Lorentz invariance Definition and 101 Threads

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...

Hi everybody! Why we don't have to prove Lorentz invariance of the Vacuum state in QFT? This fact is quite obvious in QED and follows from Lorentz invariance of electric charges. But in general case? I don't know, but it seems to me this fact is not so obvious as it treated.

The measured energy density of the vacuum has a disturbing discrepance with the one theorized by imposig Poincare invariance in QFT, usually referred to as the "vacuum catastrophe". On the other hand the Heisenberg indeterminacy principle leads to a nonzero vacuum expectation value for the...

Tests of lorentz violation in space outside earth, planets, our sun, other stars, galaxies and galaxygroups have shown no violations. That is fine. But do you ladies and gentlemen, know if anyone have tested (experimental and/or theorethical) if there may happen lorentz violations (or if the...

I want to prove the invariance of the Klein-Gordon Lagrangian \mathcal{L}=\frac 1 2 \partial^\mu \phi \partial_\mu \phi-\frac 1 2 m^2 \phi^2 under a general Lorentz transformation \Lambda^\alpha_\beta but I don't know what should I do. I don't know how to handle it. How should I do it? Thanks

This is a pretty basic question, but I haven't seen it dealt with in the texts that I have used. In the proof where it is shown that the product of a spinor and its Dirac conjugate is Lorentz invariant, it is assumed that the gamma matrix \gamma^0 is invariant under a Lorentz transformation. I...

I have a question related to the Lorentz invariance. (on the book of Mark Srednicki Quantum Field Theory, page 35 prob. 2.9 c) There are representations of \Lambda and S. In order to show that result of problem, I use number of two ways. 1. I expanded \Lambda to infinitesimal form using...

The Rarita-Schwinger action is \int \sqrt{g} \overline{\psi}_a \gamma^{abc} D_b \psi_c Here ##g = \det(g_{\mu \nu})##, and the indices ##a, b \dots ## are 'internal' indices that transform under e.g. ##\mathrm{SO} (3,1) ## in ##3+1## dimensions. ##\gamma^{abc} = \gamma^{[a} \gamma^{b}...

Homework Statement Show that [\hat{\phi}(x_1),\hat{\phi}^\dagger(x_2)] = 0 for (x_1 - x_2)^2 < 0 where \phi is a complex scalar field Homework Equations \hat{\phi}=\int\frac{d^3 \mathbf{k}}{(2\pi)^3 \sqrt{2\omega}}[\hat{a}(k)e^{-ik\cdot x} + b^\dagger(k)e^{ik\cdot x}]...

[This is mostly about notation] I was working on a problem where I had to prove that div(B) remains invariant under lorentz transformations. That was not too hard, so I came up with div(B) = \partial_{\mu} B^{\mu} must equal div(B) = \partial'_{\mu} B'^{\mu} so I did a...

Hello, My question is on coupling the photons to our Dirac field for electrons, we have the Dirac equation: (i\not{\partial -m })\psi=0 By Lorentz invariance we can change our space-time measure by: \partial ^\mu \rightarrow \partial ^\mu+ieA^\mu\equiv D^\mu Though I cannot see...

In several textbooks of QM I have read that Lorentz invariance is manifest in Heisnberg picture. How can we deduce that?

I am slightly confused with the invariance of four-volume element. The orthodox way to show it is to prove that Jacobian is one, that I did, however in many textbooks I find a reasoning that because we have Lorentz contraction on one hand and time dilation on the other hand, the product is...

Can anybody help me with the proof that E_p \delta ({\bf p}- {\bf q}) is a Lorentz invariant object? I did a boost along z axes and used the formula \delta (f(x)) = \frac{\delta(x-x_0)}{|f'(x_0)|} and the factor in front of the delta function indeed is invariant but within the function I...

Hi folks, I've been reading into the concepts of chirality & helicity and often I find a statement that chirality is Lorentz invariant in contrast to helicity (which of course depends on the frame). BUT I don't see in which way chirality IS Lorentz invariant. For massless particles things...

Hi all, I'm studying quantum field theory and I'm watching video lectures on Harward University website (Professor Colemann's lectures). Now, in lesson number six at 1h-6 minute a student asks why after trasforming field by a Lorentz transformation he doesn't transform also integration...

