What is Lorentz invariance: Definition and 101 Discussions

In relativistic physics, Lorentz symmetry, named after Hendrik Lorentz, is an equivalence of observation or observational symmetry due to special relativity implying that the laws of physics stay the same for all observers that are moving with respect to one another within an inertial frame. It has also been described as "the feature of nature that says experimental results are independent of the orientation or the boost velocity of the laboratory through space".Lorentz covariance, a related concept, is a property of the underlying spacetime manifold. Lorentz covariance has two distinct, but closely related meanings:

A physical quantity is said to be Lorentz covariant if it transforms under a given representation of the Lorentz group. According to the representation theory of the Lorentz group, these quantities are built out of scalars, four-vectors, four-tensors, and spinors. In particular, a Lorentz covariant scalar (e.g., the space-time interval) remains the same under Lorentz transformations and is said to be a Lorentz invariant (i.e., they transform under the trivial representation).
An equation is said to be Lorentz covariant if it can be written in terms of Lorentz covariant quantities (confusingly, some use the term invariant here). The key property of such equations is that if they hold in one inertial frame, then they hold in any inertial frame; this follows from the result that if all the components of a tensor vanish in one frame, they vanish in every frame. This condition is a requirement according to the principle of relativity; i.e., all non-gravitational laws must make the same predictions for identical experiments taking place at the same spacetime event in two different inertial frames of reference.On manifolds, the words covariant and contravariant refer to how objects transform under general coordinate transformations. Both covariant and contravariant four-vectors can be Lorentz covariant quantities.
Local Lorentz covariance, which follows from general relativity, refers to Lorentz covariance applying only locally in an infinitesimal region of spacetime at every point. There is a generalization of this concept to cover Poincaré covariance and Poincaré invariance.

View More On Wikipedia.org
Recent contents Top users
  1. Gvido_Anselmi

    Vacuum state Lorentz invariance

    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.
  2. TrickyDicky

    QED vacuum and Lorentz invariance

    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...
  3. Enoy

    Exploring Lorentz Violations in Vacuum: A Deep Space Investigation

    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...
  4. ShayanJ

    Lorentz invariance of Klein-Gordon Lagrangian

    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
  5. S

    Question about Lorentz Invariance and Gamma Matrices

    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...
  6. L

    Question related to the Lorentz Invariance

    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...
  7. B

    Lorentz invariance of Rarita-Schwinger action

    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}...
  8. E

    Lorentz Invariance of Propagator for Complex Scalar Field

    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}]...
  9. P

    Maxwell Equations Lorentz Invariance - Notation

    [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...
  10. F

    Lorentz invariance of an equation (metric)

  11. S

    Minimal Subsitution from Lorentz Invariance

    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...
  12. C

    Heisenberg picture manifests Lorentz invariance?

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

    Lorentz invariance of four-volume element [itex] d^4x [/itex]

    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...
  14. L

    Lorentz invariance of [itex] E_p \delta ({\bf p}- {\bf q}) [/itex]

    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...
  15. E

    Lorentz invariance of chirality

    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...
  16. E

    Is the Charge Q Lorentz Invariant in Quantum Field Theory?

    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...
  17. D

    Axial anomaly and broken Lorentz invariance

    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?
  18. S

    Relevance of Local Lorentz Invariance Violations

    What is the relevance of Local Lorentz Invariance Violations if they would be detected in any future experiments? Does it mean there is absolute space and time in the microscopic sector below where current experiments can't probe or other absolute parameters since there would be preferred frame...
  19. J

    Proving the Lorentz invariance of an integration measure? QFT related?

    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...
  20. TrickyDicky

    Point-like particles, Lorentz invariance and QM/QFT

    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...
  21. tom.stoer

    Breaking of Lorentz invariance

    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...
  22. R

    What If Lorentz Invariance Violation Were Detected?

    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...
  23. R

    Lorentz Invariance as local limit of Bigger Manifold

    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...
  24. H

    Lorentz invariance of wave eqn.

    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...
  25. TrickyDicky

    Does GR imply small Lorentz violations in practice?

    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...
  26. R

    Thread on Lorentz Invariance Violation

    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...
  27. M

    Lorentz invariance and General invariance

    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...
  28. C

    A question about Lorentz invariance for Klein-Gordon field

    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) ) = (...
  29. N

    Can a theory have local Lorentz invariance but not diffeo invariance?

    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...
  30. R

    Coulomb Gauge, Lorentz Invariance & Photon Polarization in Field Theory

    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...
  31. E

    Entropy, microscopic quantum theory of space-time, lorentz invariance

    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...
  32. J

    Curled up dimensions and Lorentz invariance

    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...
  33. C

    New limit on lorentz invariance violation

    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...
  34. ZapperZ

    Lorentz invariance verified almost to Planck scale?

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

    Proving lorentz invariance of Dirac bilinears

    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 =...
  36. D

    Time discreteness and lorentz invariance

    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...
  37. P

    Lorentz Invariance & Finding Lambda Expression

    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{...
  38. R

    Prove Lorentz Invariance of a^{\mu}b_{\mu} Equation

    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 &...
  39. J

    Simple math question regarding Lorentz Invariance

    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...
  40. F

    Quantum Field Theory: Field Operators and Lorentz invariance

    [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...
  41. K

    Lorentz invariance and General Coordinate transformations

    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...
  42. B

    Show Lorentz invariance for Euler-Lagrange's equations- how?

    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.
  43. D

    Lorentz Invariance and Non-Galilean Invariance of Maxwell's Equations

    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.
  44. J

    Understanding Lorentz invariance

    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...
  45. L

    How to Prove Lorentz Invariance of Volume Element in Momentum Space?

    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.
  46. A

    And another one on Lorentz invariance

    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...
  47. A

    Another one on Lorentz Invariance

    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...
  48. dextercioby

    Remark on electric charge Lorentz invariance

    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...
  49. C

    Minkowski spacetime interval's Lorentz invariance

    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:
  50. E

    Four vectors and Lorentz invariance

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