Invariance Definition and 454 Threads

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...

Homework Statement Show that because a pure rotational displacement field u(r) has no effect, that the energy of a crystal only depends on the symmetric strain tensor epsilon_ij. Homework Equations As in Ashcroft & Mermin (22.72), the energy of a crystal as a function of displacement field...

Wald Appendix D talks on why g^{\mu\nu}\nabla_{\mu}\nabla_{\nu}\phi is not conformally invariant when n is not equal to 2. I want to prove that the Klein Gordon Action (V=0) is not conformally invariant. However the term that I have in the action is just...

In the expression of Biot-Savart law B = (µo/4π) ∫ (I dl x r^)/r2 why dl does not depend on the coordinate systems ? in books they are using del X dl = 0

Assume u:R\rightarrow C^n and define shift operator S(\tau) with S(\tau)u(t)=u(t-\tau) and truncation operator P(\tau) with P(\tau)u(t)=u(t) for t\leq\tau and 0 for t>\tau Then P(\tau)S(\tau)=S(\tau)P(0) for every \tau>=0. Can someone please prove last statement..

What is means that unintegrated parton distributions and matrix elements are supposed to be gauge invariant??

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...

I know what gauge invariance is, but I'm not sure what gauge covariance is. Is it that a given field has a gauge covariant derivative? And under which circumstances do we get a field that is gauge invariant but not gauge covariant? And I would appreciate an example (other than the one...

I'm having problems showing that Newton's second law of motion stays invariant (has the same form) under a Galilean transformation. If we write the general Galilean transformation as t=t'+t_{t} \bar{x}=R\bar{x}'+\bar{u}t'+\bar{t}_{\bar{x}} where R an orthogonal transformation, then velocity...

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...

"Proving" the Jacobi identity from invariance Hi all, In an informal and heuristic manner, I have heard that the "change" in something is the commutator with it, i.e. \delta A =[J,A] for an operator A where the change is due to the Lorentz transformation U = \exp{\epsilon J} = 1 + \epsilon J...

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?

hi, value of c is experimental however c itself is theoretically lorentz invariant. So value of c depends upon fabric of cosmos right? Thanks.

Given x0 and y0 such that x0 > y0 > 0. Define, for n = 0,1,2,, xn+1 =xn +yn , yn+1 = 2xnyn .Find the limits of {xn} and {yn}. why is the answer lim{xn} = lim{yn} = sqrt(x0y0)?

To what extent is the PoR an extension of the galilean PoI? A stated consequence of the Galilean PoI is that inertial observers cannot determine by experiment if they are "in motion" or "at rest", with a similar consequence being mentioned for the PoR - to what extent to these differ, does...

In the first volume of Differential Geometry, Ch. 1, Spivak states that if U \subset \mathbb{R}^n is homeomorphic to \mathbb{R}^n, then U is open. This seems obvious: \mathbb{R}^n is open in \mathbb{R}^n, so its pre-image under a homeomorphism f:U \rightarrow \mathbb{R}^n is open. The pre-image...

If only left handed fields couple in the weak force, and we can boost to a frame that changes left handed fields to right handed ones, how can that theory be relativistically invariant? thanks for the help!

I've seen a few short proofs that if that some transformation \Lambda preserves the spacetime interval, then \Lambda^\top g \Lambda = g where g is the spacetime metric. They have all relied on an argument using some simple algebra to show that (\Lambda^\top g \Lambda) x \cdot x = g x...

Hi all, I'm trying to understand relativity for the first time. First of all I'm sorry for my bad English, I'll try to be as clear as possible. My doubt is the following: In my books and on many web sites I have red the thought experiment of the train and the two bolts of lightning to explain...

One of the foundations of General Relativity is diffeomorphism invariance - the fact that the laws of physics are invariant under smooth coordinate transformations, and thus the laws must involve tensors. My question is, why doesn't this imply scale invariance; after all, isn't a change of...

Here is an equation from proof of invariance of interval: This equation is from bernard schutz's first course in GR: I could not understand what M stands for. Can someone help me with this? I don't have advanced knowledge. I am a beginner UG.

As I understand it the heart of gauge symmetry is that I can change the phase at different points different amounts and the Lagrangian/action is unchanged. What I am not clear on is whether the changes I can make are completely arbitrary - I can make any change I want at any point - or whether...

Fisher matrix=(minus the) average of the second derivative of the log-likelihood with respect to the parameters It seems to me the Fisher matrix for Gaussian data is invariant with respect to any (non-singular) linear transformation of the data; if correct this is a very useful property...

Hi, I'm very ashamed to not understand how even the simplest gluon amplitudes are conformally invariant. See eg http://arxiv.org/abs/hep-th/0312171 pages 11-12. M(1^-,2^-,3^+)=\delta(\sum_i \lambda_i\tilde{\lambda}_i)\frac{\langle12\rangle^4}{\langle12\rangle \langle...

Hi In my book it says that if the dielectric function ε is time invariant, we can write a solution to Maxwells equations of the form E(r, t) = E(r)exp(jωt). I agree that the ME are separable, but I don't see how they know that the time-dependence is harmonic? What is so special about exp(jωt)...

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...

