Transformation Definition and 1000 Threads

How does it work? (The derivative rules of FT) We look at $$F[x(t)]=\hat{x}(f)$$ $$\mathcal{l} \text{ is a distribution, with}\tilde{x}=tx(t)$$ $$\mathcal{F}[Dl(x)]=\mathcal{F}l'(x)=2\pi il(\mathcal{F}\tilde{x})=2\pi i \mathcal{F}l(\tilde{x})$$ Till here I fully understand. But next step...

In Newmann-Penrose formalism, a Null rotation with ##l## fixed is $$l^a−>l^a\\ n^a−>n^a+\bar{c}m^a+c\bar{m}^a+c\bar{c}l^a\\ m^a−>m^a+cl^a\\ \bar{m}^a−>\bar{m}^a+\bar{c}l^a$$ Using this transformation, how to prove? $$π−>π+2\bar{c}ϵ+\bar{c}^2κ+D\bar{c}$$ Ref: 2-Spinors by P.O'Donell, p.no, 65

Hi All; I was trying to understand Lorentz Transformation equation and special theory of relativity, but as I compared the derivation with a thought experiment which I imagined I found the whole Lorentz Transformation Equation fails. The details of the problem is given below. I know I m wrong...

Hi All; I was trying to understand Lorentz Transformation equation and special theory of relativity, but as I compared the derivation with a thought experiment I created I found the whole Lorentz Transformation Equation fails. The details of the problem is given in the pdf file attached. I know...

Homework Statement Given the transformation fh : R 3 → R 3 defined by fh(x, y, z) = (x−hz, x+y −hz, −hx+z), where h ∈ R is a parameter. a) Find, for all possible values of h, Ker(fh), Im(fh), their bases and dimensions. b) Is fh an isomorphism for some value of h? Homework Equations Ax=o The...

Alternate title: Is the textbook contradicting itself? imgur link: http://i.imgur.com/3sTVgwr.jpg But imgur link: http://i.imgur.com/33Ufncb.jpg So...it would appear that transposing has the property of linearity, but no matrix can achieve it...is transposing a linear transformation? The...

Mod note: Moved from Precalc section 1. Homework Statement Given l : IR3 → IR3 , l(x1, x2, x3) = (x1 + 2x2 + 3x3, 4x1 + 5x2 + 6x3, x1 + x2 + x3), find Ker(l), Im(l), their bases and dimensions. My language in explaining my steps is a little sloppy, but I'm trying to understand the process and...

Homework Statement Hi this isn't really a question but more so understanding an example that was given to me that I not know how it came to it's conclusion. This is a question pertaining linear transformation for coordinate isomorphism between basis. https://imgur.com/a/UwuACHomework Equations...

Homework Statement Point transformation in a system with 2 degrees of freedom is: $$Q_1=q_1^2\\Q_2=q_q+q_2$$ a) find the most general $P_1$ and $P_2$ such that overall transformation is canonical b) Show that for some $P_1$ and $P_2$ the hamiltonain...

I am having a hard time understanding vector transformations. I know that vectors must transform a certain way and that dual vectors (or covectors) transform the "opposite" way. What is strange to me is that the basis vectors transform like dual vectors and the basis dual vectors transform like...

Homework Statement I've posted a few of these recently. I have one question about this problem -- hopefully my calculations are correct. f: R2 to P1, f(a,b)=b+a2x Is this a linear transformation? Homework Equations f(u+v) = f(u) + f(v) f(cu) = cf(u) where u and v are vectors in R2 and c is...

While 2nd law of thermodynamics emphasizes past->future time direction, CPT theorem says that at least microscopic physics has some symmetry between past and future. For example the Feynman-Stueckelberg interpretation suggests to see anti-particles as traveling back in time. So thermodynamics is...

If I have the following relations: X = sqrt(1-V^2)*cos(U) Y = sqrt(1-V^2)*sin(U) Z = V where (-pi < U < pi) and (-1 < V < 1) are independent random variables, both with uniform distributions. How do I use the CDF method to find X_pdf(x)? X_pdf(x) = X_cdf'(x) = ( P( X < x ) )' = ( P(...

Homework Statement R2 to R1 f(x,y)=xy Determine if the transformation is linear or not Homework Equations T(V1+V2) = T(V1) + T(V2) T(cV1) = Tc(V1) The Attempt at a Solution If the function f(x,y) = xy we can define another function f(a,b)=ab Therefore, f(x,y) = f(a,b), so xy=ab, so all...

Homework Statement A train travels in the +x direction with a speed of β = 0.80 with respect to the ground. At a certain time, two balls are ejected, one traveling in the +x direction with x-velocity of +0.60 with respect to the train and the other traveling in the −x direction with x-velocity...

