Transformation Definition and 1000 Threads

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 about this classical invariance problem I'm working on. I'm almost done, and I understand the theory I think, so my question may seem a bit more math-oriented (it's been a few years since crunching equations). I have found that under a gauge transformation for a single particle...

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...

Hello, I was wondering what the exact definition of conformal transformations is. This is a question in the context of Shape Dynamics. In Shape dynamics, time is viewed as a global parameter of the universe, and as such is invariant under spatial coordinate transformation. Part of the...

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...

A gauge field W_\mu is known to transform as W_\mu\to W'_\mu=UW_\mu U^{-1} +(\partial_\mu U)U^{-1} under a gauge transformation U, where the first term UW_\mu U^{-1} means it transforms under the adjoint representation. Can anyone explain to me why it means a transformation under the adjoint...

Homework Statement Dear friends, let U and V independent variables that are both defined on [-∏, ∏] and are uniformly distributed. If x = cos(U + V) and y = sin(U-V), what is the area where the variables X and Y are defined? Homework Equations U + V = arccos(x) U - V = arcsin(y) For a test...

Question: (A) Show that the following transformation is a canonical transformation: Q = p + aq P = (p - aq)/(2a) (B) Find a generating functions for this transformation. Attempt of Solution: Alright, so this seems to be a very straight forward problem. Transformations are canonical...

can anyone help explain the mechanism of coupled equation transformation and when and how can i transform similar equations?

Homework Statement Prove: \cos\alpha\cdot\cos\alpha'+\cos\beta\cdot\cos\beta'+\cos\gamma\cdot\cos \gamma'=\cos\theta See drawing Snap1 Homework Equations None The Attempt at a Solution See drawing Snap2. i make the length of the lines 1 and 2 to equal one, for simplicity. The...

Imo, this problem is crazy hard. Homework Statement Let X have the negative binomial distribution with pmf: f_X(x) = \binom{r+x-1}{x}p^{r}(1-p)^{x}, x=0.1.2..., where 0<p<1 and r is a positive integer. (a) Calculate the mgf (moment generating function) of X. (b) Define a new...

[SIZE="4"]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...

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...

We know that the derivative of the general Schwartz - Christoffel map (function) is: f'(z) = λ(z - x_1)^{a_1}...(z-x_n)^{a_n} Question: In various sources around the web, it is mentioned that x_n can be taken to be the "point at infinity", and the last factor can be removed from the above...

Change of variables for integral Homework Statement Determine whether the following equality holds: \displaystyle\int_0^{\infty} \frac{e^{-\dfrac{(x^2+4z^2)}{4z}}}{2z} \, \mathrm{d}z = \displaystyle\int_0^{\infty} \frac{e^{-\dfrac{(1+z^2)x}{2z}}}{2z} \, \mathrm{d}z, \forall x,z \in...

Homework Statement Question is attached Homework Equations σ(x) = 0 σ(y)= P/A t(xy)= Tc/j The Attempt at a Solution I know how to do the stress transformation, but my only issue is noticing why σ(x)= 0, I can't see it, can someone help me.

Dear All, I am teaching myself tensors for the first time. I am using D'Inverno's book and got stuck at page 73. Basically, he says: demand that the first term on the left of the equation to be a type (1,1) tensor. Then he gets the affine connection transformation. I basically wrote the...

I have read some basics knowledge about General Relativity and I see that it deal perfectly with gravity. But what about accelerated frames? Is there something similar to Lorentz Transformation for accelerated frame in General Relativity? (so that i can solve, maybe, the general twin paradox)...

Hi there, I'm having trouble understanding the Fourier transform of a function where the result in the frequency domain has imaginary components. For example, if you take the Fourier transform of Sin[t] , the result is I Sqrt[\[Pi]/2] DiracDelta[-1 + \[Omega]] - I Sqrt[\[Pi]/2]...

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

Homework Statement Let us study the subgroup of the Poincare group that leaves the point ##x=0## invariant, that is the Lorentz group. The action of an infinitesimal Lorentz transformation on a field ##\Phi(0)## is ##L_{\mu \nu}\Phi(0) = S_{\mu \nu}\Phi(0)##. By use of the commutation...

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...

Hello guys, Let ##T: \mathbb{R^2} \to \mathbb{R^2}##. Suppose I have standard basis ##B = \{u_1, u_2\}## and another basis ##B^{\prime} = \{v_1, v_2\}## The linear transformation is described say as such ##T(v_1) = v_1 + v_2, T(v_2) = v_1## If I want to write the matrix representing ##T##...

I really don't understand what it is and what is the use of constant, like in this equation of transformation. x=k(x' + vt). The equation can also be good if it is just like this, x=x' + vt Thank you.

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...

Homework Statement This complies when I type it in my Latex editor, but not on here. If you could either let me know how to fix that or copy and paste what I have into your own editor to help, that'd be great. Thanks! While Ryder is setting up to derive a transformation rule for Dirac...

I have doubts regarding a statement related to the following proposition: Let ##(V,<,>)## be a finite dimensional vector space equipped with an inner product and let ##f:V \to V## be a linear transformation, then the following statements are equivalent: 1)##<f(v),f(w)>=<v,w>## for all ##v,w \in...

See: http://en.wikipedia.org/wiki/Y-%CE%94_transform#Basic_Y-.CE.94_transformation Is possible to express the following relationships: using matrix?

A variant of a problem from Halmos : If AB=C and BA=D then explain why (C-D)^2 is commutative with all 2x2 matrices if A and B are 2x2 matrices. This result does not hold for any other nxn matrices where n > 2. Explain why. Edit: I tried to show that ((C-D)^2) E - E((C-D)^2) is identically...

