Representation Definition and 722 Threads

For setting the fermionic state ## |n_1 n_2\rangle## where ##n_i## is the number of particles in the orbital ##i## we can use the following both representations for the state ##|1 1\rangle##: $$ \hat {\mathbf c_1} ^{\dagger} \hat {\mathbf c_2} ^{\dagger} |vac\rangle $$ or $$ \hat {\mathbf c_2}...

In matrix representation, the special unitary group is distinguished from the more general unitary group by the sign of the matrix determinant. However, this presupposes that the special unitary group is formulated in matrix representation. For a unitary group action NOT formulated in matrix...

Show that $$\frac{\pi}{4} = 1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \cdots$$

Snapshot of Mary L. Boas' Mathematical Physics book So, the marked lines say `If we think of P as the point z = x +iy in the complex plane, we could replace (2.3) by a single equation to describe the motion of P` But, until now I have only learned of representing points in the form (x,y), now...

An infinite product representation of Bessel's function of the first kind is: $$J_\alpha(z) =\frac{(z/2)^\alpha}{\Gamma(\alpha+1)}\prod_{n=1}^\infty(1-\frac{z^2}{j_{n,\alpha}^2})$$ Here, the ##j_{n,\alpha}## are the various roots of the Bessel functions of the first kind. I found this...

The Kallen-Lehmann representation is a (non perturbative) result in QFT that is proved with what seems to me like very minimal assumptions: https://en.m.wikipedia.org/wiki/Källén–Lehmann_spectral_representation According to this wiki page, in gauge theories something goes wrong and you can no...

So, I've been watching eigenchris's video series "Tensors for Beginners" on YouTube. I am currently on video 14. I, in the position of a complete beginner, am taking notes on it, and I just wanted to make sure I wasn't misinterpreting anything. At about 5:50, he states that "The array for Q is...

The graphical pattern of particles in the weak hypercharge and weak isospin plane, visible in this wiki page, shows the mixing angle between the Yw and Q axes. Actually , from the weak hypercharge (-2) of a right-handed electron and its electric charge (-1), one obtains an angle Pi/3, not the...

Dear all,I have four questions. Hopefully, someone can answer. Thank you :) 1. A qubit is described as a two-orthogonal basis state. How about two entangled qubits? 2. What is the actual reason for a qubit cannot be cloned/copied? Is it because without knowing the value of the complex...

Hi Pfs Spin networks are defined by the way their links and their nodes are equipped with SU(2) representations and intertwiners. Could you give an example of two different spin networks with the same number of nodes, links between them, the same coloring of the links (and their orientations)...

Hi; This is in fact not a homework question, but it rather comes out of personal curiosity. If you look at the graph of the two functions in the image attached, what is the simplest functional representation for such a symmetrical pattern?

This screenshot contains the original assignment statement and I need help to solve it. I have also attached my attempt below. I need to know if my matrices were correct and my method and algebra to solve the problem was correct...

Suppose ##f## is holomorphic in an open neighborhood of the closed unit disk ##\overline{\mathbb{D}} = \{z\in \mathbb{C}\mid |z| \le 1\}##. Derive the integral representation $$f(z) = \frac{1}{2\pi i}\oint_{|w| = 1} \frac{\operatorname{Re}(f(w))}{w}\,\frac{w + z}{w - z}\, dw +...

I am very new to C programming so am struggling with this question and how exactly to begin it, when we are doing this are we to use something like sprintf? Thank you.

Hello. I wonder about the representation of vectors, so I wanted to ask: how many different ways vectors be represented? As far as I know two: Geometrically and Algebraically. There is only one way to represent vectors in geometrically: arrows, however there are several or more methods to...

Homework Statement:: We have an 8-bit floating point representation, one bit for the sign, 3-bit biased exponent, and 4-bit for the normalized mantissa. What is the smallest and largest number you can represent? Relevant Equations:: - Would the smallest number just be 0 0 0 0 0 0 0 0 and...

If ##U## is an unitary operator written as the bra ket of two complete basis vectors :##U=\sum_{k}\left|b^{(k)}\right\rangle\left\langle a^{(k)}\right|## ##U^\dagger=\sum_{k}\left|a^{(k)}\right\rangle\left\langle b^{(k)}\right|## And we've a general vector ##|\alpha\rangle## such that...

Greetings! I´m trying to solve the following exercice I have done the following drawing for the cross section and I want to know if I need to add a top view or any other additional view? (is the cross section enough) thank you!