Homework Statement If in a system with i degrees of freedom the $$Q_i$$ are given what is the best way to proceed for finding the $$P_i$$ so that we have an overall canonical transformation. say for a two degree freedom system we have $$Q_1=q_1^2 $$ and $$ Q_2=q_1+q_2$$ Homework Equations...

Homework Statement A ball that weights 1kg is thrown in the air, the hand being 1m above the ground. The velocity the ball was thrown at was 14m/s and it's maximum height was 6.5m above the ground. What is the efficiency for this energy transformation? Homework Equations Do I just get the...

Homework Statement There are three observers, all non accelerating. Observer B is moving at velocity vBA with respect to observer A. Observer C is moving at velocity vC B with respect to observer B. All three observers and all their relative velocities are directed along the same straight line...

I asked this question to PhysicsStackExchange too but to no avail so far. I'm trying to understand the way that the Higgs Mechanism is applied in the context of a U(1) symmetry breaking scenario, meaning that I have a Higgs complex field \phi=e^{i\xi}\frac{\left(\rho+v\right)}{\sqrt{2}} and...

Hi, Could you please explain me why, under the transformation of a complex valued field Φ→eiαΦ, for an infinitesimal transformation we have the following relation? δΦ=iαΦ Thanks a lot

Homework Statement I'm trying to find the direction and magnitude of Earth's gravity on some projectile. The question states that I can ignore z, and that the origins of the x and y axes should be on the surface of the planet. I should then use Newton's law of Gravity to find the direction and...

Hi, the following is taken from Peskin and Schroeder page 36: ##\partial_{\mu}\phi(x) \rightarrow \partial_{\mu}(\phi(\Lambda^{-1}x)) = (\Lambda^{-1})^{\nu}_{\mu}(\partial_{\nu}\phi)(\Lambda^{-1}x)## It describes the transformation law for a scalar field ##\phi(x)## for an active...

Homework Statement I have a particle moving with uniform velocity in a frame ##S##, with coordinates $$ x^\mu , \mu=0,1,2,3. $$ I need to show that the particle also has uniform velocity in a frame ## S' ##, given by $$x'^\mu=\dfrac{A_\nu^\mu x^\nu + b^\mu}{c_\nu x^\nu + d}, $$ with ##...

Ok, so as far as I understand it, it is impossible to turn linear momentum (p) into rotational momentum (L), but I don't quite understand why. The main thought experiment I have in my head is this: A ball in space is traveling with a momentum mbVb, and gravity and friction are assumed to be...

I have to find a unitary transformation that takes me from one quantum state to another (or if there is such a transformation), given the two quantum states in matrix form. The matrices are huge (smallest is 16x16) , so doing it on paper is not an option. Does anyone know how I can do this in...

Homework Statement Show that if a transformation ##\Phi \rightarrow \Phi + \alpha \partial \Phi/ \partial \alpha## is not a symmetry of the Lagrangian, then the Noether current is no longer conserved, but rather ##\partial_{\mu}J^{\mu} = \partial L/ \partial \alpha##. Use this result to show...

I will start with a summary of my confusion: I came across seemingly contradictory transformation rules for left and right chiral spinor in 2 books, and am unable to understand what part is Physics and what part is convention. Or is it that one of the two books incorrectly writes the...

Homework Statement The lagrangian is given by: L = -\frac{1}{4} F^2_{\mu \nu} + (\partial_{\mu} \phi_1 - m_1 A_{\mu})^2 + (\partial_{\mu} \phi_2 - m_2 A_{\mu})^2 Homework Equations Find the gauge transformation of the fields that corresponds to a symmetry. Find the combination of scalar...

1. Problem statement: Assume that u is a vector and A is a 2nd-order tensor. Derive a transformation rule for a 3rd order tensor Zijk such that the relation ui = ZijkAjk remains valid after a coordinate rotation.Homework Equations : [/B] Transformation rule for 3rd order tensors: Z'ijk =...

So I am going through the exam guide for my exam tomorrow and there is a second problem that stump me. We transform the cartesian axis to <1/√3,1/√3,1√3> and <1/√2,0,-1/√2> which are orthogonal and we find the third axis by taking the cross product which gives <-881/2158,881/1079,-881/2158>...

Hi, I have a reference device that outputs euler angles, which are angles that relate the sensor body frame to the north east down frame. These angles are called pitch roll and yaw. The sensor is an accelerometer. I know how to get the rotation matrix that will put accelerations from the...

I'd like to prove the fact that - since a rotation of axes is a length-preserving transformation, the rotation matrix must be orthogonal. By the way, the converse of the statement is true also. Meaning, if a transformation is orthogonal, it must be length preserving, and I have been able to...

Homework Statement Homework EquationsThe Attempt at a Solution I would just like to know what is being requested when it asks me to draw sketches in order to illustrate that T is linear. Does it have something to do with altering to position of the line L itself? Any help would be very much...

