All Questions
26
questions
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Is there a Lorentz invariant action for a free multi-particle system?
I want to write down a Lorentz-invariant action of free multi-particle systems.
I know that a Lorentz-invariant action for each particle might be expressed as
$$
S[\vec{r}]=\int dt L(\vec{r}(t),\dot{\...
- 145
1
vote
1
answer
94
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Variational Principle for Free Particle Motion (Relativistic)
This is the same problem as someone asked before: Problem understanding something from the variational principle for free particle motion (James Hartle's book, chapter 5)
The question below:
Here ...
- 349
1
vote
2
answers
256
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Why is the action integral of relativity particles $S = -mc\int ds$? [duplicate]
In my classical mechanic course material, it states that
(In context of relativity) The path of a particle is called its "world line". Each world line can be noted mathematically using the ...
- 301
2
votes
1
answer
185
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Inconsistency in Goldstein’s Lagrangians for Relativistic Point Particles?
In Goldstein’s Classical Mechanics (3rd edition), section 7.10 focuses on covariant lagrangians for point particles. Here, we begin by stating
$$L=-mc\sqrt{x’_{\nu} x’^{\nu}}, \tag{7.162}$$
with ...
- 109
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votes
1
answer
68
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Examples of solvable simple systems in relativistic mechanics [closed]
What examples are there of simple (special) relativistic systems in which the equations of motion are solvable? There are countless examples of these in non-relativistic mechanics, e.g. the simple ...
- 801
8
votes
2
answers
611
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How is the Hamiltonian & Lagrangian non-relativistic & relativistic respectively?
I have read from the textbook of Matthew Schwartz on page 49 of the PDF viewer (or page 30 of the textbook) where he says:
I am interested in the last sentence of this paragraph where he says that ...
- 1,896
0
votes
1
answer
102
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Special relativity v.s. "homogeneous time" within an inertial reference frame
I am asking a conceptual question.
As we learned from classical mechanics, say Lagrangian formulation, as stated in Chap 7.9 of Classical Dynamics book by Thornton-Marion (5th Ed) p.260:
in our ...
- 4,336
14
votes
6
answers
2k
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Does universal speed limit of information contradict the ability of a particle to pick a trajectory using Principle of Least Action?
I'm doing some self reading on Lagrangian Mechanics and Special Relavivity. The following are two statements that seem to be taken as absolute fundamentals and yet I'm unable to reconcile one with the ...
user297575
1
vote
1
answer
73
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How to solve for the velocities when calculating the conjugate momenta in special relativity?
I try to get the momenta $$p_{\sigma} = \frac{\partial L}{\partial \dot{x}^{\sigma}}$$ from the free one particle Lagrangian $$L = -mc\sqrt{-\eta_{\mu\nu}\dot{x}^{\mu}\dot{x}^{\nu}}.$$ I got to the ...
- 147
1
vote
1
answer
333
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Deriving the relativistic point particle action from QFT
In principle, the action of a free relativistic particle of mass $m$ and trajectory $x^\mu(\tau)$
$$ S = -m \int d\tau \sqrt{\frac{dx_\mu}{d\tau}\frac{dx^\mu}{d\tau}} $$
should be obtainable as the ...
- 13
0
votes
0
answers
82
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Why does this method of deriving the classical free particle Lagrangian not work?
I was reading volume two in Landau and Lifshitz's Course of Theoretical Physics (The Classical Theory of Fields). In it, Dr. Landau develops the relativistic Lagrangian as follows: one has $$S=\alpha\...
- 3,967
7
votes
1
answer
166
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Modifying Feynman-Wheeler absorber theory to work with arbitrary potentials?
I'm trying to consider relativistic multi-body dynamics in special relativity. In classical mechanics, it's easy to write a simple $n$-body system with arbitrary potential $V$:
\begin{equation}
m \...
- 716
2
votes
0
answers
161
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Problem understanding something from the variational principle for free particle motion (James Hartle's book, chapter 5)
I am currently studying general relativity from James Hartle's book and I have trouble understanding how he goes to equation (5.60) from equation (5.58). It's about the variational principle for free ...
1
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0
answers
183
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Book recommendation for relativistic classical mechanics
I need some good resource recommendations for the relativistic hamiltonian mechanics under special theory of relativity, with a good discussion on relativistic Hamilton-Jacobi formulation.
9
votes
2
answers
982
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Why does the 'metric Lagrangian' approach appear to fail in Newtonian mechanics?
A well known derivation of the free-space Lagrangian in Special Relativity goes as follows:
The action $\mathcal{S}$ is a functional of the path taken through
configuration space, $\mathbf{q}(\lambda)...
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