Transformations Definition and 863 Threads

My book has introduced the idea of gauge invariance in terms of classical electrodynamics (attached file). However, I am not sure I completely understand how it works. On the one hand they use a lot of time on specifying how you can add to the vector potential the gradient of any scalar, whilst...

Homework Statement The problem is attached. The problem statement is to "determine whether the function is a linear transformation between vector spaces." Homework Equations N/A The Attempt at a Solution T(0)=[1 0 0]^t ≠ 0, thus T is not linear. Did i do that right? It seems...

Starting with: x'=\gamma(x-vt) & x=\gamma(x'+vt') I know that I can derive t'=\gamma(t-vx/c^2)... however I can't seem to make it fall out mathematically. The suggested method is to cancel x'. Can anyone help me out on the steps? Much appreciated! :)

Hello PF! Homework Statement The graph of the function y = 2x2 + x +1 is stretched vertically about the x-axis by a factor of 2, stretched horizontally about the y-axis by a factor of 1/3 and translated 2 units right and 4 units down. Write the equation of the transformed function Homework...

I'm taking a quantum field theory course and the topic of active vs passive transformations came up. I have previously taken a physics course and active/passive transformations were never explicitly discussed. What is the difference between the two? In particular I'm trying to follow the...

Homework Statement Im not sure what each of the variables do in y=cax-p +q Homework Equations The Attempt at a Solution my understanding is that -q is for vertical shifts/transformations -p is for horizontal shifts/transformations -and c is for vertical stretching not...

Homework Statement An electron and a positron are observed from the lab to move in opposite directions with a speed of 0.5c and 0.7c, respectively. Find the speed of the positron when observed in the electron's rest frame. Homework Equations in attached PDF The Attempt at a...

Hi. I am trying to understand a statement from Peskin and Schroeder at page 59 they write; "The one particle states |\vec p ,s \rangle \equiv \sqrt{2E_{\vec p}}a_{\vec p}^{s \dagger} |0\rangle are defined so that their inner product \langle \vec p, r| \vec q,s\rangle = 2 \vec E_\vec{p}...

Are Lorentz transformations only work between inertial frames? if so, is there a simple counter-example e.g. for them not to work?

Homework Statement (x+2y+3)dx+(2x+4y-1)dy=0 a1= 1 b1=2 a2=2 b2=4 a2/a1=b2/b1 Therefore z=x+2y Here is where I get confused I understand that they must get a dz in the equations thus they take the derivative with respect to y of the following equation z=x+2y thus giving dz=dx+2 or...

Homework Statement Suzanne observes 2 light pulses to be emitted from the same location, but separated in time by 3μs. Mark sees the emission of the same two pulses separated in time by by 9μs. a) How fast is Mark moving relative to Suzanne? b) According to Mark, what is the separation in...

The following question seems to be simple enough...Anyway, I hope if someone could confirm what I am thinking. Is canonical transformation in mechanics unique? We know that given \ (q, p)\rightarrow\ (Q, P), \ [q,p] = [Q,P] = constant and Hamilton's equations of motion stay the same in the...

Homework Statement The pion has an average lifetime of 26.0ns when at rest. For it to travel 10.0m, how fast must it move? Homework Equations Lorentz velocity transformation? The Attempt at a Solution I'm very lost... am I supposed to use u'x = (ux-v)/(1-vux/c2)? I thought I was following...

I thought Lorentz Transformations left Δt2-Δx2 invariant but, for example a frame moving at .5C for Δt =1 has Δx = .5 so Δt2-Δx2 = .75 If this is transformed by : to a rest frame Δt =0.65 has Δx = 0 and Δt2-Δx2≠ 0.75 not sure where I have gone wrong here, any help would be...

Homework Statement You are piloting a small airplane in which you want to reach a destination that is 750 km due north of your starting location. Once you are airborne, you find that (due to a strong but steady wind) to maintain a northerly course you must point the nose of the plane at an...

I'm trying to understand what a one-parameter group of transformations really is. At one lecture I was told that they are trivial lie groups. In Arnold's "Ordinary Differential Equations" they are defined as an action by the group of real numbers; a collection of transformations parametrised by...

Homework Statement Today in my final i was given this exercise: Given β_1=\{v_1,v_2,v_3\} and β_2=\{u_1,u_2,u_3,u_4\}, basis of the vector spaces V and U respectively. a) Find the linear transformation T:U\rightarrow V so that T(v_i)≠T(v_j) if i≠j, T(v_1)=u_1+u_2 and T is injective b) Find...

