
2answers
272 views

### Action for a point particle in a curved spacetime

Is this action for a point particle in a curved spacetime correct? $$\mathcal S =-Mc \int ds = -Mc \int_{\xi_0}^{\xi_1}\sqrt{g_{\mu\nu}(x)\frac{dx^\mu(\xi)}{d\xi} \frac{dx^\nu(\xi)}{d\xi}} \ \ d\xi$$
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 ...
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 ...
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 ...
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. ...
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 $$S~=~\int d^{4}x \frac{a^{2}(t)}{2}(\dot{h}^{2}-(\nabla h)^2).$$ ...
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 ...
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 ...
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 ...
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 ?
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 ...
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?
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 ...
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 ...
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). ...
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 . ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 [ ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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}} ...
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 ...
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 ...
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?
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 ...
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 ...
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?
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 ...
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 ...
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.
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 ...
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