Transformation Definition and 1000 Threads

We have all seen Lorentz transformations being written like this ##\Lambda ^\mu\;_\nu##, but why are they never written as ##\Lambda _\nu\;^\mu##?

Given a scalar function, we consider the following transformation: $$\delta f(x) = f'(x') - f(x) $$ Given a coordinate transformation $$x' = g(x)$$ But since ##f(x)## is a scalar isn't it true that ##f'(x') = f(x) ## Then the variation is always zero? What am I missing?

We make an infinitesimal Lorentz transformation of the Lagrangian and require it to be invariant. We then arrive at the following expression. $$\epsilon^{\mu\nu}j_{\mu\nu} = P_{\mu}\epsilon^{\mu\nu}X_{\nu}$$ which can be written as $$\epsilon^{\mu\nu}j_{\mu\nu} =...

Homework Statement Find the Thevenin equivalent at terminals a-b V1 = 70V V2 (dependent) = 4Vo R1 = 10Kohm R2 = 20Kohm Homework Equations ##V=RI## ##1/req = 1/r1 + 1/r2 + ... +1/rn## The Attempt at a Solution Found the current i = 1mA by KVL using Vo = 10ki then did source...

How to prove any orthogonal transformation can be represented by the product of many mirror transformations, please?What's the intuitive meaning of this proposition? Thank you.

If space only had one dimension would Einstein's speed of light postulate still lead to Lorentz transformation for motion along that one dimension? Relativity of simultaneity can obviously be demonstrated in one dimension (lightning bolts hitting opposite ends of stationary and moving train)...

Hi all, I am currently working on a creating a mathematical model of a longboard and am in need of advice. The pictures describe the sitaution. Side view Top view Back view The pictures depict a simplified longboard - the brown line is the deck and the black lines represent the...

Hi! I'm doing my master thesis in AdS/CFT and I've read several times that "Fields transforms in the adjoint representation" or "Fields transforms in the fundamental representation". I've had courses in Advanced mathematics (where I studied Group theory) and QFTs, but I don't understand (or...

Homework Statement I am having a issue relating part of this question to the Galilean transformation. Question Relative to the laboratory, a rod of rest length ##l_0## moves in its own line with velocity u. A particle moves in the same line with equal and opposite velocity . How long dose it...

From a previous, now closed thread (Perok): "Technically, the Lorentz Transformation is not about observers but about reference frames." Sorry, I still don't get this. In frame A with observer A at the origin, x is the distance of the event X he sees measured on his rod, i.e. as...

The Lorentz transformations are mathematically simple. I had always imagined they could be easily derived. I however just found out from another PF thread that this is not so. Their originators Lorentz and Poincaré simply stated them without derivation. And the "proofs" I have seen to date have...

I know, $$ L=T-V \;\;\; \; \;\;\; [1]\;\;\; \; \;\;\; ( Lagrangian) $$ $$ H=T+V \;\;\; \; \;\;\;[2] \;\;\; \; \;\;\; (Hamiltonian)$$ and logically, this leads to the equation, $$ H - L= 2V \;\;\; \; \;\;\...

Homework Statement I'm considering a non-linear chiral theory where the Lagrangian is in terms of the field #\Sigma = e^{\frac{2i\pi}{f}}# where #\pi# is my pion matrix containing pion, kaon, and #\eta#. I need to calculate the transformation of #\pi# up to order #\pi^2# under an axial...

Homework Statement According to observer ##O##, a blue flash occurs at ##x_b =10.4m## when ##t_b =0.124 μs##, and a red flash occurs at ##x_r =23.6m## when ##t_r =0.138 μs##. According to observer ##O'##, who is in motion relative to ##O## at velocity ##u##, the two flashes appear to be...

Hi! When we want to look at different singular points for e.g Bessel's eq. $$u´´(x) + \frac{u'(x)}{x} + (1- \frac{n^2}{x^2})u(x)$$. We usually evaluate the equation letting x= 1/z. But I don't algebraically see how such a substitution ends up with $$w´´(z) +( \frac{2}{z}-...

Hello, I’m new to the cosmological inflation so in this paper: https://arxiv.org/abs/1809.09975 Has some one an idea how to make the Weyl transformation of the metric ## g_{\mu\nu}## Equation (3) , and how to get the potential (4) from the action (3) by this transformation as explained after...

Please tell me if Lorentz Transformation would be altered in any way if the invariance of c is explained, instead of postulated.

