Transformations Definition and 823 Threads

I am trying to understand the derivation of the Dirac adjoint. I understand the derivation of the following identities involving Spinors, the Gamma matrices and Lorentz transformations: (Sμν)† = γ0Sμνγ0 s[Λ] = exp(ΩμνSμν/2) s[Λ]† = exp(Ωμν(Sμν/2)†) The part I'm having trouble with is...

Homework Statement Spaceship A of length 30m travels at 0.6c past spaceship B. Clocks in frame S' of spaceship A and S of spaceship B are synchronised within their respective frames of reference and are set to zero, so that t' = t = 0 at the instant the front of spaceship A passes the rear of...

Homework Statement How do I go about finding the most general form of the canonical transformation of the form Q = f(q) + g(p) P = c[f(q) + h(p)] where f,g and h are differential functions and c is a constant not equal to zero. Where (Q,P) and (q,p) represent the generalised cordinates and...

Within my project thesis I stumbled over the term SU(2)_V, SU(2)_A transformations. Although I know U(1)_V, U(1)_A transformations from the left and right handed quarks( U(1)_V transformations transform left and right handed quarks the same way, while U(1)_A transformations transform them with a...

Due to its form, gauge transformations for the typical electrodynamics potentials are "local" in nature. That`s: they exists for path connected topological spaces. So, there exists global gauge transformations or are all of them local in nature?. If the answer is "yes", i.e. if there are global...

Hey guys, This isn't a homework question but i learned about it in school. I'm trying to gain a more fundamental understanding or function transformations. that's the typical parent function for example: f(x)=x^2 I would move the function 3 units up, I would write it lil this: g(x)=x^2+3

I apologize in advance for this dumb question, I think I know the answer but I just want to be sure.A photon has energy E = pc = hf Do the Energy-Momentum transformations: apply exactly to photons? Or must we introduce certain corrective terms? Let's say all this takes place in free space.

Hey guys, In what circumstance or scenario would you use Lorentz transformations as a opposed to time dilation or length contraction? The reason that I ask this is because in all of the problems that I have worked with, the observer is always stationary relative to the event. For example, if...

You are probably familiar with the following two Lorentz transformations: x' = (x - vt) / sqrt(1 - v2/c2) and t' = [t - (vx/c2)] / sqrt(1 - v2/c2) Well I am having some issues interpreting what each variable refers to. You see, here is how I've been thinking of it: If you have one stationary...

Homework Statement As the title says, I need to show this. A conformal transformation is made by changing the metric: ##g_{\mu\nu}\mapsto\omega(x)^{2}g_{\mu\nu}=\tilde{g}_{\mu\nu}## Homework Equations The Weyl tensor is given in four dimensions as: ##...

Hi, Can anyone clarify what precisely is meant by "nonlocal transformations" in the BV formalism? Specifically, they claim that for any gauge theory with an open algebra, it is possible to go to a different basis for the algebra whereby one achieves closure (and even one where the gauge...

Homework Statement I thought that in the situation where mass is attached to the string and put into motion (vertically), energy goes between 1/2 kA^2 and 1/2 mV^2 like here - http://imgur.com/RU4P6UW However in student's book I saw the table, which said that potential energy of gravity is...

Hi Everyone. There is an equation which I have known for a long time but quite never used really. Now I have doubts I really understand it. Consider the unitary operator implementing a Lorentz transformation. Many books show the following equation for vector fields: U(\Lambda)^{-1}A^\mu...

Homework Statement LOOKING AT PART (c) The ball is traveling at velocity c/√2. The car is traveling at velocity c/√2. Ball is thrown up through the sun roof or something I don't know. Homework Equations The Attempt at a Solution I don't know how to think about this in 3D. I've done parts (a)...

I am revising the basics of linear transformations and trying to get a thorough understanding of linear transformations and their matrices ... ... At present I am working through examples and exercises in Seymour Lipshutz' book: Linear Algebra, Fourth Edition (Schaum Series) ... ... At...

Firstly, my apologies to Deveno in the event that he has already answered these questions in a previous post ... Now ... Suppose we have a linear transformation $$T: \mathbb{R}^3 \longrightarrow \mathbb{R}^2$$ , say ... Suppose also that $$\mathbb{R}^3$$ has basis $$B$$ and $$\mathbb{R}^2$$...

