Representation Definition and 722 Threads

Hi Guys, I was wondering if it is possible (why or why not) to define the floor function, Floor[x], as an infinite Taylor Series centered around x=a? Any sort of help is greatly appreciated! flouran

Homework Statement This has been driving me insane, and I'm sure it's something mind-boggling obvious but I can't seem to find it. I'll go through the work through here, I'm trying to prove that \int_0^1{x^xdx}=\sum_{n=1}^{\infty}\frac{(-1)^{n+1}}{n^n}. 2. The attempt at a solution...

For carbohydrates, the \alpha position is to the right in a Fischer projection and down in a planar representation. Is it axial or equatorial in a chair conformation? My book also says that all the OH groups in \beta-D-glucose are in axial positions. Is this true?

Hi, I'm very new on Group Theory, and lacking of easy to understand document on it. I can't get Representation of SO(3) Groups. Is there anyone can tell me useful information about it? Thanks, Tore Han

Homework Statement given that X(operator) and P (operator) operate on functions,and the relation [X,P]=ih/2π,show that if X(operator)=x ,and P (operator) has the representation P=-ih/2π*∂/∂x +f(x) where f(x) is an arbitrary function of x Homework Equationsquantum mechanic by Liboff...

can someone explain to me that is a spinor and how do I calculate the spin operators from it? for ex. (from homeword) the spinor is (|a|*e^(i*alpha), |b|*e^(i*beta))

URGENT: QM Series Representation of Bras, Dirac Brackets Homework Statement Suppose the kets |n> form a complete orthonormal set. Let |s> and |s'> be two arbitrary kets, with representation |s> = \sum c_n|n> |s'> = \sum c'_n|n> Let A be the operator A = |s'><s| a) Give the...

Homework Statement Prove: Representation of vectors by any basis is unique. Homework Equations The Attempt at a Solution The minimal span set and the maximum linearly independent set gives a basis.

PLEASE HELP ! THANK YOU (: 1. My teacher gave us a drawing with 4 vectors on it. Vector A = 130 N and is at a 20 degree angle. Vector B = 100 N and is at a 70 degree angle. Vector C = 70 N and is on the x-axis. Vector D = 50 N and is at a 10 degree angle. Given this picture we are told to...

Homework Statement Let G be the group S_3. Find the permutation representation of S_3. (Note: this gives an isomorphism of S_3 into S_6) The Attempt at a Solution Is there only ONE permutation representation, because the question asks for "the" p.r. I don't know where to start.

Hi there! As most people already might know, we can decompose the 27 dimensional representation for the baryons under SU(3) flavour symmetry as 27 = 10 + 8 + 8 + 1. I can find a lot of information about the particles that lie in the decuplet and in the octet, but nothing about which particle...

I'm taking a course in control theory, and have been wondering for a while what the benefits are when you describe a system based on the Laplace method with transfer functions, compared to when you use the state space representation method. In particular, when using the Laplace method you are...

The Wikipedia article on Real Numbers says every "a real number can be given by an infinite decimal representation, such as 2.4871773339..., where the digits continue in some way" I don't think this is right. Doesn't there have to be some real numbers that cannot be named, even if we allow that...

I'm having difficulty with the D^{l}(\theta) representation of 3D rotations what do the mean i suppose one you construct it for l = 1 you get the general rotation Euler matrix for 3-d Space, but what do the l = other integers or half integers mean physically? is the D matrices the...

I'm considering that, the (1/2,1/2) representation of Lorentz group is the four-vector representation, and this four-vector representation has spin 0,1. As we know, this four-vector representation can serve for the gauge field A_\mu, i.e. photon. However, the photon has spin 1. So we face a...

How would you represent tensors as matrices? I've searched all over, and my book on GR (Wald) only has one example where he makes a matrice from a tensor, and I still don't understand the process.

I'm strugging with a portion of Rudin's proof. Quick statement of the bulk of the theorem: Let X be a locally compact Hausdorff space. Let A be a positive linear functional on Cc(X) (continous functions with compact support). Then (among other things), there exists a measure u() that...

Hi there, I suppose there is a standard palette for atoms representation? i.e. white for hydrogen, red for oxygen? Is there a site or a link that provides such information?