Hi, Suppose I am given a sequence of special symbols and I want to produce the next sequence of symbols according to certain rules that transform one symbol into one or more symbols. They are 10 symbols in total, say; A, B, C, D, E, F, G, H, I, J The rules are: A transformed into B and it is...

For the illuminant A for the illuminant B Did I got them correct? Thank you

Hello. There are 4 types of infinitesimals: 1) dx=1/N, N is the number of elemets of the set of the natural numbers (letter N is used to indicate the cardinality of the set of natural numbers) 2) Hyperreal numbers: ε=1/ω, ω is number greater than any real number. 3) Surreal numbers: { 0, 1...

From the wikipedia page for Fibonacci numbers, I got that the matrix representation for closed-form expression for Fibonacci numbers is: \begin{pmatrix} 1 & 1 \\ 1 & 0\\ \end{pmatrix} ^ n = \begin{pmatrix} F_{n+1} & F_n \\ F_n & F_{n-1}\\ \end{pmatrix} That only works...

I've tried to use the 1st equation as a matrix to determine, but it clearly isn't a diagonal matrix. My guess is that I need to find the spin matrix along the direction ##\hat{n}##, but do I need to find the eigenstates of ##\sigma \cdot \hat{n}## first and check if they form a diagonal matrix...

We've two operators ##\hat{a}##,##\hat{b}##. I know their position representation ##\langle r|\hat{b} \mid \psi\rangle=b## ##\langle r|\hat{a}| \psi\rangle=a ## Is it generally true that the position representation of the combined operator ##\hat{a}\hat{b}## is ##a b## where ##a, b## are the...

One of the component of angular momentum operator is ##\hat{L}_{x}=\hat{y} \hat{P}_{z}-\hat{z} \hat{P}_{y}## I want it's position representation. My attempt : I'll find the representation of the first term ##\hat{y} \hat{P}_{z}##. The total representation is the sum of two terms. The...

1 example to represent the question in semantic net. Second question-: every student loves to party. Represent this in semantic net. The answer is below-:

I've used a particular clifford algebra expression for a quantum mechanics wave vector to see if the Born rule can become a simple linear inner product in a clifford algebra formulation. The expression $$\Psi=\sum_i (e_i+Jf_i)\psi_i$$ turned out to be successful, where ##J## is the imaginary...

Hello, My question pertains to the formula below: In particular, I would like to ask about the spectral density function shown below: What does the spectral function physically represent? Is there any interpretation of its meaning, whether it has a relation to the physical spectrum of the...

In the article by E. Majorana "Oriented atoms in a variable magnetic field", in particular, it's considered (and solved) the problem of describing a state with spin J using 2J points on the Bloch sphere. That is, if the general state of the spin system , (1) then, according...

From what I remember of my optics course, any element such as a lens (be it thick or thin), can be represented by a matrix. So they are sort of operators, and it is then easy to see how they transform an incident ray, since we can apply the matrix to the electric field vector and see how it gets...

Hi, I have a question regarding the envelope function in parameter representation. Let an array of curves in cartesian coordinates be given in parameter representation, with curve parameter 𝑡 and array variable 𝑐 𝑥=𝑥(𝑡,𝑐) 𝑦=𝑦(𝑡,𝑐) Condition for envelope is: 𝜕/𝜕𝑡 𝑥(𝑡,𝑐) 𝜕/𝜕𝑐 𝑦(𝑡,𝑐)=𝜕/𝜕𝑐...

Hey! :giggle: Consider a representation of signed integers of base $B$, in which the digits are listed in descending order of importance, with the least significant digit corresponding to a positive, and the next digits to an alternate negative and positive value. Thus, a number of this...

Hi, I was reading the following book about applying deep learning to graph networks: link. In chapter 2 (page 22), they introduce the graph Laplacian matrix ##L##: L = D - A where ##D## is the degree matrix (it is diagonal) and ##A## is the adjacency matrix. Question: What does an...

The question may be ambiguous but it's really simple. One says that the baryon octet is the D(1,1) representation of SU(3), but then uses the same one for mesons. D(1,1) means one quark and one antiquark, which corresponds perfectly to mesons. But how can it explain baryons? My information and...

hi guys I was trying to verify the integral representation of incomplete gamma function in terms of Bessel function, which is represented by $$\gamma(a,x) = x^{\frac{a}{2}}\;\int_{0}^{∞}e^{-t}t^{\frac{a}{2}-1}J_{a}(2\sqrt{xt})dt\;\;a>0$$ i was thinking about taking substitutions in order to...

