Transformation Definition and 1000 Threads

In SR the speed transformation formula (in response to a change of inertial frame of reference) is usually derived from the Lorentz transformation of space and time coordinates. I would like to find a direct derivation starting from the existence of a maximum speed limit (c) in respect to any...

Homework Statement t:P_3 -----> P_3 p(x) |---> p(x) + p(2) Determine whether or not this function is linear transformation or not. Homework Equations For a function to be a linear transformation then t(0) = 0 , there are other axioms that must be satisfied, but that is not the problem...

My local PBS station broadcasts a physics series on a sub-channel. They call it The Mechanical Universe locally. PBS recently broadcast The Lorentz Transformation . It appears that one may view these on line, as the Lorentz Transformation began to load after I allowed it to pop-up. There are...

Hey guys, i did this source transformation as an alternate method to find the transfer function of a circuit, however I am getting a different transfer function of 2/(2s+(s+3)(s^2+1)) to the solution in the following image. Any help would be really appreciated :)

Homework Statement [/B] I'm trying to derive (14.25) in B&J QFT. This is ##U(\epsilon)A^\mu(x)U^{-1}(\epsilon) = A^\mu(x') - \epsilon^{\mu\nu}A_\nu(x') + \frac{\partial \lambda(x',\epsilon)}{\partial x'_\mu}##, where ##\lambda(x',\epsilon)## is an operator gauge function. This is all being...

We have a r.v. X with p.d.f. = sqrt(θ/πx)*exp(-xθ) , x>0 and θ a positive parameter. We are required to show that 2 θX has a x^2 distribution with 1 d.f. and deduce that, if x_1,……,x_n are independent r.v. with this p.d.f., then 2θ∑_(i=1)^n▒x_ι has a chi-squared distribution with n...

Homework Statement let A be the matrix corresponding to the linear transformation from R^3 to R^3 that is rotation of 90 degrees about the x-axis Homework Equations find the matrix A The Attempt at a Solution I got stuck on rotating z component. I tried T([e1,e2,e3])=[0 -1 0]...

Was reading how do vectors transform under chiral transformation and found the following: If $$V^\mu$$ is a vector; set $$ V^\mu = \bar{\psi} \gamma^\mu \psi= $$ $$\bar{\psi}\gamma^\mu e^{-i\alpha\gamma^5}e^{i\alpha\gamma^5}\psi =$$ $$\bar{\psi}\gamma^\mu\psi = V^\mu $$ My questions are why...

Transform the left hand member into the right hand member. $\frac{\tan\alpha+\tan\beta}{\sec\alpha-\sec\beta}=\frac{\sec\alpha+\sec\beta}{\tan\alpha-\tan\beta}$By using cross multiplication I was able to prove this identity but what I actually want to accomplush is to transform the left member...

I already did everything that I can to transform the left side member to the right side member but I always get a jumbled terms. Please give me a hand on this problem. $(2\sin^{2}(\theta)-\cos^{2}(\theta))^{2}-9(2\sin^{2}(\theta)-1)^{2}=(2-3\sin^{2}(\theta))(2+3\sin(\theta))(3\sin(\theta)-2)$

Hey there, I trying to understand the following coordinate transformation of the equation of continuity (spherical coordinates) for a vaporizing liquid droplet\frac{\partial \rho}{\partial t} + \frac{1}{r^2} \frac{\partial}{\partial r} (r^2 \rho v) = 0 into \epsilon \sigma \frac{\partial...

Find the matrix for the transformation that projects each point in R3 (3-D) perpendicularly onto the plane 7x + y + 3z = 0 . The attempt at a solution is attached for question 1 (actually instructor's solution) I kind of understand it but ... why is n <dot> v = equation of the plane? Does v...

Find the matrix for the transformation that projects each point in R3 (3-D) perpendicularly onto the plane 7x + y + 3z = 0 . The attempt at a solution is attached for question 1 (actually instructor's solution) I kind of understand it but ... why is n <dot> v = equation of the plane? Does v...

Hi there, I am reading a material on the application of Fourier transformation in physics. One application is to transform the position-dependent function to k-dependent function, i.e.## F(k) = FFT[f(x)]## We know that the in physics, the wavenumber could be written in momentum as...

