Representation Definition and 766 Threads

Hi guys! I'm having some problems in understanding the direct products of representation in group theory. For example, take two right weyl spinors. We can then write\tau_{0\frac{1}{2}}\otimes\tau_{0\frac{1}{2}}=\tau_{00}\oplus\tau_{01} Now they make me see that...

(At least, I think it's simple.) Disclaimer: I'm approaching this subject from the vantage point of a chemist, so be careful with how much lingo/jargon/rigor you lay on me :redface: The claim is that if you have two representations of a group, \Gamma_1 and \Gamma_2, with bases \{ f_i \} and \{...

Homework Statement See Attachment Homework Equations None I can think of The Attempt at a Solution I'm fairly certain that phi_yx is zero Also I tried factoring out the cos and splitting up the equation into it's respective components, but to no avail. Am I even going about this correctly?

Hi everybody, I have a question: We know that the geometrical representation of 1st order derivative is the slope of a function. Then what is the geometrical representation of derivatives having order more than 1? I mean what does it actually represent in a function? Please some body clear my...

Give a parametric representation of the following surfaces in terms of the given parameter variables: a) The first octant portion of the sphere (x^2) + (y^2) + (z^2) = 16 in terms of the spherical variables theta and phi. b)The graph of the function z = (x^3) - sqrt(y) in terms of the...

After you find the irreducible representation of a molecule, how do you determine the number of IR active bands? For example, in methane, the pointgroup is Td , then you found that the irreducible representation is A1 + T2. How do you find the number of IR active and Raman active bands...

I am lecturing out of R.Bartle, The Elements of Integration and Lebesgue Measure, for the first time. In the most recent lecture I got stuck not being able to argue an inequality on page 107. I cannot post the text here, sorry. But if anyone has the book, can you also explain how to derive the...

http://planetmath.org/encyclopedia/InducedRepresentation.html The thing I don't get is the definition of a group element g's action on a vector \sigma v. In the link it defines the action as g(\sigma v):=\tau (hv), where \tau is the unique left coset of G/H containing gg_{\sigma}(i.e. such...

Homework Statement Find the power series representation for the function f(x)=x/(x^2-3x+2) and determine the interval of convergence. Homework Equations The Attempt at a Solution First I separate into partial fractions 2/(x-2) - 1/(x-1) 2/(x-2) = sum n=0 to infinity (x/2)^n...

Homework Statement There is a freely moving particle of mass m. Prove that the matrix elements of the time development operator, T(t,0), in the position representation is <q'|T|q''> = [(m/2i*pi hbar t)^1/2] Exp[-m(q'-q'')^2/2it hbar] Homework Equations H = (p^2)/2m The Attempt at a...

The equation is z = y^3. I know how to do normal planes and spheres, but I don't know what to set for r(u,v) when it comes to paraboloid cylinders.

Homework Statement The spin of an electron points along the +x direction. a) What is this state in the representation where +z= \left( {\begin{array}{c} 1 \\ 0 \\ \end{array} } \right) -z= \left( {\begin{array}{c} 0 \\ 1 \\ \end{array} } \right) b)...

Homework Statement In circuits, when we represent a battery we note by a long vertical line(positive) followed by a short vertical line(negative). But in some circuits, we follow a long line followed by a short line, again a long line and a short line with dots between them. What does this...

I'm having difficulty understanding this concept of uniqueness. What's the precise definition of it? Let say we have some direct sum decomposition, (1)Are \left( {\begin{array}{*{20}{c}} {{R_1}} & 0 \\ 0 & {{R_2}} \\ \end{array}} \right) and \left( {\begin{array}{*{20}{c}}...

I was wondering if there is a representation of gamma matrices unitarily equivalent to the standard representation for which Dirac Spinors with positiv energy and generic momentum have only the first two component different prom zero. Anyone can help me?

Edit : Removing my personal theory as I realized they are not tolerated or allowed on these forums.

