Generators Definition and 288 Threads

IN Srednicki's QFT he seems to make two different choices for normalizing the generators of lie algebras. In chapter 24 (eqn 24.5) he chooses Tr (TaTb) = 2 δab and in chapter 69 (eqn 69.8) he chooses Tr (TaTb) = (1/2) δab Is there a reason for this? Is there any particular reason to make one...

Homework Statement (I have dropped the hats on the ##\alpha_{n}^{u}## operators and ##L_{m}##) ##[\alpha_{n}^u, \alpha_m^v]=n\delta_{n+m}\eta^{uv}## ##L_m=\frac{1}{2}\sum\limits_{n=-\infty}^{\infty} : \alpha_{m-n}^u\alpha_{n}^v: \eta_{uv}-\delta_{m,0}## where : denotes normal-ordered. Show...

Hi, I understand you can induce an electrical current by passing a magnet through a copper pipe. If so, why do generators (and motors for that matter) use coils in stead? Do coils allow a stronger current or greater efficiency? Where can I go to find out the most energy-efficient design for a...

The ##{\bf su}(2)## Lie algebra in a representation ##\bf R## is defined by ##[T^{a}_{\bf R},T^{b}_{\bf R}]=i\epsilon^{abc}T^{c}_{\bf R},## where ##T^{a}_{\bf R}## are the ##3## generators of the algebra. In ##2## dimensions, these generators are the Pauli matrices ##T^{1}_{\bf 1} =...

Homework Statement Using the commutation relations ##[x,p_x] = i\hbar## etc, together with the ##SO(3)## generators ##J_k (k=x,y,z)## in their operator form to calculate ##[J_x, \mathbf{r}]## and ##[J_x, \mathbf{p}]## where ##r = (x, y, z)## and ##p = (p_x, p_y, p_z)##. Then show that ##[J_k...

Hi all, I read in Cheng and Li's book "Gauge theory of elementary particle physics" Ch 11, specifically : Eq. (11.46) that the hypercharge commutes with the SU(2) generators, i.e., ##[Q-T_3,T_i]=0##, I'd like to understand what that mean and how this could be proved ?

Homework Statement For a balanced star connection i have given angles for V1=90 V2=0 V3=-90 i have to find the voltage required to produce the same phase currents as in standard three phase voltage source e.g V1=120 V2=0 V3 =-120 Homework EquationsThe Attempt at a Solution Im not even sure...

hi every one , I need an information about the development of steam generator technology in nuclear power plants . please suggest me some websites or textbooks for reference . thank you in advance .

I was reading some lecture notes on super-symmetry (http://people.sissa.it/~bertmat/lect2.pdf, second page). It is stated that ". In order for all rotation and boost parameters to be real, one must take all the Ji and Ki to be imaginary". I didn't understand the link between the two. What does...

So Assume that I have an AC generator and I am giving it enough power to keep spinning with the same rate. So I have limited power usage. The generator creates maximum voltage V and because power is limited that leaves me with only 1 specific current. Now if I connect this generator to a...

Homework Statement Let n>=2 n is natural and set x=(1,2,3,...,n) and y=(1,2). Show that Sym(n)=<x,y> Homework EquationsThe Attempt at a Solution Approach: Induction Proof: Base case n=2 x=(1,2) y=(1,2) Sym(2)={Id,(1,2)} (1,2)=x and Id=xy so base case holds Inductive step assume...

I am curious as to how much energy is lost by resistance that exists between the magnet and the cooper coils. For instance, if a the work done to push a magnet through a copper coil tube produces a certain amount of power, how much of work is lost due to the magnet resistance as the magnet is...

this might have been answer before. Question is, what in physics or chemistry creates a load on a generator when the demand increases. For example, If no lights are turned on connected to a generator, it will spin freely. but the more lights are turned on the harder is to spin the generator...

1. The two rotors (purple, green) are electricaly isolated but mechanically fit to rotate along same axis 2. The motor action on the left side rotor will move the armature set, this will produce currents in right side rotor that will pass via a variable load. 3. do you see the magnetic fields...

Given that ##g T_a g^{-1} = D^b_a T_b## one can show that the generators in the adjoint representation of a group ##G## are the structure constants of the lie algebra satisfied by the ##T_a##. Write ##g## infinitesimal, so that ##g = 1 + \mathrm {i} \alpha^a T_a## and ##D^c_a = \delta^c_a + i...

