Lorentz Definition and 1000 Threads

I am attempting to read my first book in QFT, and got stuck. A Lorentz transformation that preserves the Minkowski metric \eta_{\mu \nu} is given by x^{\mu} \rightarrow {x'}^{\mu} = {\Lambda}^\mu_\nu x^\nu . This means \eta_{\mu \nu} x^\mu x^\nu = \eta_{\mu \nu}x'^\mu x'^\nu for all x...

Not sure if Velocity Addition belongs in introductory Physics but it seems relatively introductory to me. I'm having trouble with all aspects of grasping how to attempt these problems logically. Obviously the math behind them is super simple; I just more or less don't know what to plug in where...

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

Hello, I was reading and trying to follow up with Pierre Ramond's "Field theory: A modern primer" and got stuck in his step to step jumping. Kindly, see attachment and note that Eq (1.2.6) = g_{ρσ}=g_{μ\upsilon}\Lambda^{μ}_{ρ}\Lambda^{\upsilon}_{σ}. My question is what do I need from tensor...

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...

Homework Statement A rocket ship carrying passengers blasts off to go from New York to Los Angeles, a distance of about 5000 km. (a) How fast must the rocket ship go to have its own length shortened by 1%? (b) Ignore effects of general relativity and determine how much time the rocket...

Homework Statement Two events occur in an inertial system K as follows: Event 1: x1 = a, t1 = 2a/c, y1 = 0, z1 = 0 Event 2: x2 = 2a, t2 = 3a/(2c), y2 = 0, z2 = 0 Is there a frame K' in which the two events described occur at the same place? Explain. Homework Equations Lorentz...

Homework Statement It is not an official question but a request for pointers. I am trying to derive the Lorentz time equation to understand the intuition behind it. My math skills are not very good so it might be an obvious question for you. Please see below for my attempt. The variables are...

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...

Homework Statement I am learning special relativity and we came across the invariant quantity s = x2 - (ct)2. Our professor wants us to prove it. I admit that this is a proof and belongs in the mathematics section but I didn't see an Algebra section and this is most easily identified by those...

Hi all, I'm trying to derive that t=δ(t'+vx'/c^2) Using x'=δ(x-vt) then substituting for x=δ(x'+vt') I should be able to isolate t and solve the problem but I am getting to the following point after simplification and can't figure out where to go next...? x'= δ[δ(x'+vt')-vt] (isolate...

[Mentor's note: This question was originally posted and responded to in a non-homework forum, therefore it does not have the usual homework template.] Hey, don't know how to solve this: In an inertial frame S, consider a light ray on the XY plane forming a 60 degree angle with the x-axis...

Depending on where I go to get a good understanding of the Lorentz transformations, I run into two formulas for time (t): T=T_0 * \frac{1}{ \sqrt{ 1-\frac{v^2}{c^2} } } and t=\left( t' + \frac{vx'}{c^2} \right) * \frac{1}{ \sqrt{ 1-\frac{v^2}{c^2} } } What is the...

Where is the glitch? 1. Let a single free electron move along x-axis with constant speed Vx. It encounters magnetic field on its right side, so the Lorentz force accelerates it along y-axis and it gains speed Vy. --- Glitch or pass? 2. The electron does not slow down in x direction when...

Hello, On p.573 of Jackson 2nd Ed. (section 12.1), he says, "From the first postulate of special relativity the action integral must be a Lorentz scalar because the equations of motion are determined by the extremum condition, \delta A=0." I agree that if the action is a Lorentz scalar, then...

A first stage of the determination. We have a body of length L = AB, which moves along the x-axis with velocity v, say that coming to us. A -------- B v <--- | | h - vertical distance | ./ - a light converges to us with the speed eq. c | / O ---------> x At some time t = 0, we see the point A...

In order for the light to take the same amount of time for both paths in the interferometer, simple geometry implies that the ratio between length and width will have to decrease. A straightforward derivation gives L/W=Sqrt(1-v^2/c^2) where the velocity v is in the direction of the length...