Hi all, I have been thinking long and hard and trying to rationalize the reason for squaring an equation. I still don't understand why we do it. It's mainly in physics that I don't get it. I understand full well and accept that to get the area of a circle you multiply pi by r^2. But why...

I have read that, in QFT, unlike QM, there is no position probability density function because position is not considered an observable. Then how is a position measurement represented/modeled in QFT? As always, thanks in advance.

Homework Statement In a given basis \{ e_i \} of a vector space, a linear transformation and a given vector of this vector space are respectively determined by \begin{pmatrix} 2 & 1 & 0 \\ 1 & 2 & 0\\ 0&0&5\\ \end{pmatrix} and \begin{pmatrix} 1 \\ 2 \\3 \end{pmatrix}. Find the matrix...

In group representation theory, identity element's representation matrix is unit matrix. But why? Could you give me an exact explanation? Thany you.

The definition of the Euler - Mascheroni constant, \gamma, is given as \gamma = \lim_{n\rightarrow\infty}\sum_{k=1}^{n}\frac{1}{k} - \ln(n) or equivalently in integral form as \gamma = \int_{1}^{\infty}\frac{1}{\left\lfloor x\right\rfloor} - \frac{1}{x}\ dx I saw a seeming related integral...

Hi, I am working through Maggiore's QFT book and have a small problem that is really bothering me. It involves finding the representation of the Poincare algebra generators on fields. I always end up with a minus sign for my representation of a translation on fields compared to Maggiore...

I am 99% sure it is not, but I would like to hear that from someone else to be more serene.

Homework Statement Prove that a representation of a finite group G is faithful if and only if its image is isomorphic to G. Homework Equations The Attempt at a Solution

Homework Statement You always see slope represented as \frac{\delta y}{\delta x}. Is there any particular reason for why the change in "y" is in the numerator and the change in "x" in the denominator? Why couldn't we represent it as delta x over delta y? Homework Equations \frac{\delta...

I would like to have a setup/software to geometrically simulate or represent the given molecule. For example I will input ; 2 hydrogen + 1 oxygen and it will output h2o and draw it's molecular shape. Also it would be much better if the software could give all the possible combinations of the...

1. Homework Statement [/b] Show that the matrix representation of the dihedral group D4 by M is irreducible. You are given that all of the elements of a matrix group M can be generated from the following two elements, A= |0 -1| |1 0| B= |1 0| |0 -1| in the sense that all...

Homework Statement I just now came to the realization that I don't know the standard for representing units. When do I include "." after the abbreviation and when do I not? Thanks. For example mi. or mi m or m. yr. or yr What's the rule? I'm sure there's got to be some general...

Just started my way ploughing through Weinberg's book, for which my progress can be measured in lines since I got so many confusions. I suppose there'll be more confusions awaiting me, so I wish all my confusions or questions from his book will make a series, and I'll label them as...

Kindly ignore if some +- signs are placed wrongly in the equations. Thank you. Rotation in three dimensions can be represented using pauli matrices \sigma^{i}, by writing coordinates as X= x_{i}\sigma^{i}, and applying the transform X'= AXA^{-1}. Here A= I + n_{i}\sigma^{i}d\theta/2. The pauli...

Does someone know a textbook that treats QM without relying on representations much? I mean like saying "lets show that this commutator (momentum and position etc.) is reasonable and then derive everything from that without ever talking about representation much". Moreover is it possible to...

I need a free description with illustrations on 4D knots theory, especially the 4D generalization of Reidermeister moves and the movie represantation. Where can I find a freely available paper?

Homework Statement Hi, This is a question from a logic course, not sure if I'm doing it right. Consider the following predicates: MP(x) : x is a Mersenne prime Prime(x) : x is Prime Using the above predicates, provide an equivalent symbolic statement for the statement below: 1) A natural...

Hello, this might be a basic question. In feynman diagram's we represent the positron as traveling backwards in time. Is that correct ? How do we interpret this ?

Homework Statement Find a power series representation for the function and determine the radius of convergence.Homework Equations f(x)=x^{2}tan^{-1}(x^{3})The Attempt at a Solution I don't have any idea on how to even start this. First I differentiated \frac{d}{dx} arctan(x)=\frac{1}{x^2+1}...