I had a look at Jackiws article on axial anomaly in scholarpedia: http://www.scholarpedia.org/article/Axial_anomaly Apparently, axial anomaly also breaks Lorentz invariance. Even if this effect would be very weak, doesn't this pull the plug on relativity?

So, first off, I'm thinking Lorentz invariant quantities are the same in any inertial frames S and S' regardless of their relative velocity. I'm thinking I need to show that \frac{d^3k}{(2\pi)^32E(\vec{k})} = \frac{d^3k'}{(2\pi)^32E'(\vec{k'})} where the primed & unprimed quantities denote...

As we know nonrelativistic quantum mechanics doesn't have the Lorentz invariance property and yet it makes a number of powerful predictions and gives rise to all the fundamental quantum properties (HUP, tunnelling effec, harmonic oscillator, superposition, wave-particle duality etc). What is...

Today one tries to find indications for quantum gravity indirectly via low-energy effects induced by "foamy" or "discrete" structures replacing space-time at the Planck regime. It is by no means clear whether and how such discrete structures necessarily indice Lorentz symmery breaking, neither...

What if someday we would have news that Lorentz Invariance Violation was detected? Is this possible at all? But our Special Relativity is based on Lorentz Invariance and the more general General Covariance in General Relativity. Does this mean that Lorentz Invariance violation is almost...

Is it possible that Lorentz invariance is just a lower limit of a larger manifold that has a priveleged frame? Even if Bell's experiments can't transmit signal faster than light. The spirit of relativity is still violated by say instantaneous correlation between 10 billion light years. As...

Hello! Hopefully somebody could give me a push from behind on this one :) Homework Statement Show that the classical wave equation is lorentz invariant. The Attempt at a Solution I tried to exchange all derivatives by the chain rule: (c^2 \frac{d^2 }{dt^2} + \frac{d^2 }{dx^2} + \frac{d^2...

How is Lorentz invariance handled in GR? I know that there is no global Lorentz invariance in GR, instead it only holds locally, meaning that it is obeyed in the limit at infinity:when r goes to infinity by considering infinite distance or infinitely small point mathematical objects. But when...

Yesterday there was a thread here on a claimed violation of Lorentz invariance, but I can't locate it today. Was the thread moved? Can someone point me to its new location? (I don't remember the exact title of the thread, but the posts referred to a letter in the Sep 2010 issue of European...

Hi I am confused about these two related but different terms Lorentz invariance/covariance and General invariance/covariance As I understand it a Lorentz invariant is a scalar which is the same in all inertial reference frames i.e. it acts trivially under a Lorentz transformation an example...

Homework Statement Hi everyone, in Peskin & Schroeder, P36, the derivative part of KG field is transformed as eqn (3.3). But why does the partial derivative itself not transform? Homework Equations \partial_{\mu} \phi (x) \rightarrow \partial_{\mu} ( \phi ( \Lambda^{-1} x) ) = (...

This is related to the thread on the meaning of diffeomorphism invariance but is adressing a distinct point (at least I think so, but I may be proven wrong). As Rovelli discusses in his book, the action of the Standard Model coupled to gravity has three types of invariance: under the gauge...

In electrodynamics, the Coulomb gauge is specified by \nabla \cdot A=0 , i.e., the 3-divergence of the 3-vector potential is zero. This condition is not Lorentz invariant, so my first question is how can something that is not Lorentz invariant be allowed in the laws of physics? My second...

The existence of entropy in gravity implies that there are microscopic degrees of freedom in space that carries the entropy. This implies space is discrete. Discrete space breaks lorentz invariance, which has been strongly constrained by both FERMI and thought experiments. String theory...

If we start with minkowski spacetime in 4 dimensions and then add several curled up spatial dimensions attached at every spacetime point, then: I'll label a spacetime point as: (ct,x,y,z)[a1,a2,a3,..,an] where the bracketted coordinates are the 'curled' coordinates. - If we label the...

Seasons greetings all, I am trying to dissect a really interesting article: http://www.nature.com.libproxy.ucl.ac.uk/nature/journal/v462/n7271/full/nature08574.html but I am struggling with some of the more technical terms in it. I have shown it to some lecturers at my uni and even they...

So whose quantum gravity theory will crash-and-burn if this is correct? http://physicsworld.com/cws/article/news/40834 Zz.

