All Questions
9
questions
10
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2
answers
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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
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
2
answers
2k
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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
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
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 ...
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
1
vote
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
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 ...
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