# Tagged Questions

any of several principles that find the physical trajectory of a system by minimizing or maximizing some value computed over the proposed path (for instance geometric optics can be reproduced by insisting on a minimum time principle).

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### Virtual Work- Is the presentation in Cornelius Lanczos wrong?

Book: The Variational Principles of Mechanics by Cornelius Lanczos Edition: 4th Chapter: 3, The Principle of Virtual Work I am on the second page of the 3rd chapter (pg 75; it has the Eqn. 31.1). ...
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### Why does overall action need to have an extremum?

Quoting from Landau's and Lifshitz' Mechanics : The integral ${\int\limits_{t_1}^{t_2}}L(q, \dot{q},t)\,dt$ for the entire path must have an extremum, but not necessarily a minimum. This, ...
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### 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 ...
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### What's the lowest nuclear charge $Z < 1$ that will support a bound two-electron ion $(Z,2e^-)$?

In my programming project I calculate the minimal energy of an atom with 2 electrons in the $L=0, S=0$ state, using a Hylleraas wave function. The values I find for $Z=2$ (He) and $Z=1$ (H$^-$) are ...
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### Do “typical” QFT's lack a lagrangian description?

Sometimes as a result of learning new things you realize that you are incredibly confused about something you thought you understood very well, and that perhaps your intuition needs to be revised. ...
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### General relativity from helicity 2 massless field theory by using Deser's arguments

Recently I have discovered the method of constructing of GR from massless field with helicity 2 theory. It is considered here, in an article "Self-Interaction and Gauge Invariance" written by Deser S. ...
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### BTZ Black Hole Central Charge and Conformal Weight

I have been trying to reproduce a calculation (equation 4.12) in this paper http://arxiv.org/pdf/1107.2678v1.pdf by Carlip reviewing the derivation of the effective central charge of the BTZ Black ...
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### Variation of the Einstein-Hilbert action in D dimensions without the Gibbons-Hawking-York term

Consider the standard Einstein-Hilbert action in $D \ne 2$ dimensions spacetimes : $$S_{EH} = \frac{1}{2 \kappa} \int_{\Omega} R \; \sqrt{- g} \; d^D x,$$ where $\Omega$ is ...
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### Functional variation of potential in integral form

I am trying to vary the following action, $$S=\int_{t_0}^{t_1} \text{d}t\,(v^\mu v^\nu g_{\mu\nu} + V(t)) =\int_{t_0}^{t_1}\text{d}t\,(v^\mu v^\nu g_{\mu\nu} + \int_{t_0}^t\text{d}s T_\mu v^\mu)$$ ...
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### Variation of a tensor quantity

How does one go about in finding a variation of a tensor quantity say, with respect to the variation in the metric tensor? I've gone through calculus of variations but I can't figure out how one ...
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### What justification is necessary for convolutional variational principles to be considered legitimate?

I recently asked a related question and was interested in why/or why we cannot use convolutional variational principles in practice or in theory. Summarizing the points I made in the earlier post: ...
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### Why are functional representations of systems important in physics or computational physics?

This was an addendum to a previous question I asked, but I figured I should make it it's own discussion. Assuming I am able derive a functional representation for any dynamical system (dissipative, ...
I am citing from Landau and Lifschitz, this statement that will seem to you well-known, trivial, etc: "Between these positions, (i.e. $q_1$ and $q_2$) the system moves then in such a way that the ...