I have 3 basis vectors: e_1 = sin^2(x), e_2 = cos^2(x), e_3 = sin(x)cos(x) I am told that the combination rule is just normal addition, and that the differential operator is defined by Dp(x) = p'(x). My task is to show that D =...

T is a linear operator from the space of 2 by 2 matrices over the complex plane to the complex plane, that is T: mat(2x2,C)\rightarrowC, given by T[a b; c d] = a + d T operates on a 2 by 2 matrix with elements a, b, c, d, in case that isn't entirely clear. So T gives the trace of the...

There the well known theorem that every open set (I'm talking about R here with standard topology) is the union of disjoint open intervals. Now, looking at the geometry, it seems that between any two adjacent open intervals which are in the union constituting our open set there is a closed...

Hey all Homework Statement Here i want to translate them and show the hex representation of these instructions: 1)add $t0, $t0, $zero 2)lw $t2, 16($s3) Homework Equations The Attempt at a Solution eg. 2) lw | $s3 | $t2 | 16 I-TYPE then translate the assembly code: 35 | 19 | 10 | 16 The...

Homework Statement Show that \int d\theta e^{\theta(\xi-\eta)}=\delta(\xi-\eta), where all of the above variable are Grassmann numbers. All this is in the holomorphic representation, where for some generic function: f(\theta)=f_0 + f_1\theta Homework Equations How do I arrive at that...

Find a power series representation for the function and determine the interval of convergence. f(x)=\frac{1+x}{1-x} This is one of the few problems in this section that I am getting stuck on. I know that I can relate it to the form of; \frac{1}{1-(x)} ...but after that I don't know what...

Homework Statement Find a power series representation for the function and determine the radius of convergence: f(x)=ln(5-x)Homework Equations Manipulate into the form 1/(1-x).The Attempt at a Solution I know how to do this with other functions, say, x/(9+x2)... It would convert to x/9 *...

Homework Statement In order to construct a character table (or to solve problems that directly ask for irreducible representations) I have to be able to decompose a representation into irreducible representations. However I don't know how to do this in general. Homework Equations I...

Homework Statement In order to construct a character table I need the character of the standard representation. The only problem is I don't know how to find the standard representation of a given group. Homework Equations The groupprops wiki tells me: "Take a representation of degree n...

http://awesome.good.is/transparency/web/1104/congress/transparency.png The biggest graph (with the dots) is just for republicans vs. democrats vs. other. But check out the smaller graphs comparing what would actually reflect the american people (on the right) and what is actually there in...

Homework Statement I need to calculate the probability distribution of 1s and 2p state of hydrogen atom in momentum and in coordinate representations. I have calculated the wave function in coordinate representation, and the dilemma is, do I simply do the Fourier transform for given wave...

Hi, I'm new in this forum. I have a problem i can't solve and searching on Google i couldn't find anything. It says: If D(g) is a representation of a finite group of order n , show that K = \sum^{i=1}_{n} D^{\dagger} (g_i) D(g_i) has the properties: b) All eigenvalues of K are...

Below is the Wikipedia URL shows the shape of EM wave. http://upload.wikimedia.org/wikipedia/commons/3/35/Onde_electromagnetique.svg" Electromagnetic laws say that' "changing magnetic field produce electric field and changing electric field produce magnetic field" In the...

This isn't an assigned problem, just a popular forum I was hoping someone here would be able to help or move it to where it should be... Homework Statement I was working out the Young's tableaux for two SU(3) representations where 3 \otimes 3 = 6 \oplus \bar{3}, where the 6 is symmetric...

Homework Statement Find the Fourier integral representation of the given function. f(x)= \left\{\begin{array}{ll} 1-\cos(x) & \mbox{ if } -\frac{\pi}{2} < x < \frac{\pi}{2} \\ 0 & \mbox{ otherwise} \end{array}\right. On a side note...how does one properly enter the above using...