This is my second term in my master's and one of the courses I've taken is QFT1 which is basically only QED. In the last class, the professor said the Klein-Gordon Lagrangian has a global symmetry under elements of U(1). Then he assumed the transformation parameter is infinitesimal and , under...

I am reading Andrew McInerney's book: First Steps in Differential Geometry: Riemannian, Contact, Symplectic ... I am currently focussed on Chapter 2: Linear Algebra Essentials ... and in particular I am studying Section 2.6 Constructing Linear Transformations ... I need help with a basic...

In the system of units where c=1, the Lorentz transformations are as follows: ## x'=\gamma (x-vt) \\ t'=\gamma (t-vx) ## In the limit ## v \ll 1 ##, we have ## \gamma \approx 1+\frac 1 2 v^2 ##, so we have, in this limit: ## x' \approx (1+\frac 1 2 v^2)(x-vt)=x-vt+\frac 1 2 v^2 x-\frac 1 2...

I'm going through Ray D'Iverno's "Introducing Einstein's Relativity", and there is a step he makes in deriving the Lorentz transformations that doesn't seem necessary to me. So I'm not sure what I'm missing. He derives them from Einsteins postulates of relativity. From the postulate that the...

Homework Statement I've just started (self-studying) Neuenschwander's Tensor Calculus for Physics and I got stuck at page 23, where he deals with transformations of displacements. I've made a summary of page 23 in the first part of the attached file. Homework Equations I want to use the...

I am reading Bruce Cooperstein's book: Advanced Linear Algebra ... ... I am focused on Section 2.1 Introduction to Linear Transformations ... ... I need help with understanding Theorem 2.7 ... Theorem 2.7, its proof and some remarks read as follows:I am having considerable trouble...

Is there an alternative set of equations similar to Lorentz Transformations that transforms vectors from one dimension to a higher or lower dimension?

How do we get (5.381)? The term involving ##V## in (5.378) is ##V(r' + vt, t)\ \Psi(r' + vt, t)##. After dividing on both sides of (5.378) by the exponential term ##e^{[i(mv.r' + mv^2t/2)/\hbar]}## [which appears in (5.379)], the term becomes ##V(r' + vt, t)\ \Psi(r', t)##. But the term as...

Homework Statement Derive the transformations ##x \rightarrow \frac{x+vt}{\sqrt{1-v^{2}}}## and ##t \rightarrow \frac{t+vx}{\sqrt{1-v^{2}}}## in perturbation theory. Start with the Galilean transformation ##x \rightarrow x+vt##. Add a transformation ##t \rightarrow t + \delta t## and solve for...

Why is relative speed taken to be symmetrical i.e. speed of one frame of reference from a second frame is equal to that of the second frame of frame refrence from the first frame

I'm doing a class on special relativity and when doing some problems, I'm never sure whether I should be using the Lorentz transformations (Eg. x' = γ(x-vt) or t'=γ(t- (v/c^2)x)) or the Time dilation and Length contraction equations to find t or x! Can anyone explain if there's any way of...

Homework Statement Hello I need some advice on how to figure out Part F of the following problem. I was able to find the correct answer but in a very illogical way. I was wondering if I could get some help understanding the lorentz transformations necessary. Here is the full problem, I have...

Fredrik submitted a new PF Insights post Matrix Representations of Linear Transformations Continue reading the Original PF Insights Post.

Homework Statement f: p2 to R2, f(ax2+bx+c) = (a+b, b+c) = V12. Homework Equations Create a p2 to R2 polynom and R2 equation that is equivalent to the above statement, so: f(dx2+ex+g) = (d+e, e+g) = V2 Therefore a=d b=e c=g f(ax2+bx+c) = (a+b, b+c) = f(dx2+ex+g) = (d+e, e+g) The Attempt at...

Hello, 1. Homework Statement Suppose we have the following Lagrangian density, in ## 3 + 1## dimensions: $$L = \frac{1}{2}\partial_{\mu}\phi \partial^{\mu}\phi - g \phi^4$$ Under the dilatation (scaling transformation): ##x \rightarrow \lambda x^{\mu}, \phi (x) \rightarrow \lambda^{-1}...