I'm trying to work through the proof of the Lorentz invariance of the Dirac bilinears. As an example, the simplest: \bar{\psi}^\prime\psi^\prime = \psi^{\prime\dagger}\gamma_0\psi^\prime = \psi^{\dagger}S^\dagger\gamma_0 S\psi = \psi^{\dagger}\gamma_0\gamma_0S^\dagger\gamma_0 S\psi =...

I understand that some do not accept LQG in particular, but any discrete spatial geometry in general, because that would be a violation of lorentz symmetry. It was explained to me as meaning that If a 2D plane were discretized into a grid or lattice, a vector would not have a continuous...

Homework Statement I have two four vectors v and w with v^{2} = m^{2} > 0, v_{0} > 0 and w^{2} > m^{2}, w_{0} > 0 . Now we consider a system with w' = (w_{0}', \vec{0}) and v' = (v_{0}', \vec{v} \, ') and in addition we consider the quantity \lambda = \vert \vec{v}' \vert \, \sqrt{...

Homework Statement Show that a^{\mu}b_{\mu} \equiv -a^0b^0 + \vec{a} \bullet \vec{b} is invariant under Lorentz transformations. Homework Equations \Lambda_{\nu}^{\mu} \equiv \left( \begin{array}{cccc} \gamma & -\beta \gamma & 0 & 0 \\ -\beta \gamma & \gamma & 0 & 0 \\ 0 & 0 & 1 &...

Let us restrict ourselves to SR for the moment at least. So we have a flat spacetime. Now consider a proper force of the form: \frac{dp^\mu}{d\tau} = a v^\mu where a is a scalar. It seems to be coordinate system independent due to the definition being in tensor notation. But it seems to...

[SOLVED] Quantum Field Theory: Field Operators and Lorentz invariance Hi there, I am currently working my way through a book an QFT (Aitchison/Hey) and am a bit stuck on an important step in the derivation of the Feynman Propagator. My problem is obviously that I am not a hard core expert...

Sorry to bring up again a question that I asked before but I am still confused about this. In SR we have Lorentz invariance. Now we go to GR and one says that the theory is invariant under general coordinate transformations (GCTs). But, as far as I understand, this is simply stating that...

Hello, I need help showing that the Euler-Lagrange equations are Lorentz invariant (if Einstein's extended energy concept is used). Is there an easy way to show this? Any help would be very much appreciated.

I am having trouble going about proving the Lorentz invariance and non-Galilean invariance of Maxwell's equations. Can someone help me find a simple way to do it? I've looked online and in textbooks, but they hardly give any explicit examples.

On p. 32 of Quantum field theory in a nutshell, Zee tries to derive the propagator for a spin 1 field: D_{\nu\lambda} = \frac{-g_{\nu\lambda} + k_\nu k_\lambda /m^2}{k^2 - m^2} using the Lorentz invariance of the equation k^\mu \varepsilon_\mu^{(a)}=0 where \varepsilon_\mu^{(a)} denotes the...

Simple question.. How do you prove the volume element of momentum space (d3k/Ek) is Lorentz Invariant? I tried making it proportional to "velocity volume element" derived from the Lorentz transformations but didn't seem to get very far.

It is clear that a conserved current \partial_{\mu} J^\mu = 0 implies the existence of a conserved charge Q= \int d^3x J^0 . Now I want to go the other way round: Suppose we have a basis of momentum eigenstates, such that these states are also eigenstates of the charge. Then clearly the charge...

I recently read an author making the following argument in QFT: if <m|A^0(t,0)|n>=B then <m|A^mu(t,0)|n>=(B/p^0)*p^mu by Lorentz invariance. Can anybody tell me under which circumstances this holds and how it comes about? I understand that <m|A^mu(t,0)|n> had to transform as a 4-vector but why...

Since there's another thread on the same subject in the GR forum, but on this forum about 8 months ago an interesting discussion on the same subject took place, https://www.physicsforums.com/showthread.php?t=114620, i want to draw everyone's attention on the post \#24 in that thread in which the...

Maybe this is really easy, but... Can someone show me how the sign reversal between the space and time components of Minkowski spacetime make its intervals Lorentz invariant (mathematical derivation) ? Thanks... :wink:

Does anyone know where I can find a mathematical proof that the norm of any four-vector is Lorentz invaraint?