It is well known that at times we do need explicit representations for the Dirac gamma matrices while doing calculations with fermions. Recently I found two different expressions for Majorana representation for the gamma matrices. In one paper, the form used is: \gamma_{0} = \left(...

Hi, I'm reading about Gelfand's representation theory for Banach algebras and I have a small problem with one of the proofs. Let A be a commutative Banach algebra with unit, define \Gamma_A=\left\{\varphi:A\to\mathbb{C}:\varphi\neq0, \varphi \text{ an algebra homomorphism }\right\} to be...

Under what conditions does a function have a power series representation? I am looking for a theorem that says if a function satisfies these conditions then it has a power series representation. Or does all functions have a power series representation?

in the .pdf article http://repository.dl.itc.u-tokyo.ac.jp/dspace/bitstream/2261/6027/1/jfs080104.pdf i have found the strange representation \delta (x) = -\frac{1}{2i \pi} [z^{-1}]_{z=x} and a similar formula for Heaviside function replacing 1/z by log(-z) , what is the meaning ...

I'm done a basic course on representation theory and character theory of finite groups, mainly over a complex field. When the order of the group divides the characteristic of the field clearly things are very different. What I'd like to learn about is what happens when the field is not...

Homework Statement Consider the linear transformation T: R2-->R2, where T(x1, x2, x3)= (3x2-x3, x1+4x2+x3) a. Find a matrix which implements this mapping. b. Is this transformation one-to-one? Is it onto? Explain. Homework Equations [T(x)]_B = ([T]_B) (x_B) The Attempt at a...

Hi all! I worked for hours on this simple commutator of real scalar fields in qft: \left[\Phi\left(x\right),\Phi\left(y\right) \right] = i\Delta\left( x-y \right) where \Delta\left(x\right) = \frac{1}{i}\int {\frac{{d^4 p}} {{\left( {2\pi } \right)^3 }}\delta \left( {p^2 - m^2 }...

Hello to everyone I'm a newcomer to the blog. I'm studying group theory and I'm dealing with irreducible representations (irreps) of C3v. Now since C3v is invariant after 6 symmetry operations I expect, as a consequence of the well known relationship g=Sum_i n^2_i (where g is the order of the...

Is this an accurate representation of the dimensions of string theory? http://youtube.com/watch?v=qU1fixMAObI

[SOLVED] Representation of j=1 rotation matrix The derivation of this involves the use of the following fact for j=1: [atex]\frac{J_y}{\hbar} = (J_y/\hbar)^3[/itex]. Is there a simple way to see this other than slogging through the algebra by expanding out the RHS using J_y =...

Consider a 3D particle in a square box. One can represent a complete set of quantum states by indexing them with their momentum component quantum numbers. So a state would be |p_x p_y p_z>. If one goes to the energy basis, two momentum states (say |1 0 0> and |0 1 0>) will correspond to the same...

Homework Statement Use differentiation to find a power series representation for f(x) = 1/ (1+x)^2Homework Equations geometric series sum = 1/(1+x) The Attempt at a Solution (1) I see that the function they gave is the derivative of 1/(1+x). (2) Therefore, (-1)*(d/dx)summation(x^n) =...

Homework Statement a. Find the permutation representation of a cyclic group of order n. b. Let G be the group S3. Find the permutation representation of S3. Homework Equations n/a The Attempt at a Solution I unfortunately have not been able to come up with a solution. I really...

Hi All, I am interested what are the advantages, in general, of using Liouville representation instead of Hamiltonian representation and for what kind of problems such advantages are valid?

Is there a thing called a coset representation? If so is it the element that factors outside the coset? i.e. {4,8,12,16,...} = 4{1,2,3,4,...} so 4 is the coset representation for {4,8,12,16,...}

Homework Statement Find a power series representation for the function and determine the radius of convergence. heres the problem: http://img301.imageshack.us/img301/4514/30437250jj2.png Homework Equations The Attempt at a Solution i believe the derivative of arctant =...

Homework Statement I was looking through my notes when I saw the following expression of a plane wave represented as a phasor A_{0}e^{i(\vec{k}\cdot\vec{r}-\omega t)} Now I can certainly understand a plane wave propagating along a given coordinate axis say, x or z, and the phasor...