My maths teacher taught me a shortcut for finding area bounded by curves of the form: $$|as+by+c|+|Ax+By+C|=d$$ Shortcut: Let required area be ##A_0## and new area after "transformation" be ##A## Then, $$A_0\begin{vmatrix} a& b\\ A& B\end{vmatrix}=A=2d^2$$ All I understood was the ##A=2d^2##...

1,2,3. Homework Statement I tried to derive the length contraction using the Lorentz transformation matrix and considering 2 events. I reached the correct result but there's a step that I had to assume that I don't understand. Consider a ruler of length L along the x-axis for an observer at...

Homework Statement Being T: ℝ2 → ℝ2 the linear operator which matrix in relation to basis B = {(-1, 1), (0, 1)} IS: [T]b = \begin{bmatrix} 1 & 0\\ -3 & 1 \end{bmatrix} True or False: T(x,y) = (x, 3x+y) for all x,y∈ℝ? Homework EquationsThe Attempt at a Solution 3 [/B] So first I convert (x,y)...

Hello everyone, I have a little problem with some transformation. I wonder how i can get that result. Can somebody explain it step by step? The " ' " means derivative. Thank you for your time ;)

Homework Statement Let A and B be n x m matrices, and λ and μ be real numbers. Prove that: (λA+μB)^T = λA^T+μB^t Homework Equations :/ The Attempt at a Solution I'm struggling to start here. If there was no λ and μ, I think I'd be able to reasonably solve this. How do I show that these...

Consider a model with an exact ##SU(N_{TC})## techni-color symmetry and a ##SU(N_{TF})_L\otimes SU(N_{TF})_R## global techni-flavour symmetry which is spontaneously broken to the diagonal sub-group ##SU(N_{TF})## by condensates producing techni-pions (TC\pi) and techni-baryons(TCb). What I'm...

Hello, I am stuck on the following problem. 1. Homework Statement Consider the continuous family of coordinate and time transformations (for small ##\epsilon##). Q^{\alpha}=q^{\alpha}+\epsilon f^{\alpha}(q,t) T= t+\epsilon \tau (q,t) Show that if this transformation preserves the action...

Here is a problem: Imagine two equally charged capacitor plates parallel to the x-y axis, whose area is large enough compared to the distance between them that fringe effects can be ignored. The bottom plate (at z=0) is + charged, and the top is - charged. The vector field E is therefore...

Given the Lorentz matrix Λuv its transpose is Λvu but what is its transpose ? I have seen ΛuaΛub = δb a which implies an inverse. This seems to be some sort of swapping rows and columns but to get the inverse you also need to replace v with -v ? Also In the LT matrix is it the 1st slot...

Homework Statement Suppose a linear transformation T: [P][/2]→[R][/3] is defined by T(1+x)= (1,3,1), T(1-x)= (-1,1,1) and T(1-[x][/2])=(-1,2,0) a) use the given values of T and linearity properties to find T(1), T(x) and T([x][/2]) b) Find the matrix representation of T (relative to standard...

Lets suppose we have a close system.In this system we have a particles.The total mass of particles is M. The total energy of system will be ##E_x+E_M=E_t## (I made the system like this) Here ##E_x## is just energy,its not important.##E_m## is the energy of masses.Now I want to move this...

<< Thread moved to the HH forums from the technical engineering forums, so no HH Template is shown >> The model: The goal: 1. Create a three phase voltage 2. Do a alpha-beta transformation 3. Do a Cartesian to Polar transformation 4 Check the output angle The expected result: Since the space...

We were asked to form the transformation matrix that rotates the x1 axis of a rectangular coordinate system 60 degrees toward x2 and the x3 axis. The thing is, I don't understand what it meant by rotating one axis toward the two other. Like, do I rotate x1 60 degrees toward the x2-x3 plane or...

Homework Statement Let T:[R[/3]→[R[/3] so that when u=[R][/3] and v=(1,2,1), then T(u)=u×v a) Show that T is a linear transformation. b) Find T((3,0,2)) c) Find a basis for Ker( T ). Give a geometric description of Ker( T ). Homework Equations Properties of a linear transformation: i) T(u+v)=...

I can't understand the transformation can anyone explain it to me.and suggest a good book on it.

Homework Statement Transform the coordinates from the red c-system to the blue system. (Picture) Homework Equations Using(X Y) for the red cartesian system and (x y) for the blue system The Attempt at a Solution The solution to this problem gives x=Xcos▼ + Ysin▼ y=-Xsin▼+Ycos▼ Im not sure...

I am confused about the order in which we apply transformations to a input of a parent function to get the corresponding input of the new function. Say for example, we have the function ##y = \sin(-2x + 1)=\sin(-2(x-\frac{1}{2}))##. Intuitively, it would seem as though we would transform a point...