All Questions
26
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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
$$
S[\vec{r}]=\int dt L(\vec{r}(t),\dot{\...
- 145
1
vote
1
answer
94
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Variational Principle for Free Particle Motion (Relativistic)
This is the same problem as someone asked before: Problem understanding something from the variational principle for free particle motion (James Hartle's book, chapter 5)
The question below:
Here ...
- 349
1
vote
2
answers
257
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Why is the action integral of relativity particles $S = -mc\int ds$? [duplicate]
In my classical mechanic course material, it states that
(In context of relativity) The path of a particle is called its "world line". Each world line can be noted mathematically using the ...
- 301
2
votes
1
answer
187
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Inconsistency in Goldstein’s Lagrangians for Relativistic Point Particles?
In Goldstein’s Classical Mechanics (3rd edition), section 7.10 focuses on covariant lagrangians for point particles. Here, we begin by stating
$$L=-mc\sqrt{x’_{\nu} x’^{\nu}}, \tag{7.162}$$
with ...
- 109
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1
answer
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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
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2
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614
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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
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1
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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 ...
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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
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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}}.$$ I got to the ...
- 147
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1
answer
334
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Deriving the relativistic point particle action from QFT
In principle, the action of a free relativistic particle of mass $m$ and trajectory $x^\mu(\tau)$
$$ S = -m \int d\tau \sqrt{\frac{dx_\mu}{d\tau}\frac{dx^\mu}{d\tau}} $$
should be obtainable as the ...
- 13
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0
answers
82
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Why does this method of deriving the classical free particle Lagrangian not work?
I was reading volume two in Landau and Lifshitz's Course of Theoretical Physics (The Classical Theory of Fields). In it, Dr. Landau develops the relativistic Lagrangian as follows: one has $$S=\alpha\...
- 3,967
7
votes
1
answer
169
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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
983
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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)...
- 91
1
vote
2
answers
69
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Given the Lagrangian of a system, is there a way to extract the total energy?
If an object of mass $m$ is under the action of a conservative force and there are no constraints on the system, can $E=K+U$ be obtained? If yes, I am more interested if the answer could be ...
- 11
6
votes
2
answers
766
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Deriving special relativity free particle Lagrangian using infinitesimal boost?
At the very beginning of Landau and Lifshitz Mechanics they derive the form of the Lagrangian for a free particle in Newtonian mechanics.
I want to see how to do the analogous derivation in special ...
- 866
4
votes
1
answer
386
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Does the negative sign in the Lagrangian $L=T-V$ relate to the $(+,-,-,-)$ Minkowski signature of relativity?
I've read many derivations of the Euler-Lagrange equation, but this is more of a physics-philosophical point.
Kinetic energy $T$ involves time derivatives, while potential involves spatial location. ...
- 568
2
votes
1
answer
226
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In classical mechanics, can the Lagrangian be thought of as a metric?
I know that there are some other discussions on this on physics stack exchange, but the other day I was playing with the expression for the Lagrangian and thinking about it's connection with ...
- 281
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1
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701
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How to check if the relativistic Lagrangian of a free particle is Lorentz invariant?
I am struggling with a concept in Classical Mechanics/Special Relativity.
I want to find the relativistic Lagrangian of a free particle, the method for which I have found in a few dfferent places, ...
- 11
3
votes
0
answers
141
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Relativistic configuration space in classical mechanics
Okay so a couple of questions. Firstly I realise that in order to study the dynamics of one particle (classically), we define the Lagrangian and Hamiltonian to be the maps from the tangent and ...
- 504
2
votes
1
answer
3k
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What is a Lagrangian of a photon? [duplicate]
In sense of classical mechanics+special relativity what is lagrangian of a photon?
Lagrangian of a relativistic massive particle is as follows:
$$ L_{massive}= -mc\sqrt{c^2-v^2} $$
So is it a zero?
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2
answers
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Why do we consider Lagrangian densities in field theory (as opposed to Lagrangians as in point mechanics)?
My question is: Why do we consider Lagrangian densities in field theory (as opposed to Lagrangians as in point mechanics)?
Is it simply because of the following?
We wish the theories to be Lorentz ...
- 3,063
2
votes
2
answers
2k
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Lagrangian for free particle in special relativity
From definition of Lagrangian: $L = T - U$. As I understand for free particle ($U = 0$) one should write $L = T$.
In special relativity we want Lorentz-invariant action thus we define free-particle ...
- 171
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votes
2
answers
4k
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Deriving the action and the Lagrangian for a free massive point particle in Special Relativity
My question relates to
Landau & Lifshitz, Classical Theory of Field, Chapter 2: Relativistic Mechanics, Paragraph 8: The principle of least action.
As stated there, to determine the action ...
- 737
4
votes
2
answers
213
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Does locality emerge from (classical) Lagrangian mechanics?
Consider a (classical) system of several interacting particles. Can it be shown that, if the Lagrangian of such a system is Lorenz invariant, there cannot be any space-like influences between the ...
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