I need the time domain response of this system as a unit RAMP input C(s) = ((2s²) + 20s) / ((s²) + 4s + 20) I get that the RAMP input is C(s) = A/s² G(s) And now I think I need to simplify it so I can get it into a form that's on the Laplace Transformation table but this is what I'm...

Dear Forum, I am familiar with the formulas between inertial frames of reference that move at a constant speed between each other. The observed object move at a constant speed or at a constant acceleration. It can be shown that while the positions and velocities are different in the two...

Hi, Im working through some chapters of Goldstein and I'm up to canonical transformations now. On page 370 it says that the variational principle for the hamiltonians K and H are both satisfied if H and K are connected by a relation of the form λ(pq' - H) = PQ' - K + dF/dt And I can see...

Why is it that if you have: U=g_1 (x, y), \quad V = g_2 (x,y) X = h_1 (u,v), \quad Y = h_2 (u,v) Then: f_{U,V} (u,v) du dv = f_{X,Y} (h_1(u,v), h_2 (u,v)) \left|J(h_1(u,v),h_2(u,v))\right|^{-1} dxdy While when doing variable transformations in calculus, you have: du dv =...

If you think about graphing an equation like f(x) = x; you think about a line through the origin in two dimensional space, where the horizontal axis represents the domain and the vertical the image. How can you get the input and the output of a transformation in the same picture? In the...

Hi, I have to take a placement exam in linear algebra this fall so I have been studying some past exams. This is a real basic question. If we have a linear transformation T:W -> W does this imply nothing about the injectivity or surjectivity of the transformation? I assume that it does not, but...

write P for the vector space of all polynomials, a_{0}+a_{1}x+a_{2}x^{2}+...+a_{n}x^{n}, , a_{0}, a_{1},...,a_{n}\inR, n=0,1,2... 1. Find a linear transformation P->P that is onto but not one-to one 2. Find such a linear transformation, that is one-to-one but not onto I have been thinking...

We consider a superfield \Phi\left(x^{\mu}, \theta_{\alpha}\right). For a small variation \delta \Phi = \bar{\epsilon} Q \Phi where the supercharge Q_{\alpha} is given by: Q_{\alpha}=\frac{\partial}{\partial \bar{\theta}^{\alpha}}-\left(\gamma^{\mu} \theta \right) _{\alpha} \partial _{\mu}...

Preface to my question: I can assure you this is not a homework question of any kind. I simply have a pedagogical fascination with physics outside of my own studies in school. Also, I did a quick search through the forum and could not find a question similar enough to what I want to know, so i...

I just purchased a book on the introduction of special relativity and I seem to be stuck on a simple mathematical step. For some reason I just can't see this! This is what it says: Gotta love getting stuck on something when the book says its "Easy to see." Confidence -1.

I have read over and over in various places about coordinate transformations, and understand the theory (really!), but can't find any worked examples of actual use of the transformation equations. Does anyone know of any web references or tutorials on the subject? To make things a little more...

Hi all, I am new to General Relativity and I started with General Relativity Course on Youtube posted by Stanford (Leonard Susskind's lectures on GR). So first thing to understand is transformation of covariant and contravariant vectors. Before I can understand a transformation, I would...

Ok just for fun,could someone please give a general linear transformation of p vectors in R(n) to R(m),by expressing the transformation as a Matrix vector product of let's say n vectors in R(m).p vectors in R(n).I've already done it for fun but I'd like to see how you guys go about it..

(First of all apologies for the long wall of text) I am to study BRST transformations, for which I'm currently trying to understand constrained Hamiltonian dynamics to treat systems with singular Lagrangians. The crude recipe followed is Lagrangian -> Hamiltonian -> Dirac brackets and their...

Part c) I'm not quite sure what to do, I've found the det(U) is 2, but no idea what this actually shows to be honest, any help?

I am a newcomer to relativity, currently studying the subject on my own, via Modern Physics by Bernstein et al. I have a question based on pgs 57-58 of the text. Suppose that two reference frames S and S' are similarly oriented, and S' is moving with constant velocity v in the positive...

I need to determine the affine transformations used to produce the following image: Been staring at it for an hour and it's frustrating me to no end because it's probably really easy. Clearly it gets scaled by 1/3 and there are 3 linear transformations that put it at (0,0), (1/3,1/3) and...

