Tagged Questions
0
votes
1answer
39 views
Relativistic Lagrangian transformations
I need to study the relativistic lagrangian of a free particle.
It's
$\ L= - m c^2 \sqrt[2]{1- \frac{|u|^2}{c^2}} $ I need to study the translation, boost and rotation symmetry. I say it doesn't ...
2
votes
2answers
96 views
Lorentz invariance of the action for free relativistic particle
I tried to check the Lorentz invariance of the standard special relativity action for free particle directly: ($c=1$)
$$
S=\int L dt=-m\int\sqrt{1-v^{2}}dt
$$
Lorentz boost:
$$ ...
0
votes
1answer
45 views
if i want action to be positive number then it require that $\tau_i$ be bigger than $\tau_f$, isn't it true? [closed]
the action is the length of the geodesic
$S=-E_o\int_i^f d\tau$
we get an action that is minimised for the correct path.
if i want action to be positive number then it require that $\tau_i$ be ...
1
vote
2answers
192 views
Why lagrangian is negative number?
In the special relativistic action for a massive point particle,
$$\int_{t_i}^{t_f}\mathcal {L}dt,$$
why is the Lagrangian
$$\mathcal {L}=-E_o\gamma^{-1}$$
a negative number?
4
votes
2answers
296 views
Lorentz invariance of the integration measure
This is regards to the lorentz invariance of a classical scalar field theory. We assume that the action which is $S= \int d^4 x \mathcal{L}$, is invariant under a Lorentz transformation. How do you ...
1
vote
2answers
155 views
What is the relativistic action of a massive particle?
all Lorentz observers watching a particle move will compute the same value for the quantity
$$ds^2 = -(c \, dt)^2 + dx^2 + dy^2 + dz^2,$$
$$ds^2 = g_{\mu\nu}dx^{\mu}dx^{\nu},$$
and ''ds/c'' is then ...
5
votes
2answers
287 views
The Lagrangian in Scalar Field Theory
This is perhaps a naive question, but why do we write down the Lagrangian
$$\mathcal{L}=\frac{1}{2}\eta^{\mu\nu}\partial_{\mu}\phi\partial_{\nu}\phi - \frac{1}{2}m^2\phi^2$$
as the simplest ...
4
votes
1answer
368 views
Deriving the action and the Lagrangian for a free particle in Relativistic mechanics
My question relates to
Landau, Classical Theory of Field, Chapter 2 - Relativistic Mechanics, paragraph 8 - The principle of least action.
As stated there, To determine the action integral for a ...
1
vote
2answers
283 views
Why is ${\partial^i}{\partial_i\phi}$ = ${\partial^i {\phi}}{\partial_i{\phi}}$?
This notation can be found on page 254 of Victor Stenger's Comprehensible Cosmos and in David Tong's Lectures on QFT (Equation 2.4 http://www.damtp.cam.ac.uk/user/tong/qft/two.pdf), and in
EDIT: on ...
0
votes
0answers
153 views
Comparing Lagrangian in Special Relativity vs General Relativity for a weak gravitational field
This is a sequel to this question.
Who knows a difference between the Lagrangian in SR and GR for a weak gravitational field in non-relativistic case? What is the reason of this difference?
3
votes
2answers
134 views
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 ...
6
votes
1answer
2k views
The Euler-Lagrange equation in special relativity
How can I derive the Euler-Lagrange equations valid in the field of special relativity? Specifically, consider a scalar field.
