lorentz invariance

  1. M

    Prove that these terms are Lorentz invariant

    1. Homework Statement Prove that $$\begin{align*}\mathfrak{T}_L(x) &= \frac{1}{2}\psi_L^\dagger (x)\sigma^\mu i\partial_\mu\psi_L(x) - \frac{1}{2}i\partial_\mu \psi_L^\dagger (x) \sigma^\mu\psi_L(x) \\ \mathfrak{T}_R(x) &= \frac{1}{2}\psi_R^\dagger (x)\bar{\sigma}^\mu i\partial_\mu\psi_R(x) -...
  2. gasar8

    Canonical invariance vs. Lorentz invariance

    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...
  3. gasar8

    A Lorentz invariant phase space - symplectic geometry

    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...
  4. Gene Naden

    A Angular momentum operator derived from Lorentz invariance

    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)##...
  5. ohwilleke

    A Corollaries of Lorentz Invariance

    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...
  6. binbagsss

    Show that d^4k is Lorentz invariant

    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...
  7. L

    Find the energy of a photon after this annihilation process

    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...
  8. F

    I Momentum cut-off regularisation & Lorentz invariance

    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...
  9. F

    I Why is energy not Lorentz invariant?

    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...
  10. F

    Prove Lorentz invariance for momentum 4-vector

    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...
  11. F

    I Motivation for the usage of 4-vectors in special relativity

    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...
  12. Y

    B About the Lorentz invariance of Planck constant

    Is it proved experimentally that the planck constant is invariant in the moving system? If that experiment exists, would you show me that in detail?
  13. D

    Lorentz invariance of the Minkowski metric

    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}_{\,\...
  14. G

    Huygens principle in odd/even dimensional flat space

    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...
  15. W

    Searching for a function that vanishes only when x^mu = y^mu

    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...
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