In Chapter 7: Hamilton's Principle, in the Classical Dynamics of Particles and Systems book by Thornton and Marion, Fifth Edition, page 258-259, we have the following equations: 1. Upon squaring Equation (7.117), why did the authors in the first term of Equation (7.118) are summing over two...

I put the level for this thread as I, but anything from B to A is acceptable here. I'm hoping this isn't too imprecise, but what are the easiest or simplest (or fastest) ways to derive the Lorentz transformation equations you know? I am not after blatant corner cutting here, by the way. Just...

Hello, I'm trying to follow Goldstein textbook to show that the Lagrangian is invariant under coordinate transformation. I got confused by the step below So ## L = L(q_{i}(s_{j},\dot s_{j},t),\dot q_{i}(s_{j},\dot s_{j},t),t)## The book shows that ##\dot q_{i} = \frac {\partial...

How can we derive Lorentz Transformation ? I used one approach using the length contraction and time dilation and simultaneity but my prof wasnt much happy about it. Is there any other way to derive it ?

Homework Statement How can we derive Lorentz Transformation using the length contraction and time dilation equations of relativity ? Homework Equations ##γ = 1/ (\sqrt{1-u^2/c^2})## ##t = t_0γ## ##L = L_0/γ## The Attempt at a Solution [/B] In position Lorentz Transformation calculations...

Hi. I came across the following statement , which seems wrong to me. Λμρ = ( ΛT )ρμ I have it on good authority (a previous post on this forum) that (ΛT)μν = Λνμ so I am hoping that the first equation is wrong ? It looks like the inverse not the transpose ? The equation Λμρ η μνΛνσ = ηρσ is...

Homework Statement Given the matrix $$ \Omega = \begin{pmatrix} 0 & -\psi & 0 & 0 \\ -\psi & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{pmatrix}$$ show that ## e^{\Omega}## is a Lorentz transformation along the x-axis with ## \beta = tanh(\psi)## Homework Equations During the lesson we...

Hi, I've seen several explanations for sr on youtube. But they all start off explaining from a different perspective. I was wondering how the fundamental postulates of sr lead to the invariance of proper time between frames, and also what "order" everything is derived in. For example, does the...

Homework Statement Show that if you add a total derivative to the Lagrangian density ##L \to L + \partial_\mu X^\mu##, the energy momentum tensor changes as ##T^{\mu\nu} \to T^{\mu\nu}+\partial_\alpha B^{\alpha\mu\nu}## with ##B^{\alpha\mu\nu}=-B^{\mu\alpha\nu}##. Homework EquationsThe Attempt...

Homework Statement Let's call the axis of the ##z## complex plain ##x## and ##y##, so a general point can be written as ##z=x+iy##. Reflect the points of the complex plain so that the mirror line of the transformation is a line parallel to the vector ##v## and it passes trough the point ##u##...

In General Relativity, "gauge" transformations are basically coordinate transformations which preserve length. In Electroweak and the gauge forces like EM.. what are being preserved? I forgot my lessons before and would like to refresh.

I've finally worked out a derivation of the Lorentz transformation that doesn't use the now out of favor i^2=-1, but it still has one weak spot: it assumes that the transformation is linear. It seems quite reasonable to me that it would be linear since it has to graph straight lines on to...

One of my homework questions said "Explain how to obtain f(x)=-(3+x)^2+1 from the graph of y=x^2." I know somehow you need to move the graph right 3, reflect about the x-axis, and move up one, but I don't know how to factor and manipulate the equation to show this.

Hello! (Wave) Let $B=(b_1, b_2)$, $C=(c_1, c_2)$ basis of $\mathbb{R}^2$ and $L$ operator of $\mathbb{R}^2$, the matrix as for $B$ of which is $\begin{pmatrix} 2 & 2\\ 1 & 0 \end{pmatrix}$. If $b_1=c_1+2c_2+b_2=c_1+3c_2$ and $A=\begin{pmatrix} a_{11} & a_{12}\\ a_{21} & a_{22} \end{pmatrix}$...

Homework Statement Based on Fig. 4, ZΔ=6+8j Ω ZY=4+3j Ω EL=200V Show that the equivalent delta-connected load is 7.846 - 2.77j Homework Equations ZY=(1/3)ZΔ The Attempt at a Solution Here's my thought process: For part (i), attempt to convert Y to Δ, So using the relevant equation above ZΔ...

Dear Everybody, I am having some problem with one exercise. And the question states: Find the transformation Matrix R that describes a rotation by 60 degrees about an axis from the origin thru the pt (1,1,1). The rotation is clockwise as you look down toward the origin. I know the standard...

