Transformation Definition and 1000 Threads

Lorentz transformation of electromagnetic field gives the relation ##E'=\gamma(E+v\times B)##. Lorentz force per unit charge is given as ##F=E+v\times B## without ##\gamma##. Don't we need coefficient ##\gamma## for F?

Consider a Lagrangian: \begin{equation} \mathcal{L} = \mathcal{L}(q_1\, \dots\, q_n, \dot{q}_1\, \dots\, \dot{q}_n,t) \end{equation} From this Lagrangian, we get a set of ##n## equations: \begin{equation} \frac{d}{dt}\frac{\partial \mathcal{L}}{\partial \dot{q}_i} - \frac{\partial...

Hello. Here is the formula that computes the sample skewness: Sk = [ (n / [(n-1)(n-2)] ] x [ ∑ (Xi - X)3 / s3 ] , where n is the number of elements in the sample, Xi is the specific i-th value of the sample, where i starts from 0 and ends at i=n, X is the arithmetic mean, s - standard...

Homework Statement Let's have a three-particle decay of equal mass ##m##; in the CM frame the three particles have equal energy ##E## and they form angles of ##\frac{2\pi}{3}## between each other. Which is the angle between two of the three particles in the rest frame of the other one. (The...

Could you please help me to understand what is the difference between notions of «transformation» and «automorphism» (maybe it is more correct to talk about «inner automorphism»), if any? It looks like those two terms are used interchangeably. By «transformation» I mean mapping from some set...

HI .I'm trying to prove that, for a linear transformation, it is worth that: f(a\bar{x}+b\bar{y})=af(\bar{x})+bf(\bar{y}) for every real numbers a and b. Until now, I have proved by myself that f(\bar{x}+\bar{y})=f(\bar{x})+f(\bar{y}). and , using this result i proved that: f(a\bar{v}) =...

Is the Lorentz transformation matrix Λμν a tensor of order two and does it transform like a tensor ?

Homework Statement I am to solve an ODE using the Fourier Transform, however I am quite inexperienced in using this method so I'd like some advice: Homework Equations a) The Fourier Transform b) The Inverse Fourier Transform The Attempt at a Solution I started by applying the Fourier...

I am confused about the field transformation under conformal transformation. Consider the scale transformation of field ##\phi## (not necessarily scalar) In CFT of Francesco et al, formula (2.121), the transformation is $$ \vec{x}\rightarrow \vec{x}'=\lambda x,\,\,\,\phi(\vec{x}) \rightarrow...

I read somewhere that, suppose a scalar field Σ transforms as doublet under both SU(2)L and SU(2)R, its general rotation is δΣ = iεaRTaΣ - iεaLΣTa. where εaR and εaL are infinitesimal parameters, and Ta are SU(2) generators. I don't quite understand this. First, why does the first term have...

<<moved from a technical forum, no template>> Need a Solution ASAP!

I am reading Hugo D. Junghenn's book: "A Course in Real Analysis" ... I am currently focused on Chapter 9: "Differentiation on $$\mathbb{R}^n$$" I need some help with the proof of Proposition 9.2.3 ... Proposition 9.2.3 and the preceding relevant Definition 9.2.2 read as follows...

I am reading Hugo D. Junghenn's book: "A Course in Real Analysis" ... I am currently focused on Chapter 9: "Differentiation on $$\mathbb{R}^n$$" I need some help with the proof of Proposition 9.2.3 ... Proposition 9.2.3 and the preceding relevant Definition 9.2.2 read as follows: In the...

I am reading Hugo D. Junghenn's book: "A Course in Real Analysis" ... I am currently focused on Chapter 9: "Differentiation on ##\mathbb{R}^n##" I need some help with the proof of Proposition 9.2.3 ... Proposition 9.2.3 and the preceding relevant Definition 9.2.2 read as follows: In the...

I have been learning SR from various sources. Most of the time from Feyman's Lectures but that's not the only place. In II_26 he gives the transformation for the E-field of a moving charge in the x direction under a standard Lorentz configuration. In Eqn 26.11 he derives a formula for the Ex...

I am reading Hugo D. Junghenn's book: "A Course in Real Analysis" ... I am currently focused on Chapter 9: "Differentiation on $$\mathbb{R}^n$$" I need some help with the proof of Proposition 9.2.3 ... Proposition 9.2.3 and the preceding relevant Definition 9.2.2 read as follows...

I am reading Hugo D. Junghenn's book: "A Course in Real Analysis" ... I am currently focused on Chapter 9: "Differentiation on ##\mathbb{R}^n##" I need some help with the proof of Proposition 9.2.3 ... Proposition 9.2.3 and the preceding relevant Definition 9.2.2 read as follows: In the...

Homework Statement I've never encountered Jacobians before, and having read up on them a bit I find the wording of the last part of this question confusing: A set of coordinates ##x'_{\mu}## in frame B is obtained from the set ##x_{\mu}## in frame A, by boosting B w.r.t A with speed beta along...

I am working through "Lessons on Particle Physics." The link is https://arxiv.org/PS_cache/arxiv/pdf/0906/0906.1271v2.pdf. I am on page 21, equation (1.5.50), which is ##S(\Lambda)=1-\frac{i}{2}\omega_{\mu\nu}\Sigma^{\mu\nu}##. I would like some motivation for this equation. I wonder what the...

Homework Statement Derick is fleeing from the cops on a car on a relativistic train. At xr= 0.0m and tr =0.000s the cops at rest see Derick leaving the back of the train and head towards the front of the train on his relativistic car. The cops see him arrive at the front at xr = 1.875*10^5m...