Hello all ! My question: Does fibre bundles are necessary for describing gauge invariance in electromagnetic case? Or fibre bundles uses only for describing gauge invariance in cases of weak, electroweak and strong interactions? Thanks

Hi. So if you have \frac{d p_{\alpha}}{ds} = \frac{q}{c} F^{\alpha \beta} u_{\beta} how could you possibly go on proving this its form is invariant under all coordinate transformations? Or any physical law of any form, really? I guess my point is how do you represent "all possible...

Hi, excuse the funny title :). In his book on quantum field theory Zee says (pag 245, fouth line) that QED gauge symmetry follows from the conservation of the current j=ψ γ^μ ψ (with the bar on the first spinor). I'm confused because that current is the noether current resulting from the...

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...

Hi, folks. I hope this is the right forum for this question. I'm not actually taking any classes, but I am doing self-study using D'Inverno's Introducing Einstein's Relativity. I have a solution, and I want someone to check it for me. Homework Statement Prove that the null geodesics of two...

Homework Statement Determine if the following system is time invariant: y(t) = x(t - 2) + x(2 - t) 2. The attempt at a solution I know from the solutions that the system is NOT time invariant, yet whenever I try to solve it I get the opposite result. Here's what I'm doing: y1(t)...

Homework Statement Prove that the system is either T.I. or is not T.I. Homework Equations y(n) = x(n)*h(n) x(n) is the input signal y(n) is the output signal h(n) is the system The Attempt at a Solution Inputing x(n-n0) into the system I get out: as the output x(n-n0)*h(n)...

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...

So I'm having trouble understanding how these two are related, i.e., how one proves the other. I understand the ideas behind both of them: For J-B, you're basically taking R^n and throwing in a sphere, so the inside of the sphere is bounded and everything outside the sphere is unbounded. For...

always say us Maxwell equations are not covariance under Galilean Transformation They say merely this because of constant speed of light that the result of Maxwell Equations But there arent any excitability prove for Non-Ggalilean invariance of Maxwell equation I Decided try to show...

Homework Statement Prove that the spacetime interval -(ct)^{2} + x^{2} + y^{2} + z^{2} is invariant. [/itex] Homework Equations Lorentz transformations \Deltax' = \gamma(\Deltax-u\Deltat) \Deltay' = \Deltay \Deltaz' = \Deltaz \Deltat' = \gamma(\Deltat-u\Deltax/c^{2}) The...

Max Tegmark has provided a four part taxonomy of multiverse theories (http://arxiv.org/abs/astro-ph/0302131). The first type can be labeled the "bubble universe" multiverse, in which universes like ours are scattered throughout an infinite space in every direction. Going the other direction...

I'm reading Allen Hatcher's topology book.In order to prove a theorem about homotopic maps induce the same homomorphism of homology groups,given a homotopy F:X \times I \to Y from f to g,the author construct a prism operators P:C_n (X) \to C_{n + 1} (Y) by P(\sigma ) = \sum\nolimits_i {( - 1)^i...

Hi all, First of all, sorry for not using the template, but I think in this situation it's better to explain my problem right away: I'm studying for a physics test, but I think I don't really understand Galilean invariance. In my textbook there is an example in which they proof that if you...

Homework Statement Show that the KdV has Galilean invariance. That is ut + 6uux + uxxx = 0 is invariant under the transformation xi = x - ct, tau = t, psi = phi - c/6 Homework Equations The Attempt at a Solution Do we use the chain rule on these and plug into the KdV?

http://books.google.com/books?id=qhDFuWbLlgQC&lpg=PP1&pg=PA11#v=onepage&q&f=false" Until he arrives at eq. 1.5 I don't understand the steps, can anyone explain it? thanks

The Schrodinger equation is linear in time. I was wondering if that means that is not invariant under time reversal. That would be a surprise because all other microscopic laws (Maxwell's equations, Newton's equations) are time invariant. Can you please clear this doubt?

I've been reading up on the idea of an invariant length (planck length possibly) and have tried my hand at modifying the lorentz transformations of SR such that they accommodate an invariant length. Unfortunately I haven't been able to find a way to do it. Does anyone know how one would go about...

Hi folks, If I have a Lie algebra \mathfrak{g} with an invariant (under the adjoint action ad of the Lie algebra) scalar product, what are the conditions that this scalar product is also invariant under the adjoint action Ad of the group? For instance, the Killing form is invariant under...

I am trying to understand the derivation of the covariant derivative in Peskin/Schroeder (chapter 15.1, page 483). This is the important stuff: n^\mu\partial_\mu\psi=\lim_{\epsilon \rightarrow 0} \frac{1}{\epsilon}\left[\psi(x+\epsilon n)-\psi(x)\right] Scalar quantity: U(y,x): U(y,x)...

Homework Statement So I'm trying to show for a specific, given EM plane wave in vacuum that kx - \omega t = k' x' - \omega' t' but I'm running into some difficulties. I'm hoping someone can show me where I'm going wrong. Here's the setup: In the lab frame K, a plane EM wave traveling in...

Hello everyone, I am new to the forum and was wondering if someone can help explain something to me. I would like to understand the meaning of a positivly invariant system. I have checked the definition on wikipedia, http://en.wikipedia.org/wiki/Positive_invariance" and it is...

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...