Homework Statement Hey guys! So I have a Lagrangian with two coupled fields like so: \mathcal{L} = \frac{1}{2}(\partial_{\mu}\phi_{1})(\partial^{\mu}\phi_{1})...

Homework Statement I'm to use source transformation to find the current through the 24 Ohm resistor 2. The attempt at a solution I used source transformation on the left 12V source and got a .5A current upwards. The 24 and 30 ohm resistor are in parallel so I found an equivalent resistance of...

Homework Statement I am supposed to show that the free Schrödinger Equation is NOT kovariant under Galilei Transformation. Homework Equations We learned in Lectures that the Galilei Transformation can be written as: \vec{x'}=\hat{R}\vec{x}-\vec{a}-\vec{v}t (1) or equivalently...

Homework Statement Suppose two observers O and O', whose positions coincide , each sets up a set of 2D cartesian coordinates (x,y) and (x',y') respectively to describe the position of a certain object at a fixed point . Derive a set of formulae for one observer to convert the other observer's...

Homework Statement I haven't learned kernel yet so if that's of use here I don't know it yet let ##T: \mathbb{R^3} \rightarrow \mathbb{R^2}## where ##T<x,y,z>=<2y,x+y+z>##[/B] prove that the range is ##\mathbb{R^2}## The Attempt at a Solution I know that T is not one-to-one, I checked that...

Homework Statement let ##T:\mathbb{R^3} \rightarrow \mathbb{R^3}## where ##T<x,y,z>=<x-2z,y+z,x+2y>## Is T one-to-one and is the range of T ##\mathbb{R^3}##? The Attempt at a Solution I took the standard matrix A ##\left[\begin{array}{cc}1&0&-2\\0&1&1\\1&2&0\end{array}\right]## det(A)=0 so...

Homework Statement Problem 29. Use the subtraction trick U(tilda) = U−U1 to reduce the following problems with non-canonical boundary conditions to the canonical ones and write down the equations in terms of the variable ˜u (do not solve them). Note that there are infinitely many u1’s that...

Hello, I'm currently going through Agrawal's book 'Nonlinear Fiber Optics' and got stuck with some mathematical cosmetics (pp. 40). It is the substition of: \vec{P_L}(\vec{r},t) = \frac{1}{2} \hat{x} \left(P_L \exp{(-i \omega_0 t)} + c.c.\right) into \vec{P_L}(\vec{r},t) = \epsilon_0...

Homework Statement Let T:R->R^2 be the linear transformation that maps the point (1,2) to (2,3) and the point (-1,2) to (2,-3). Then T maps the point (2,1) to ...Homework Equations T(xa+yb) = xT(a)+yT(b)The Attempt at a Solution Okay so I have the solution to this problem, but its understanding...

Homework Statement There's a person and he ate a hamburger which its 2000 kcal.And he wants to spend this energy . he will be weightlifting and he will lift 45 kg to 2 meters.How many times he can lift it ? Homework Equations W=Fx or W=mgh The Attempt at a Solution 2000...

We have the KG Lagrangian density: \mathcal{L}= \partial_{\mu} \phi \partial^{\mu} \phi^* - m^2 \phi \phi^* Suppose instead of taking \phi \rightarrow e^{ia}\phi with a \in \mathbb{R} we take a \in \mathbb{C}. Then is it true to say that \mathcal{L}'= e^{-2~ Im(a)} \mathcal{L} and so gives...

Apriori -- before taking any of the postulates of special relativity into account -- we might say that the lorentz transformations between two frames K and K', where K' is moving w. speed v along the x-axis of K, is given by $$\vec{x}' = F(\vec x, t)$$ and $$t' = G(\vec x, t).$$ Now, i want...

Hi, First of all, I'm not sure if this thread belongs to the BSM forum because the question I'm posing here is a simple CFT question which could well be posed in the forum on GR or Particle Physics/QFT. I will defer to the judgment of the moderator to put this in the right place if it already...

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...

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...

I'm being asked to derive the velocity transformation between vy and vy' and my result isn't exactly matching my goal but I don't know what I'm doing wrong. It's an introductory modern physics course and we're covering special relativity. Assume a reference frame S' moving in some constant...

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...

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...

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.