Transformation Definition and 1000 Threads

Homework Statement The piece wise function is -x-2, x<-1 x^2-3x, -1≤ x ≤5 3x+5, x>5 The problem is to transform the function with...

(Forgive me if this is in the wrong spot) I understand how tensors transform. I can easily type a rule with the differentials of coordinates, say for strain. I also know that the moment of inertia is a tensor. But I cannot see how it transforms as does the standard rules of covariant...

I don't fully understand the argument below used to derive the Lorentz transformation equation ##y'=y##. Suppose we have a rod of unit length placed stationary in frame S. According to an observer in frame S' (which is moving at a velocity v relative to frame S), this rod is moving and its...

Let's consider a signal which is continuous in both time and amplitude. Now we consider the amplitude of this signal at specific time instants only. This is my understanding of sampling a signal in time domain. When performing a Fourier transform on a time discrete signal, we have to apply the...

I have one circuit and another with a source transformation figure a and b respectively. My question after transforming the 30 mA source shouldn't the current going into node 5 equal the current going into node 4? Figura a. Before the transformation of the source Figure b. After the...

We are always taught in books that a Lorentz transformation is possible as long as the Lorentz matrices ##\Lambda## in ##\vec{x}{\ }' = \Lambda \vec{x}## are not function of ##\vec{x}##. The reason for this is obvious, since in this way the relation ##t^2 - x^2 - y^2 - z^2 = t'^2 - x'^2 - y'^2...

How author derives these old basis unit vectors in terms of new basis vectors ? Please don't explain in two words. \hat{e}_x = cos(\varphi)\hat{e}'_x - sin(\varphi)\hat{e}'_y \hat{e}_y = sin(\varphi)\hat{e}'_x + cos(\varphi)\hat{e}'_y

Consider the transformation from Poincare-AdS##_3## geometry to global AdS##_3## geometry: $$ds^{2} = \frac{dr^{2}}{r^{2}} + r^{2}g_{\alpha\beta}dx^{\alpha}dx^{\beta}, \qquad \text{Poincare-AdS$_3$}$$ $$ds^{2} = \frac{dr^{2}}{r^{2}} + r^{2}\left(-dt^{2}+r^{2}d\phi^{2}\right), \qquad...

The generators ##N^{\pm}{}_\mu = \frac{1}{2}(J_\mu \pm iK_\mu)## obey the algebra of ##SU(2)##. On the RHS we see the Lorentz generators of rotations and boosts, respectively. I considered the case where ##N^{\pm}{}_\mu = (1/2) \sigma_\mu##, i.e. the (1/2, 1/2) representation of the Lorentz...

Homework Statement Prove or disprove: Every translation is a product of two non-involutory rotations. Homework EquationsThe Attempt at a Solution :[/B] I am not sure if I got the right proof for the special situation: A translation is the product of two reflections with parallel reflections...

1. The problem is: In point form, outline the process through which electricity is generated, highlighting the energy transformations that occur. Then state an advantage and disadvantage for this type of electricity production. The attempt at a solution I will be describing the energy...

Homework Statement [/B] A.) Simplify the circuit (Figure 1) by using a Y-to-Δ transformation involving the resistors R2, R3, and R5 as shown in (Figure 2) . Determine the resistances of the equivalent Δ. B.) Determine the equivalent resistance Rab in the circuit. Hopefully these two figures...

Dear all, I am encoutering some difficulties while calculating the Hamiltonian after the transformation to the interaction picture. I am following the tutorial by Sasura and Buzek: https://arxiv.org/abs/quant-ph/0112041 Previous: I already know that the Hamiltonian for the j-th ion is given...

According to this pdf http://www.springer.com/cda/content/document/cda_downloaddocument/9783319011066-c2.pdf?SGWID=0-0-45-1429331-p175291974 Newton's second law is not invariant under Lorentz transformations. To find out the part that says so, use CTRL+F and type "Newton"; it's the first result...

Homework Statement In a article I have found this transformation (exp to bessel function) . I have two questions. Homework EquationsThe Attempt at a Solution a)where did the Cos go after setting n=1 and n=-1 ? in the third equations ( it is equal to -wmt-pi/2)? why?) b)how did the writer...

Hello, I have the following PDE equation: a*b/U(u)*V(v) = 0 where a and b are arbitrary constants, and U an V are two unknown functions. To me it appears this has no solution, however I would like to ask if anyone has some suggestions, such as transforming it to another type using Fourier or...

Let's assume that a light source is moving parralel to x-axis and is in point x,y,z in lab frame. Suppose it emits a light ray. In the rest frame that coincides with the lab frame, the light source is in point x',y and z. However, because of relativistic aberration the two light rays will make...