Homework Statement What would the geometric explanation of exp(-i*x) be? Homework Equations Exp(-i*x), i being (-1)^1/2 The Attempt at a Solution I'm pretty sure this is just a circle, created clockwise? Just want to check.

Homework Statement Find the phasors of the following time functions: (a) v(t)\,=\,3\,cos\left(\omega\,t\,-\,\frac{\pi}{3}\right) (b) v(t)\,=\,12\,sin\left(\omega\,t\,+\,\frac{\pi}{4}\right) (c) i(x,\,t)\,=\,2\,e^{-3\,x}\,sin\left(\omega\,t\,+\,\frac{\pi}{6}\right) (d)...

I'm trying to derive the Gell Mann matrices for fun, but I really don't know representation theory. Can somebody help me? I have Hall's and Humphrey's books, but only online versions and staring at them makes me go crosseyed, and I'm to broke to buy a real book on representation theory. Let...

Just checking here. Propositional logic connectives like AND and OR have analogs or representations in set theory. For example, the logical connective AND is represented in set theory by intersection, an element of X AND Y is the element of the intersection of sets X and Y. And similarly, the...

[SOLVED] Representation with Fibonacci numbers Homework Statement Let k >> m mean that m \geq m+2. Show that every positive integers n has a unique representation of the form n = F_{k_1} + F_{k_2} + \cdots F_{k_r}, where F_{k_i} are Fibonacci nuimbers and k_1 >> k_2 >> \cdots k_r >> 0...

Why is there 'combinatorial' in front of both of combinatorial group theory and combinatorial representation theory? What does it imply? What is the difference and similiarities between cgt and crt besides the fact that they both have the word combinatorial in front of them?

What is the connection between the two if any? What kind of algebra would Lie groups be best labeled under?

"An irreducible representation of..." So I was reading this paper by Max Tegmark linked from another thread, and one particular thing he said-- although didn't really have anything to do specifically with the paper it was part of-- caught my eye: So this is something I've actually seen...

[SOLVED] Power series representation, I really need help! :-] please let me know if i did this correctly f(x)=\arctan{(\frac{x}{3})} f'(x)=\frac{\frac{1}{3}}{1-(-\frac{x^2}{3^2})} \frac{1}{3}\int[\sum_{n=0}^{\infty}\frac{(-1)^{n}x^{2n}}{3^{2n}}]dx...

I'm totally confused on the relationship between kets written | \uparrow \rangle, | \downarrow \rangle and | \uparrow \uparrow \rangle, | \uparrow \downarrow \rangle | \downarrow \uparrow \rangle, | \downarrow \downarrow \rangle (Problem) I have a system of two spin-1/2 particles...

I read this in a paper: Suppose there is a theory describing fermions transforming nontrivially under SU(3) gauge symmetry. L = \Psi^{\bar}(\gamma^A D_A+Y(\Phi))\Psi. The covariant derivative is: D_A\Psi=(\partial_A-i E_A^{\alpha}T_{\alpha})\Psi. Where E_A^{\alpha} are SU(3) gauge fields...

In plain old QM, we can in principle take any state and expand it either in terms of momentum eigenstates or position eigentstates (i.e., the wave function). But in practice this usually means solving the Schrodinger equation, i.e., working in the postion representation from the start and then...

Homework Statement \sum_{n=0}^\infty (0.5)^n * e^{-jn} converges into \frac{1}{1-0.5e^{-jn}} Prove the convergence. Homework Equations Power series, and perhaps taylor & Macclaurin representation of series. The Attempt at a Solution This isn't a homework problem...

Phasor representation of AC voltage and current. I\,=\,5\angle{0^o}\,=\,5\,+\,j0\,A V\,=\,100\angle{30^o}\,=\,86.6\,+\,j50\,V in general V\,=\,A\angle{\theta^o}\,=\,A cos{\theta}\,+\,jA sin{\theta}\,V and similarly for I It is assumed that the angular frequency \omega is...

Just wanted to check and see if this is right. The k-component of the vector is what I'm unsure of...I've always sucked at converting to parametric form. :) Homework Statement Convert to parametric form: x^{2} + y^{2} = 9, z = 4arctan(y/x) The Attempt at a Solution The i- and...