I am working through Lessons in Particle Physics by Luis Anchordoqui and Francis Halzen. The link is https://arxiv.org/PS_cache/arxiv/pdf/0906/0906.1271v2.pdf. I am on page 21. Between equations (1.5.53) and (1.5.54), the authors make the following statement: ##S^\dagger ( \Lambda ) = \gamma ^0...

So I am working through Lessons in Particle Physics by Luis Anchordoqui and Francis Halzen, the link is https://arxiv.org/PS_cache/arxiv/pdf/0906/0906.1271v2.pdf I am in the discussion of the Dirac equation, on page 21, trying to go from equation 1.5.49 to 1.5.51. And I get stuck. Equation...

Homework Statement q,p transforms canonicaly to Q,P where given Q=q(t+s)+(t+s)p ,t is time and s is constt To find P Homework Equations Poisson bracket {Q,P}qp=1 The Attempt at a Solution Using Poisson bracket I find (t+s)*(dP/dp-dP/dq)=1

For example, Lorenz transformation of time means That measurement of time changes from one observer to another. I have read that this means moving clocks run slower. But this can't be true because Lorenz transformation of time depends on both of the seed of the observer and the object he...

Many discussions cite CP transformation as the exchange of particles for anitparticles. But other places it says that charge conjugation alone is sufficient to turn a particle into its antiparticle. So, the question is, when you exchange particles for anitparticles, is it a CP transformation or...

Homework Statement In a reference frame ##S## there is a particle with mass ##m## and charge ##q## which is moving with velocity ##\vec{u}## in an electric field ##\vec{E}## and in a magnetic field ##\vec{B}##. Knowing the relativisitc laws of motion for a particle in an EM field, find the...

I currently styding applications of Lie groups and algebras in quantum mechanics. U^{\dagger}(R)V_{\alpha}U(R)=\sum_{\beta}R_{\alpha \beta}V_{\beta} Where ##U(R)## represents rotation. Letter ##U## is used because it is unitary transformation and ##R_{\alpha \beta}## matrix elements of matrix...

Homework Statement I am asked to show that E[\exp(a*W_t)]=\exp(\frac{a^2t}{2}) Let's define: Z_t = \exp(a*W_t) W_t is a wiener process Homework Equations W_t \sim N(0,\sqrt{t}) The Attempt at a Solution I want to use the following formula. if Y has density f_Y and there's a ral function g...

Homework Statement With respect to a given Cartesian coordinate system S , a vector A has components Ax= 5 , Ay= −3 , Az = 0 . Consider a second coordinate system S′ such that the (x′, y′) x y z coordinate axes in S′ are rotated by an angle θ = 60 degrees with respect to the (x, y) coordinate...

What does it means for a physical theory to have hamiltonian, if it is formulated in lagrangian form? Why doesn't someone just apply the lagrangian transformation to the theory, and therefore its hamiltonian is automatically gotten?

Homework Statement I have attached the question. Translated: Suppose T: R^4 -> R^4 is the image so that: ... Homework Equations So I did this question and my final answers were correct: 1. not surjective 2. not injective. My method of solving this question is completely different than the...

Books say 3 possibilities for this situation as insert within Lacz, insert outside Lacz, no inserted vectors, then these goes the transformation with Ecoli. But we can't know transformation yield %100. Thus, if we make blue white screening there is more possibilities. Lacz-- inserted within...

Hi. If we want cell to accept vector dna in transformation, we treated with calcium chloride or chilled on ice etc.. But i have a trouble with one issue about that. Books say that ; We must choose the vector that specific according to the cell that will do transformation. But we will treat with...

Homework Statement Show, by completing the square in the exponent, that the Fourier transform of a Gaussian wavepacket ##a(t)## of width ##\tau## and centre (angular) frequency ##\omega_0##: ##a(t)=a_0e^{-i\omega_0t}e^{-(t/\tau)^2}## is a Gaussian of width ##2/\tau##, centred on ##\omega_0##...

In the momentum representation, the position operator acts on the wavefunction as 1) ##X_i = i\frac{\partial}{\partial p_i}## Now we want under rotations $U(R)$ the position operator to transform as ##U(R)^{-1}\mathbf{X}U(R) = R\mathbf{X}## How does one show that the position operator as...

Homework Statement An electric dipole instantaneously at rest at the origin in the frame K' has potentials \Phi'=\mathbf{p}\cdot\mathbf{r}'/r'^3 and \mathbf{A}'=0 (and thus only an electric field). The frame K' moves with uniform velocity \mathbf{v}=\vec{\beta }c in the frame K. Show that in...

Homework Statement Let ##T:ℝ^3→ℝ^2## be the linear transformation defined by ##\begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix}\mapsto \begin{bmatrix} x_1 + x_2 + x_3\\ 0 \end{bmatrix}##. i. Find the standard matrix for ##T##. Homework EquationsThe Attempt at a Solution For this problem I was...

Hi Forum I am trying to get a better grasp of the relation between electric field and the magnetic field. The overall question is "What is The origin of selfinductance in a current loop?" Here are my thourghts: A battery is connected to a say circular wire with some resistance. The current...

Homework Statement Homework EquationsThe Attempt at a Solution I have attempted and completed all questions. However, I am now trying part (b) with transforming the voltage source into a current source. I am unable to work out the current and I am unsure what to do next. I have included my...

Hi everyone! Sorry for my bad English! Please, suppose you have a subject A that opens his arms like a "T", in each hand he holds a laser and shoots the light at the same time. There are 2 targets at the same distance and, to A, the light hits both targets simultaneously. I Know that in some...

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...