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# Questions tagged [action]

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

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### Does $δS = 0$ mean that "the small changes in the actions equal to zero"?

Please correct me if I'm wrong. What I understood from the Principle of Stationary Action is that for an object moving from point A to point B, at every point of the path with the least action, the ...
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### Relation between $SL(2,R)$ and $U(1)$ symmetry

I have an action that I have proven to be invariant under an $SL(2,R)$ symmetry. But I actually want my action to be invariant under an $U(1)$ symmetry (because i know that for the system I am ...
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### Question about integral containing derivative of Dirac delta distribution

The result of the integral of the dirac delta δ(x-a) times a function f should be f(a) right? Then why isn't the integral just the final result directly without doing all of this, where did the ...
1 vote
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### How can I derive the equations of motion with the least action principle from the action of $p$-Form Electrodynamics? [closed]

I know this is the correct formula for the action for a arbitrary $p$. I know how to obtain the equations of motion for $p=1$, but I struggle to find a way to do this with an arbitrary $p$. I also ...
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### Corners in the worldsheet and Ricci scalar term in the Polyakov action

I have a question about a passage in Polchinski's textbook , regarding the topological term in the Polyakov action. In the Polyakov action for a closed manifold, we can add a term proportional to ...
1 vote
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### Complex phase of the path integral in QM?

The square modulus of an amplitude must be real. Given that, I am having some trouble understanding the square modulus of a path integral being absolutely real. Given \begin{equation} \int\!Dq(t)\...
1 vote
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### Action Variable for 1d Potential

I have the following 1d potential: $V(q) = A\left(\frac{q}{d}\right)^{2n}$ where $A$ and $d$ are positive constants. The momentum is: $p = \pm \sqrt{2m\left[E-A\left(\frac{q}{d}\right)^{2n}\right]}$ ...
1 vote
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### How to canonicalize a coupled scalar kinetic term?

I am working with a classical action in curved space-time that looks something like: \begin{equation} S = \int d^4x \frac{1}{16G\pi}\sqrt{-g} \left[R - \frac{K_\Phi}{\Phi^2} \partial_\mu \Phi \partial^...
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### Variation of Action and Border Terms

I need to compute the following very general (piece of) variation: \begin{equation} \int d^4x \delta (\sqrt{-g} R ) f \tag{1} \end{equation} where $R$ is Ricci scalar and $f$ a generic scalar ...
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### From EH action to Newtonian Mechanics action? [closed]

How does one start from the Einstein Hilbert action go to the action of a (point particles + some field) in special relativity and then Newtonian mechanics for a local neighborhood around a point for ...
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### Different relativistic actions [duplicate]

I am slightly confused about different action integrals in relativity. When you work through some introductions to general relativity, you usually get in contact with the relativistic action integral \...
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### Do we have a choice of coordinates and frames on the total space of the frame bundle (covariance on Frame bundle)?

Suppose we have some spacetime $M$, general covariance implies that our laws of physics shouldn't depend upon the choice of coordinate system or parameterization for things like an Action functional. ...
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### How does one show the equivalence principle is manifest in the EH action? [duplicate]

How does one start from the Einstein Hilbert action and show that in a small neighborhood the metric must be Lorentzian (equivalence principle)?
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### Is calling it "The Principal of Extremal/Stationary Action" pedantry? [duplicate]

I understand that the equations appear to permit paths of maximal action, but is there any real physical case where this actually occurs? Would it not be more sensible to refer to this as the ...
1 vote
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### Why are we interested in the dimensional analysis/power counting in string theory?

I'm learning bosonic strings on my string theory course; here is part of my notes about the dimensional analysis on the world sheet $\Sigma$ and the spacetime manifold $\mathcal{M}$: I learned this ...
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### Auxiliary field in Quantum Field Theory

I'm reading this answer which explains 'What is auxiliary field in Quantum Field Theory?' As a simple example, we can imagine that the real field must follow some constraints. In the path integral we ...
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### Using the principle of inertia to motivate the principle of least action?

Can we motivate the principle of least action with the principle of inertia that causes a mass particle to resist changes in its momentum? After all, the principle of inertia is the starting point and ...
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### Action for boundary term in Chern-Simons theory (David Tong's note)

This question is about obtaining the boundary action from Chern-Simons theory. While reading David Tong's chapter 6 on quantum Hall effect, I cannot derive an equation between (6.9) and (6.10) of the ...
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### Problem with different expressions of functional determinant

This question is a follow-up of my previous one, after having done some calculations. In this previous question I used a minimal example of my problem with $\det(\Delta) = \det(\partial^2+A(x))$, but ...