Homework Statement Find Möbius transformation that maps: a) circle ##|z+i|=1## into line ##Im(z)=2## b) circle ##|z-i|=1## into line ##Im(z)=Re(z)## c) line ##Re(z)=1## into circle ##|z|=2##Homework Equations ##f(z)=\frac{az+b}{cz+d}##The Attempt at a Solution a) Firstly to move the circle...

Hi All, I think I have confused myself ... perhaps you can tell me where my reasoning is wrong. The idea is that in general coordinates the partial derivative of a vector, \frac{\partial A^i}{\partial x^j}, is not a tensor because an additional term arises (which is the motivation for...

Is it true that there always exist a unitary matrix that can take a state vector of an arbitrary pure state to another arbitrary pure state ? (of course assuming same hilbert space). If true, how do we prove it ? it look like it is true via geometrical arguments but i have not been able to...

Homework Statement Let B = {(1, -2),(2, -3)} and S be the standard basis of R2 and [-8,-4;9,4] be a linear transformation expressed in terms of the standard basis? The Attempt at a Solution 1) What is the change of basis matrix PSB ? 1,2 -2,-3 2)What is the change of...

How can I geometrically interpret this coordinate transformation (from x,y space to \check{x},\check{y} space)? x = \check{x}cos(β) - \check{y}sin(β) y = \frac{1}{2}(\check{x}2 -\check{y}2)sin(2β) -\check{x}\check{y}cos (2β)

Let L: R3 -> R3 be L(x)= \begin{pmatrix} x1+x2\\ x1-x2\\ 3x1+2x2 \end{pmatrix} find a matrix A such that L(x)=Ax for all x in R2 From what I understand I need to find the transition matrix from the elementary to L(x). However it is'nt a square matrix and it has variables instead of numbers...

Homework Statement a) Determine power series ##\sum _{n=0}^{\infty }a_nt^n## if you know that its laplace transformation is ##-s^{-1}e^{-s^{-1}}## b) Determine function ##g## that this power series will be equal to ##J_0(g(t))##Homework Equations The Attempt at a Solution Hmmm, I am having...

Homework Statement Let ##y_1^{'}+y_1=y_2##, ##y_2^{'}+5y_2=y_3##, ##y_3^{'}+y_3=f## and ##y_1(0)=y_2(0)=y_3(0)=0##. Find ##Y_1(s)## in terms of ##F(s)##. Homework Equations The Attempt at a Solution I am completely lost here. I tried to rewrite the system so that I would...

Homework Statement Find Laplace transformation for functions ##f(t)##: a) ##5cos(7t+\pi /4)## b) ##e^{3t}sintcost##Homework Equations The Attempt at a Solution a) I know that for ##cos(\omega t)## the laplace is ##\frac{s}{s^2+\omega ^2}## but what can I do with that ##\pi /4## ? I believe I...

hello i want to derive the Transformation of acceleration between two reference frames i searched in internet and found a book but i don't understand just one step i attach a picture so you can see what i found in the internet my problem is eq. (1.10) \begin{align}du=\frac{dU}{\gamma...

Homework Statement utt=a2uxx Initial conditions: 1)When t=0,u=H,1<x<2 and u=0,x\notin(1<x<2) 2)When t=0,ut=H,3<x<3 and u=0,x\notin(3<x<4) The Attempt at a Solution So I transformed the first initial condition \hat{u}=1/\sqrt{2*\pi} \int Exp[-i*\lambda*x)*H dx=...

I have a linear transformation, T, from P3 (polynomials of degree ≤ 3) to R4 (4-dimensional real number space). I have a second linear transformation, U, from R4 back to P3. In the first step of this four-step problem, I have shown that the composition TU from R4 to R4 is the identity linear...

Let there be a triangle with coordinates A(2,2) , B(5,2) and C(5,4) I have learned two ways to shear an object(x-axis invariant) in the Cartesian coordinate system. The first way is to find the coordinate vector of a point and multiply the y-component of the vector by the shear factor(2)(Don't...

Homework Statement A girl is riding a bicycle along a straight road at constant speed, and passes a friend standing at a bus stop (event #1). At a time of 60 s later the friend catches a bus (event #2) If the distance separating the events is 126 m in the frame of the girl on the bicycle...

Homework Statement Given a transformation of the plane F(x,y) = (2x+y,x-2y), find F-1. Homework Equations Actually this exercise had an item (a) which I had to prove this is a transformation. So I proved this function is injective and surjective. I know F(x,y) = (u,v) IFF F-1(u,v) =...

Umm what just happened? I understand as far as u=x+y and v = y/x and when he does the 2d curl. What I don't get is the step thereafter when he flips it. How does he know to flip it? Further, when he flips it wouldn't that make the dvdu inside the integral cancel and hence leave him with dxdy?

Homework Statement Homework Equations The Attempt at a Solution What I don't understand is how I'm supposed to find those limits for U and V. That's not at all what I'm getting. I've tried solving for the max and min x,y coordinates from the given graphs but that doesn't yield...

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...

Is the transformation of an operator under INFINITESIMAL unitary transformation, U^-1AU or UAU^-1?? I saw that two books defined it differently?

Homework Statement The Attempt at a Solution I don't think I'm interpreting the question correctly. Maybe someone can point me in the right direction? There are 2 conditions: if y =/=0 then f(x,y) = x^2/y and if y=0 then f(x,y) = 0 Let u =(1,1) and v = (1,1) f(v) = f(1,1) =...

Homework Statement f(x,y) -> |x+y| The Attempt at a Solution The answer is that the above transformation is not linear but my working shows otherwise. Here's my go: let u = (1,1) and v = (1,1) f(u) = f(1,1) = 2 f(v) = f(1,1) = 2 f(u) + f(v) = 4 f(u+v) = f(2,2) = 4...