Now, i am extremelly confused about all this thing. More preciselly, i can't understand how 1.29 was obtained. It was used the A representation? How do he uses it? There is something to do with the canonical basis?

A regulation NFL playing field of length x and width y has a perimeter of 346_2/3 or 1040/3 yards. (a) Draw a rectangle that gives a visual representation of the problem. Use the specified variables to label the sides of the rectangle. (b) Show that the width of the rectangle is y = (520/3)...

Hi, as follow-up to this thread I've a question about general representation of a two-port network. Basically it is ad hoc built four-terminal linear network (using controlled sources + nullator-norator pair): for it I found a general representation ##AV + BI = 0## as in the picture above. If...

In the 4-dimensional representation of ##\beta##, ## \beta=\begin{pmatrix}\mathbf I & \mathbf 0 \\ \mathbf0 & -\mathbf I\end{pmatrix} ,## and we can suppose ## \alpha_i=\begin{pmatrix}\mathbf A_i & \mathbf B_i \\ \mathbf C_i & \mathbf D_i\end{pmatrix} ##. From the anti-commutation relation...

$$\langle p | W | p' \rangle = \int \langle p | x \rangle \langle x W | x' \rangle \langle x' p' \rangle dx dx'$$ $$\langle p | W | p' \rangle = \int \langle p | x \rangle \delta(x-x') W(x) \langle x' | p' \rangle dx dx'$$ $$\langle p | W | p' \rangle = \int \langle p | x' \rangle W(x') \langle...

Trying to use <+|+>=1=<-|-> and <-|+>=0 to prove each iteration of the equation, so I have 6 different versions to prove. But the part I'm currently stuck on is understanding how to simplify any given version. I've written out [S_x,S_y]=S_xS_y\psi-S_yS_x\psi and expanded it in terms of the...

While searching for a software to plot a crystallographic representation of a particular material, I have come across two sources that seem to give two very different views of a same material. In this case, it is CoSb3. On the one hand there is from ASE (Atomic Simulation Environment), a...

I was reading the page about interpreters on wikipedia and one particular section caught my eye: "An interpreter generally uses one of the following strategies for program execution: Parse the source code and perform its behavior directly; Translate source code into some efficient...

I'm following the lecture notes by https://www.thphys.uni-heidelberg.de/~weigand/QFT2-14/SkriptQFT2.pdf. On page 169, section 6.2 he is briefly touching on the non-abelian gauge symmetry in the SM. The fundamental representation makes sense to me. For example, for ##SU(3)##, we define the...

In a differential geometry text, a torus is defined by the pair of equations: I initially thought this was somehow a torus embedded in 4 dimensions, but I do not see how we can visualize two orthogonal 2-dimensional Euclidian spaces. How is this a representation of a 2 dimensional torus...

If I have a wavefunction ##\Psi(X)## that is invariant under the group ##Z_2##, what specifically does that mean? There can be several operators that are representations of the group ##Z_2##, for example the operators $$\mathbb{Z}_2=\{ \mathbb{I}, -\mathbb{I} \},$$ or $$\mathbb{Z}_2=\{...

I see the top version used everywhere. But isn't the bottom version better? Because the top version makes it seem like H2 bonds with the C to its right and the other H2 bonds with the N. Whereas the bottom version shows the bonds correctly. Should I draw it like the top version and stop annoying...

How did you find PF?: Surfing web Can someone advise on this? In most diagrams showing how mass effects the gravitation field (earth for instance), bending fabric of space, it is demonstrated on one plane. Why is it shown this way and is there any other way of illustrating this?

$$\hat{S_+} = \hbar \begin{bmatrix} 0 & \sqrt{2} & 0 \\ 0 & 0 & \sqrt{2} \\ 0 & 0 & 0 \end{bmatrix}$$ $$\hat{S_-} = \hbar \begin{bmatrix} 0 & 0 & 0 \\ \sqrt{2} & 0 & 0 \\ 0 & \sqrt{2} & 0 \end{bmatrix}$$ $$\hat{S_x} = \hbar/\sqrt{2} \begin{bmatrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 0...

Hello! I have checked commutator matrix form of $$\vec{p}=im/\hbar [H,\vec{x}]$$ but I realized i don't undertand something I have $$[H,\vec{x}]=H\vec{x}-\vec{x}H$$ and $$(H\vec{x})_{i}=H_{ij}x_j$$ & $$\ ( \vec{x}H)_{i}=x_jH_{ji}$$ but what is the second term matrix representation...