It is well known that from a two-dimensional solution of Laplace equation for a particular geometry, other solutions for other geometries can be obtained by making conformal transformations. Now, I have a function defined on a disc centered at the origin and is given by f(r) = a r where a is...

Homework Statement Determine if the following is a linear transformation or not f : IR2 → IR, f(x, y) = x + y Homework Equations T(x+y) = T(x) + T(y) T(ca) = Tc(a) The Attempt at a Solution I can't tell you how much I've read, how many youtube videos I've watched over the last couple of...

Homework Statement Find the infinitesimal dilation and conformal transformations and thereby show they are generated by ##D = ix^{\nu}\partial_{\nu}## and ##K_{\mu} = i(2x_{\mu}x^{\nu}\partial_{\nu} - x^2\partial_{\mu})## The conformal algebra is generated via commutation relations of elements...

In Peskin and Schroeder page 37, a diagram illustrates how, under the active transformation, the orientation of a vector field must be rotated forward as the point of evaluation of the field is changed. I understand that the change of the orientation of the vector field is the same idea as...

This is what I have so far: I'm trying to show that the matrix D has to be unitary. It is the matrix that transforms the wavefunction.

Homework Statement Find the thevenin equivalent circuit by performing source transformations only. Homework EquationsThe Attempt at a Solution Answers: Vth=60v and Rth=30. I managed to get Rth correct, but I'm not sure if everything I did was "legal". I can't seem to find Vth.

Homework Statement Show explicitly that ei*ε*κu * ei*ε*κv * e-i*ε*κu* e-i*ε*κv = Identity + ε2 [Kv,Ku + O (ε3) The Attempt at a Solution Kv,Ku = Kv*Ku - Ku*Kv I'm not sure exactly how to approach this problem. I know that U (tau) = ∏ ei*su*Ku and that for operators O --> O' = U O U†...

If a theory is gauge invariant and one chooses to fix a particular gauge, having done this is it then possible to make a gauge transformation from this chosen gauge to another gauge, or have we already "spent" the gauge symmetry? Apologies if this is a really basic question, but I've got myself...

Hi everyone I'm taking a linear algebra class at university right now and this is one of my homework questions . I am unsure how to even approach these questions. Any pointers in the right direction would be greatly appreciated. I apologize in advance for not showing any attempt at this...

Here is the question: Provide a logical argument that demonstrates that when applying any two reflections, the outcome will always either be equivalent to a rotation or a translation. This is what I came up with: •Translation A reflection is defined as, “a transformation in which a...

Hi, I have a reference device that outputs euler angles, which are angles that relate the sensor body frame to the north east down frame. These angles are called pitch roll and yaw. The sensor is an accelerometer. I know how to get the rotation matrix that will put accelerations from the...

I was reading Einstein's seminal work: http://hermes.ffn.ub.es/luisnavarro/nuevo_maletin/Einstein_1905_relativity.pdfGo to this part: II. ELECTRODYNAMICAL PART § 6. Transformation of the Maxwell-Hertz Equations for Empty Space. On the Nature of the Electromotive Forces Occurring in a Magnetic...

Homework Statement (a) A light signal is fired at ##60^o## North of West. Calculate the west-east velocity component of the signal according to an observer traveling due East at 0.5c. State your answer as a multiple of c. (b) Calculate the North-South velocity component of the light signal...

Can't quite see why a one-to-one linear transformation is also onto, anyone?

Hope this derivation helps someone!

Any advice on my derivation layout?

Say we have an adjoint representation (specifically in n x n matrix format) of a Lie algebra. I have noted that we can create another n x n representation using a similarity transformation on the adjoint rep. I know I haven't discovered anything new but none of my sources mention this. Is...

Alright. I was looking into a 2D rotation matrix and there are two equations: one is through the transformation of the component of p (always with respect to x,y), x,y into x',y' and the other is through the transformation of the unit vectors i,j into i',j'. In a sense 1 is passive the other is...

Homework Statement T(a0 + a1t+a2t2) = 3a0 + (5a0 - 2a1)t + (4a1 + a2)t2 Find the image of the vectors : 1. 1 2. t 3. t2 Homework Equations T(a0 + a1t+a2t2) = 3a0 + (5a0 - 2a1)t + (4a1 + a2)t2 The Attempt at a Solution I don't know how my book solves these transformations, but the answers are...