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Results tagged with variational-principle
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user 251344
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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Functional and total variations in einbein action [duplicate]
I'm currently studying String theory by Becker& Becker, Schwarz textbook. The exercise 2.3 consists in verifying diffeomorphism invariance of einbein action wich is given by
$$ S_0 = \frac{1}{2} \int …
- 1,330
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2
answers
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Problems to understand closed string BCs in Polyakov action
I apologize if this is an odd question. In the derivation of equations of motion in the Polyakov action
$$S_P = -\frac{T}{2}\int d^2\sigma \sqrt{-h} h^{ab}\partial_a X^\mu\partial_bX^\nu \eta_{\mu \nu …
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Accepted
Problems to understand closed string BCs in Polyakov action
After Bolbteppa answer and Gold helpful comment and some reading on [1] I decided to write this answer. For simplicity, let $X^\mu(\tau, \sigma) := \gamma^\mu(\sigma)$ for fixed $\tau$ with $\sigma \i …
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Dirichlet boundary condtions in Nambu-Goto string action
The Nambu-Goto action for an open string with parameter domain $[0,\tau_1]\times[0,\sigma_1]$ is given by
\begin{equation}
S_{NG} = \int_{0}^{\tau_1} d\tau \int_{0}^{\sigma_1} \ d\sigma \ \mathcal{L}( …
- 1,330
4
votes
1
answer
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Area element with worldsheet metric in Polyakov action
I became confused while reading this article for the following reason:
For $p=1$ we have strings such that the Nambu-Goto action is proportional to the area of the worldsheet embedded by the maps $X^\ …
- 1,330
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Problem with Klein-Gordon equation derivation
In Notes for a course on Classical Fields by R. ALdrovandi, one the the exercises in page 94 is to derive the klein Gordon equation $(\Box + m²)\phi = 0$ from the following lagrangian density
\begin{ …
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Physical intuition for the Geodesic Equation derivation via a Variational Principle: Why max...
The most commom derivation I've seen of the geodesic equation of a massive particle is by the use of the Variational Principle. My problem is that I can't realize what the meaning of find a spacetime …
- 1,330
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Derivatives of Lagrangian for relativistic massive point particle
For a relativistic point particle with mass $m$ whose worldline is parameterized by $x(\lambda)$ the standard Lagrangian is:
$$L(\dot{x}) = -mc\sqrt{g_{ab}\dot{x}^a \dot{x}^b} \tag1$$ where $g$ is a L …
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