Hi all, I was trying the understand theory behind Fourier and Laplace Transform (especially in the context of control theory) by reading the book "Complex Variables and the Laplace Transform for Engineers" written by "Wilbur R. LePage". In section 6-10 of the book the author touches on the...

Riley Hobson and Bence define covariant and contravariant bases in the following fashion for a position vector $$\textbf{r}(u_1, u_2, u_3)$$: $$\textbf{e}_i = \frac{\partial \textbf{r}}{\partial u^{i}} $$ And $$ \textbf{e}^i = \nabla u^{i} $$ In the primed...

Homework Statement You have to calculated the Laplace transformation for 1/ cos(t) Homework Equations That's all The Attempt at a Solution i tryed whit some trigonometric formulas but i don't get anywhere : 1/cos(t) = cos(t) / (1- sin ^2 (t)) or 1/cos(t) = cos(t) + sin(t) x tg(t) or...

Hi. I'd like to ask about the calculation of Noether current. On page16 of David Tong's lecture note(http://www.damtp.cam.ac.uk/user/tong/qft.html), there is a topic about Noether current and Lorentz transformation. I want to derive ##\delta \mathcal{L}##, but during my calculation, I...

Homework Statement "Find ##S_\alpha## where ##S: M_{2×2}(ℝ)→M_{2×2}(ℝ)## is defined by ##S(A)=A^T##. Homework Equations ##A^T=\begin{pmatrix} a_{11} & a_{21} \\ a_{12} & a_{22} \end{pmatrix}## ##\alpha= \{ {\begin{pmatrix} 1 & 0 \\ 0 & 0 \end{pmatrix}, \begin{pmatrix} 0 & 0 \\ 1 & 0...

Homework Statement How to obtain the famous formula of velocity transformation using a chain rule. I know that there is a straightforward way by dividing ##dx## as a function of ##dx`## and ##dt`## on ##dt## which is also a function of them. But I would rather try using the chain rule. Homework...

Is the attached solution complete? In particular, do we need to prove that ##V'(r_{12}')=V(r_{12})##, where ##V'(r_{12}')## is the potential energy function in the reference frame ##S'##, moving at a uniform velocity with respect to the reference frame ##S##, and ##r_{12}'## is the distance...

In the second volume, Field Theory, of popular series of Theoretical Physics by Landau-Lifschitz are given following equations as in attached file from the book. Here is considered metric change under coordinate transformation. How is the new, prime metric expressed in original coordinates is...

Consider the Dirac Lagrangian, L =\overline{\psi}\left(i\gamma^{\mu}\partial_{\mu}-m\right)\psi, where \overline{\psi}=\psi^{\dagger}\gamma^{0} , and show that, for \alpha\in\mathbb{R} and in the limit m\rightarrow0 , it is invariant under the chiral transformation...

Homework Statement Attached Homework EquationsThe Attempt at a Solution [/B] where ##\tau## and ##\sigma## are world-sheet parameters. where ##h_{ab}## is the world-sheet metric. To be honest, I am trying to do analogous to general relativity transformations, since this is new to me, so in...

Is the Lorentz transformation given by the equations valid only if the origin of S and S' coincides at t=t'= 0 and the other axis (x,y,z) remains parallel to (x',y',z') respectively?

Homework Statement Let be T : ℙ2 → ℙ2 a polynomial transformation (degree 2) Defined as T(a+bx+cx²) = (a+1) + (b+1)x + (b+1)x² It is a linear transformation? Homework Equations A transformation is linear if T(p1 + p2) = T(p1) + T(p2) And T(cp1)= cT(p1) for any scalar c The Attempt at...

For using Galilean transformation, I have to assume that speed of light w.r.t. ether frame is c. W.r.t. ether frame, E = E0 eik(x-ct) W.r.t. S' frame which is moving with speed v along the direction of propagation of light, E' = E0 eik(x'-c't') Under Galilean transformation, x' = x-vt, t' = t...

Hello friends, I'm trying to construct transformation matrix S such that it transforms Dirac representations of gamma matrices into Chiral ones. I know that this S should be hermitian and unitary and from this I arrived an equation with 2 matrices on the LHS (a known matrix multiplied by S from...

Since force is transformed via: F'x= Fx ; F'y= Fy/ ϒ; F'z=Fz/ ϒ (F' is the force related to the moving frame, F is the force on the rest frame and ϒ=1/√1-v2/c2 ).I expect that G (Gravitational constant) will be transformed between moving and rest frame in order to satisfy force transformation...

If I have a particle with: Momentum: p Spin: s Energy: E Position: x Time coordinate: t Charge: q And I preform a CPT transformation on said particle, what will these variables become? Can you show me mathematically? Also, could you show me how this effects the wavefunction/quantum state of...