Homework Statement Not sure whether to put this in advanced or intro forum, but ill just put it in here. So here's the context of the question: a linear swarm of 3 meteors are traveling at a speed of 0.9c towards our solar system (in the solar system reference frame). Each adjacent meteor is...

Basically I am trying to lorentz transform the magnetic field along θ of a bunch particles which have a gaussian distribution to the radial electric field. However the magnetic field in θ is dependent on the longitiudinal distribution. Now initially i thought we would just use the standard LT...

Hi, While reading "Superspace: One Thousand and One Lessons in Supersymmetry" by Gates et al. I came across the following paragraph: Maybe I haven't understood what exactly they're trying to say here, but 1. Why is the Lorentz Group SL(2, R) instead of SL(2, C)? 2. Why is the two-component...

Two part inquiry PART I Situation: I have a B-field and I'm pulling a straight piece of wire through that B-field You pull the wire perpendicularly through the B-field at velocity v; charges between points a and b will experience the Lorentz Force and will begin to move along...

I am trying to derive the algebra and I get a factor of 2 wrong... Consider the Lorentz group elements near the identity \Lambda_1^\mu\,_\nu = \delta^\mu\,_\nu + \omega_1^\mu\,_\nu, \quad \Lambda_2^\mu\,_\nu = \delta^\mu\,_\nu + \omega_2^\mu\,_\nu and write a representation as...

Definition/Summary A Lorentz transformation is the relation between the coordinates of two inertial observers who use the same event as their origin of coordinates. A Lorentz boost is a Lorentz transformation with no rotation (so that both observers use the same coordinate-name for the...

Hello everyone. I am attempting to teach myself about special relativity, and have learned a derivation for the Lorentz transformation. Before I go any farther I want to clear up the parts I don't understand right now and check that I am correct about the parts I do understand. Here I will...

I have encountered a difficulty which arises from my attempt to combine non collinear Lorentz transformations in analyzing the following problem: A thin rod is cut from a metal plate leaving a slot of exactly the same size. The two are separated and set in motion thus: the rod lies along x...

Hi all, What is the difference between Lorentz transformations and yt?. That is, the Lorentz transformations for moving between two reference frames are not the same as the relativistic ones. For example considering a frame F that is stationary and an inertial frame F' with velocity v. Time...

A lorentz transformed electric field has it's own name. It's called a magnetic field. That makes me wonder if there is a name for a lorentz transformed gravity field? Also is it theoretically possible to build a "gravity transformer"? i.e. a transformer that uses moving mass instead of...

Is there anywhere I can see the explicit derivation for a massless real scalar and for the EM field? thank you.

Hi, I am trying to derive the Lorentz force law in the following form: q \frac{dw^\mu}{d\tau} = q w^\mu \partial_\nu A_\sigma \epsilon_\mu^{\nu \sigma} by varying the following Lagrangian for a classical particle: S = \int d^3 x \left( -m \int d\tau \delta(x-w(\tau) ) + q \int d\tau...

Hi! I'm having problems with this homework my professor gave us this morning: Prove that Maxwell's equations is invariant under Lorentz Transformation. I'm just currently in third year, and we haven't been taught tensors yet. The extent of what I know mathematically is only until gradient...

My question is essentially a variation of the Ehrenfest paradox in SR. But hopefully with some experimental data. In the LHC, for example, a fixed number of particle bunches with some length are injected into the main ring. Now, as the velocity of the particles increases, the bunches would be...

When a wire is placed in a magnetic field and current flows in that wire work is done on the wire and be calculated: 1) W = Fd 2) F = IL x B 3) W = ( IL x B )x d Must there be any derivations beyond what is above? If everything is "given" or... measured via instruments. Then...

To=(time of moving object.) T=(Time of standing object.) ^=power of number. sqrt=square of number.(x^1/2)Law of einstein say: T= To / ( sqrt( 1 - u^2/c^2 ) ) Lorentz law say: T= (To + u*Xo/c^2) / ( sqrt( 1 - u^2/c^2 ) )Why there is difference?? Is for other things?? I thought is for the same...