I would like to ask about unitary transformation. UA(IV) UB*UA(IV) UAT(UB*UA(IV))=UB(IV) UB(IV)*(X) IVT(UB(IV)*(X))=UB(X) UBT*UB(X)=X From the information above, UAT,IVT and UBT are the transpose of the complex conjugate. The aim of this code is to get the value of X in the step 4. This is...

This is intuitively very simple problem but I am unable to complete it with Mathematical rigor. Here is the deal: A coordinate system $(u,v,w,p)$ in which the metric tensor has the following non-zero components, $g_{uv}= g_{ww}=g_{pp}=1$. Find the coordinate transformation between $(u,v,w,p)$...

Hello PF, in Carroll’s “Spacetime and Geometry”, he works out the transformation law for connection coefficients in his introduction to covariant derivatives, and I’m wondering if there is a typo in the final equation. He starts with$$\nabla_{\mu} V^{\nu} = \partial_{\mu} V^{\nu} +...

I want the proof for a general wavefunction Ψ(x,t).

Homework Statement For a left invariant vector field γ(t) = exp(tv). For a gauge transformation t -> t(xμ). Intuitively, what happens to the LIVF in the latter case? Is it just displaced to a different point in spacetime or something else? Homework EquationsThe Attempt at a Solution

Homework Statement attached: Homework Equations where ##J_{yz} ## is The Attempt at a Solution [/B] In a previous question have exponentiated the generator ##J_{yz}## to show it is the generator of rotation around the ##x## axis via trig expansions so ##\Phi(t,x,y,z) \to \Phi(t,x,y cos...

Hi, i need some help here. Can you help me?:sorry: Here is the problem. Exercise statement: The switch have been closed for a long time y is opened at t=0. Using Laplace's transtormation calculate V0(t) for t ≥ 0 This is what i made to solve it: 1) I know while the switch is closed, the...

Homework Statement Let ##V## and ##W## be vector spaces, ##T : V \rightarrow W## a linear transformation and ##B \subset Im(T)## a subspace. (a) Prove that ##A = T^{-1}(B)## is the only subspace of ##V## such that ##Ker(T) \subseteq A## and ##T(A) = B## (b) Let ##C \subseteq V## be a...

Homework Statement [/B]Homework EquationsThe Attempt at a Solution [/B] From Poisson bracket relation I have arrived at this point Can anyone please suggest to proceed further

I was reading about the homothetic transformation, and it seems that the perspective transform is a type of this.

hi guys i recently was reading about hawking radiation and how he overcome the lack of a theory for quantum gravity by using a mathematical trick ( to see the effect of gravity on quantum fields ) and this trick was the Bogoliubov transformation ... , i just want some one to briefly explain...

Homework Statement 1. (a) Prove that the following is a linear transformation: ##\text{T} : \mathbb k[X]_n \rightarrow \mathbb k[X]_{n+1}## ##\text{T}(a_0 + a_1X + \ldots + a_nX^n) = a_0X + \frac{a_1}{2}X^2 + \ldots + \frac{a_n}{n+1}## ##\text{Find}## ##\text{Ker}(T)## and ##\text{Im}(T)##...

how do you graph this in Desmos ? Assume the rest of the calculation is correct much thank you ahead...:cool:

Let me show you part of a book "Mechanics From Newton’s Laws to Deterministic Chaos" by Florian Scheck. I do not understand why these integrands can differ by more than time derivative of some function M. Why doesn't it change the value of integrals? It seems this point is crucial for me to...

In discussion with my friend, we reached a conclusion that transformation formula of velosity v to another IFR moving V, i.e. v'=\frac{v+V}{1+vV/c^2} is valid even if v is hypothetical velocity,i,e, v=\frac{x_2-x_1}{t_2-t_1} v'=\frac{x'_2-x'_1}{t'_2-t'_1} where interval of ##(t_1,x_1)\rightarrow...

Hello all, I am reading through the Jackson text as a hobby and have reached a question regarding the Hamiltonian transformation properties. I will paste the relevant section from the text below: I don't understand what he's getting at in the sentence I highlighted. To attempt to see what...

In 1851 Fizeau made a famous experiment which corroborated de Fresnel's drag coefficient of the luminiferous ether. In the experiment two light beams traveled through a tube of moving water (at 7cm per second), one moving against the water flow (let's called it beam A), and one for the water...