Hello everyone, I am confused with the minus sign of x'=x-vt. When there are 2 references frames called K and K' which K is at rest and K' moves to right with velocity V with respect to K. Let there is another frame which is my frame of reference called O. The vector sum of the displacement...

I wonder if it is possible to express a simple principle into a mathematical form. The simple principle says if at time t0 an isolated system is composed of some elements with some properties then at t1 it is composed of other elements with different properties, then in principle it is possible...

< Mentor Note -- thread moved to HH from the technical physics forums, so no HH Template is shown > Hi, I was working on a the source transformation and i got to the part where there are two current sources in the circuit. The current sources were added together (giving they were going in the...

I am trying to analyse response of a dynamic system. The source disturbance is about x,y,theta (rotation about x ) & Phi of one coordinate system (red coloured coordinate system in the attached figure). I need to get the response in another coordinate system ( green coloured coordinate system...

##x= r Cosh\theta## ##y= r Sinh\theta## In 2D, the radius of hyperbolic circle is given by: ##\sqrt{x^2-y^2}##, which is r. What about in 3D, 4D and higher dimensions. In 3D, is the radius ##\sqrt{x^2-y^2-z^2}##? Does one call them hyperbolic n-Sphere? How is the radius defined in these...

I have taken AP Statistics, and this is for the final project. What we have learned consists of some simple significant tests (t test, z test for proportions, two sample tests, chi squared, and logarithmic transforms). My partner and I are considering creating a scatter plot of distance between...

Homework Statement Write the Galilean coordinate transformation equations for the case of an arbitrary direction for the relative velocity v of one frame with respect to the other. Assume that the corresponding axes of the two frames remain parallel. (Hint: let v have componentsvx, vy, vz.)...

Hello! Can someone explain to me how does a scalar field changes under a Lorentz transformation? I found different notations in different places and I am a bit confused. Thank you!

Hi everyone! I'm having trouble with the following exercise: Let ##\mathrm {Aff}(ℝ)## be the vector space of the affine maps from ##ℝ## to ##ℝ##: $$φ_{a,b}:ℝ→ℝ$$ $$x→a x + b$$ Find the contravariant and and covariant coordinate of the map: $$φ_{1,1}:ℝ→ℝ$$ $$x→x + 1$$ with respect to the...

From Wikipedia: So, assuming we have a massive ball of water that keeps growing, but somehow manages to remain at a fixed density, the moment the Schwarzschild radius overtakes the physical radius, will the gravitational properties of the ball of water undergo a sudden, dramatic change?

Homework Statement Given: An object at rest with respect to an inertial reference frame S. 2 other inertial reference frames S' and S''. S' has velocity (vx, vy) = (-.6c, 0) with respect to S. S'' has velocity (vx, vy) = (-.6c, +.6c) with respect to S. Assumptions: If I transform my...

I have a question about weights of a basis set with respect to the other basis set of one specific vector space. It seems the weights do not covert linearly when basis sets convert linearly. I've got this question from the video on youtube "linear transformation" Let's consider a vector space...

Homework Statement Say I have a matrix: [3 -2 1] [1 -4 1] [1 1 0] Is this matrix onto? One to one? Homework EquationsThe Attempt at a Solution I know it's not one to one. In ker(T) there are non trivial solutions to the system. But since I've confirmed there is something in the ker(T), does...

Hi I was looking at the Lorentz transformation and I see that it moves in the x-axis if vt is positive. How can I re-arrange the lorentz transformations in a way that will cause the moving frame of reference to get closer to me. I was trying with x'=gamma(x-vt) but I don't know what x is equal...

1. Problem ##g_{uv}'=g_{uv}+\nabla_v C_u+\nabla_u C_v## If ##g_{uv}' ## is given by ##ds^2=dx^2+2\epsilon f'(y) dx dy + dy^2## And ##g_{uv}## is given by ##ds^2=dx^2+dy^2##, Show that ## C_u=2\epsilon(f(y),0)##? Homework Equations Since we are in flatspace we have ##g_{uv}'=g_{uv}+\partial_v...

Homework Statement If ##A## is an ##n \times n## matrix, show that the eigenvalues of ##T(A) = A^{t}## are ##\lambda = \pm 1## Homework EquationsThe Attempt at a Solution First I assume that a matrix ##M## is an eigenvector of ##T##. So ##T(M) = \lambda M## for some ##\lambda \in \mathbb{R}##...

Hi folks, This is the Lorentz transformation in 1D, x axis: I want to get the second term of the time t equation, I mean vx/c2, in two dimensions, I mean for a point in the XY plane. I know this term arises because if we want to syncronize a point B with the origin what we do is sending a...