In Ryder's Quantum Field Theory it is shown that the Lie Algebra associated with the Lorentz group may be written as \begin{eqnarray} \begin{aligned}\left[ A_x , A_y \right] = iA_z \text{ and cyclic perms,} \\ \left[ B_x , B_y \right] = iB_z \text{ and cyclic perms,} \\ \left[ A_i ,B_j...

When the Lorentz force is applied on a wire that has current flowing in a magnetic field, by changing the direction of the electron(not it's KE) would this possibly change the direction of the Lorentz force? Can the wire be controlled in a way that the force's direction stays the same path?

Homework Statement Prove that under an infinitesimal Lorentz transformation: x^\mu \to x^\mu+\omega^\mu_\nu x^\nu so: \phi\to\phi-\omega^\mu_\nu x^\nu\partial_\mu\phi the Lagrangian varies as: \delta \mathcal{L}=-\partial_\mu(\omega^\mu_\nu x^\nu \mathcal{L}) The Attempt at a...

Hello all, I have an exam on Monday and am having trouble with this problem, any help would be greatly appreciated! Q: A straight stick of length L' is at rest in the moving S' frame. The stick appears to have length L in the S frame. The S' frame is moving at a velocity √(2/3) c...

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}...

When a wire has current I in a magnetic field B, there is the Lorentz force is it considered a conservative force or not? Please do explain as to why it is.

Consider a pole of 1 light second long in the ##y## direction (the vertical line(s) in the enclosed figure). It is moving in the ##-x## direction. According SR, the pole's length is not contracted because its length is not parallel to the propagation direction. However, given the time of flight...

how can we write and interpret Lorentz generators in light cone coordinates?

We have a few posters struggling with this, I thought I'd post a step by step guide, to see if it would help. That seems easier than trying to untangle the confused threads we have. We'll see if it works... Setup and notation: We have a rocket, which has a front and a back. We have a...

When a wire is placed in a magnetic field, Lorentz force acts on an electron in a direction perpendicular to velocity and to the magnetic field, since the magnetic force is perpendicular to the velocity the electron will only change direction with no velocity change, what happens after that, I...

Hi folks -- does anyone know of a proof that particle (quanta) number in QFT is / is not Lorentz invariant? I'd be happy to hear of it -- so thanks!

In a Lorentz group we say there is a proper orthochronous subspace. How can I prove that the product of two orthchronous Lorentz matrices is orthochronous? Thanks. Would appreciate clear proofs.

I am trying to derive the conserved charge from the symmetry of the action under Lorentz transformations, but I am doing something wrong. Noether's theorem states that the current is J^\mu = \frac{\partial \cal L}{\partial(\partial_\mu \phi)} \delta\phi - T^{\mu \nu}\delta x_\nu For an...

I recently read Griffiths paper on Hidden momentum, and still didn't found it complete. Following is the short summary. The usual setup of current carrying loop and a charge lying nearby, according to the paper, Shockley and James presented the problem, that is, when we let the current die...

I'm currently going through my courses notes for relativity. We looked at Einsteins two postulates and then said that time must therefore dilate due to constant speed of light. That I understand, however I'm still confused about the Lorentz's transformations. My notes start with a basic form of...

So i am working on a question, which is beyond my knowledge of Lorentz transformations and some help is greatly appreciated. I have a 4 velocity, u=γ(v vector,c) and its transformation properties are the standard lorentz boost. I don't quite understand how I am supposed to do this given that...

I understand how contravariant 4-vectors transform under a Lorentz transformation, that is: ##x'^μ= \Lambda^\mu~_\nu x^\nu## [1] and how covariant 4-vectors transform: ##x'_\mu=(\lambda^{-1})^\nu~_\mu x_\nu##. [2] Now, I have come across the following relations...