1. Homework Statement
I have an assignment to prove that specific intensity over frequency cubed is Lorentz invariant. One of the main tasks there is to prove the invariance of phase space d^3q \ d^3p and I am trying to prove it with symplectic geometry. I am following Jorge V. Jose and Eugene...
I have an assignment to show that specific intensity over frequency cubed \frac{I}{\nu^3}, is Lorentz invariant and one of the main topics there is to show that the phase space is Lorentz invariant. I did it by following J. Goodman paper, but my professor wants me to show this in another way...
I am working through Lessons in Particle Physics by Luis Anchordoqui and Francis Halzen; the link is https://arxiv.org/PS_cache/arxiv/pdf/0906/0906.1271v2.pdf. I am on page 11, equation 1.3.20. The authors have defined an operator ##L_{\mu\nu} = i( x_\mu \partial \nu - x_\nu \partial \mu)##...
I've commonly heard it said that Lorentz invariance is equivalent to saying that special relativity is obeyed, although I also recall discussions arguing that this is not precisely and technically correct, although the two concepts heavily overlap.
I also understand that Lorentz invariance has...
1. Homework Statement
Show that ##d^4k## is Lorentz Invariant
2. Homework Equations
Under a lorentz transformation the vector ##k^u## transforms as ##k'^u=\Lambda^u_v k^v##
where ##\Lambda^u_v## satisfies ##\eta_{uv}\Lambda^{u}_{p}\Lambda^v_{o}=\eta_{po}## , ##\eta_{uv}## (2) the Minkowski...
1. Homework Statement
The problem is as follows: in a reference frame there is one electron at rest and one incoming positron which annihilates with the electron. The positron energy is E and two gamma rays are produced. Find first the energy of the photons in the center of mass frame as...
Why is it that introducing a hard cut-off ##p^{2}=\Lambda^{2}## breaks Lorentz invariance? Is it simply that it introduces an energy scale and energy is not a Lorentz invariant quantity?
Sorry if this is a trivial question, but I just want to make sure I understand the reasoning as I've...
As I understand it, since space-time is modelled as a four dimensional manifold it is natural to consider 4 vectors to describe physical quantities that have a direction associated with them, since we require that physics should be independent of inertial frame and so we should describe it in...
1. Homework Statement
I am meant to show that the following equation is manifestly Lorentz invariant:
$$\frac{dp^{\mu}}{d\tau}=\frac{q}{mc}F^{\mu\nu}p_{\nu}$$
2. Homework Equations
I am given that ##F^{\mu\nu}## is a tensor of rank two.
3. The Attempt at a Solution
I was thinking about...
I recently had someone ask me why we use 4-vectors in special relativity and what is the motivation for introducing them in the first place. This is the response I gave:
From Einstein's postulates( i.e. 1. the principle of relativity - the laws of physics are identical (invariant) in all...
I understand that in order to preserve the inner product of two four vectors under a change of coordinates x^{\mu}\rightarrow x^{\mu^{'}}=\Lambda^{\mu^{'}}_{\,\, \nu}x^{\nu} the Minkowski metric must transform as \eta_{\mu^{'}\nu^{'}}=\Lambda^{\alpha}_{\,\...
A well known math theorem says that - if the spatial dimension is odd - D'Alembert equation gives rise to a solution containing a term which is completely supported on the light cone.
A mathematical wrap up could be the following:
"in dimension 3 (and in fact, for all odd dimensions), the...
Hi all,
Just doing some hobby physics while I put off working on my research. In one dimension, the function
\begin{equation}
f(a,b)=[1-\exp(-(a-b)^2)]
\end{equation}
vanishes when a=b. In Minkowski spacetime though, such a function is not so easy to find (if you require Lorentz invariance). If...