Homework Statement Let X1 and X2 be random variables having a joint pdf, fX1X2(x1,x2). Suppose that Y1=X1X2, and Y2=X1X2 Use the transformation result to derive an expression for the joint pdf of Y1 and Y[SUB]2 in terms of that for X1 and X2 Homework Equations The single random...

I often read sentences like, "if space is homogeneous, then the Lorentz transformation must be a linear transformation." What exactly does it mean to say that space is homogeneous, and how does it imply that the Lorentz transformations are linear?

A conformal transformation is a coordinate transformation that leaves the metric invariant up to a scale change g_{\mu\nu}(x) \to g'_{\mu\mu}(x)=\Omega(x)g_{\mu\nu}(x). This means that the length of vectors is not preserved: g_{\mu\nu}x'^{\mu}x'^{\nu}\not=g_{\mu\nu}x^{\mu}x^{\nu} But is...

Homework Statement Are the Lorentz transformations empirical laws? If so, are they empirically testable? Homework Equations The Attempt at a Solution I'm guessing they are. But how do you test the LT?

Hi, I'm having trouble interpreting projective transformations. Let's confine ourselves to the projective plane P(\mathbb{R}_0^3). The transformations of the projective plane are GL(\mathbb{R}, 3) / \sim. But these include things like reflections in planes and lines through the origin...

If we consider the set R of all linear transformations from an p-dimensional vector space Z to Z (T:Z -> Z), what do we know about the dimension of the set R? In other words, what do we know about any basis for R? What are its properties?

I need some help or at least some assurance that my thinking on linear transformations and their matrix representations is correct. I assume when we specify a linear transformation eg F(x,y, z) = (3x +y, y+z, 2x-3z) for example, that this is specified by its action on the variables and is not...

Homework Statement Given the Lagrangian density L(\phi^{\mu})=-\frac{1}{2}(\partial_{\mu}\phi^{\nu})(\partial^{\mu}\phi_{\nu}) + \frac{1}{2}(\partial_{\mu}\phi^{\mu})^2+\frac{m^2}{2}(\phi^{\mu}\phi_{\mu}) and gauge transformation \phi^{\mu}\rightarrow \phi^{\mu} + \partial^{\mu}\alpha...

Homework Statement Define a function T: Psub3-->R3 by: T(p)=[p(3),p'(1), integral from 0 to 1 of p(x)dx] for p a polynomial in P sub3, the polynomials of degree less than or equal to 3. a. Show that T is a linear transformation b. Identify Psub3 with R4 in the usual way and write T...

Homework Statement H is the upper-half plane model of the hyperbolic space Find all Mobius transformations that send M to N. Homework Equations a) M = {0, 1, ∞}, N = {∞, 0, 1} b) M = {0, 1, ∞}, N = {0, ∞, 2} c) M = {i, -i, 3i}, N = {∞, i + 1, 6} The Attempt at a Solution...

http://dl.dropbox.com/u/33103477/linear%20transformations.png My attempt was to first find the transformed matrices L1 and L2. L1= ---[3 1 2 -1] -------[2 4 1 -1] L2= ---[1 -1] -------[1 -3] -------[2 -8] -------[3 -27] Now reducing L1, I have -------[1 0 7/10 -3/10]...

Hi, quick question. "In electroweak theory, the neutrino belongs to an SU(2) doublet" So, does the neutrino belong to an SU(2)xU(1) (electroweak) doublet or just SU(2)? Thanks!

Why is it that only Canonical transformations preserve the Hamilton's equations? Or what makes non-canonical transformations not preserve the Hamilton's equations?

Hi Pf, Here is a question regard a test review that we have. I am not looking for the answer but rather a clarification about the notation. 1. What does the following mean? T1: \Re2 \rightarrow \Re2 by x \rightarrow Ax? 2. What does it mean to go \Re2 \rightarrow \Re2 Thanks.

Homework Statement The string in Fig. 8-35 is L = 120 cm long, has a ball attached to one end, and is fixed at its other end. The distance d to the fixed peg at point P is 75.0 cm. When the initially stationary ball is released with the string horizontal as shown, it will swing...

Homework Statement F(s) = s/((s-1)(s^2+1)) F(s) = (s/(s^2+4s+5))(e^(-3s)) Homework Equations Don't believe there are any. The Attempt at a Solution Not particularly sure. I can solve ((s-2)(e^-s))/(s^2-4s+3), but seem to be having problems with these.