The generators ##\{ L^1, L^2 , L^3 , K^1 , K^2 , K^3 \}## of the Lorentz group satisfy the Lie algebra: \begin{array}{l} [L^i , L^j] = \epsilon^{ij}_{\;\; k} L^k \\ [L^i , K^j] = \epsilon^{ij}_{\;\; k} K^k \\ [K^i , K^j] = \epsilon^{ij}_{\;\; k} L^k \end{array} It has the Casimirs C_1 =...

So which method works better for random number generation(in terms of flatter frequency spectrum): transistor breakdown or Zener noise? I want to know whether to use a Zener diode or a Transistor when building a white noise generator. And FTR I intend to use Germanium because of its higher...

When we run our Gensets individually, we are getting a Power Factor of 0.55 and 0.65 for our 250 KVA and 365 KVA Gensets respectively.3. An Electrical Engineer advised us to install a 90 KVAR Power Capacitor and an Automatic Power Factor Control Panel to get a PF of 0.85 for our existing load...

I realize there has been quite a few threads on this topic lately but I wanted to ask some questions that I have here. The following are statements from my lecture notes and I have write my questions after each statement. In the gauge sector of the electroweak theory, we can write down...

Hello! (Wave) We consider the irreducible polynomial $g=y^4+y+1 \in \mathbb{F}_2[y]$ and let $b$ be a root of $g$. I want to find all the roots of $g$ and also three generators of $\mathbb{F}_{16}^{\ast}$ as for the basis $\{1, b, b^2, b^3 \}$. Given that $b$ is a root of $g$ we can see that...

Looking for some guidance on the effect of long term paralleling of different generation sets in a private network as follows: 2 x 2.5MVA diesel generators stepped up to 11kV through DYn11 (in reverse to obtain a neutral while islanding) 3 x 1.0MVA Gas turbines stepped up to 11Kv through Yyn11...

Hi I am working on a wind turbine competition as far as the competition is going, designing my turbine and everything else, it's actually going quite well so far. But the one aspect which I have been scratching my head for a while has been the generators I have to use to make electrical energy...

Hi all, The trace of two SU(3) generators can be calculated by: ## T_{ij} T_{ji} = \frac{1}{2} ##, now how to calculate the trace of SU(3) generators: ## T_{il} T_{lk} T_{kj} T_{ji} ## ?

recently i began reading about triboelectric effect and triboelectric generators(and/or triboelectric nanogenerators) but i really need somebody to explain me this. those generators produce the amount of energy mentioned in this pic just from the contact and separation of the layers?. like if...

Homework Statement Hi, so during an experiment, I spun a magnet inside a coil of wire in order to induce an emf, and measure the input power and output power. One of the things I found was that the slower the magnet spun (ie the smaller the input voltage to the motor) the larger the induced...

I'm only familiar with a gas powered generator that I use at home when the power is out. But I'm designing a contraption that will be able to spin a generator with considerable torque. But the RPM will not be consistent. I can limit the upper end but it will often be below max RPM. Am I...

The generators of ##SO(n)## are pure imaginary antisymmetric ##n \times n## matrices. How can this fact be used to show that the dimension of ##SO(n)## is ##\frac{n(n-1)}{2}##? I know that an antisymmetric matrix has ##\frac{n(n-1)}{2}## degrees of freedom, but I can't take this idea any...

Hi, [FONT=PT Sans] I'm trying to figure which is more fuel efficient, turbine vs stroke generators. This honda stroke engine generator does 1000w for 3.8 hrs with 0.6 gallons of fuel or 2.3 liters, so the power per liter of fuel is 1,300 kW...

Homework Statement Consider a semi simple lie algebra. Show that if ##T_a## are the generators of a semi simple Lie algebra then ##\text{Tr}T_a=0##. 2. Homework Equations The commutation relations of the generators and the cyclic properties of the trace. The Attempt at a Solution $$[T_a...

Hello, This is not a homework question. I'm not a student. In fact I'm retired. The other day, I was passing by a wind turbine. I thought "wouldn't it be better to have hundreds of small generators with small wings connected together instead of one huge generator with huge wings?" But I did...

Hi, I was wondering how to find a minimal set of generators for the symmetric groups. Would it be difficult to fill-in the following table? ##\begin{array}{cl} S_3&=\big<(1\;2),(2\;3)\big> \\ S_4&=\big<(1\;2\;3\;4),(1\;2\;4\;3)\big>\\ \vdots\\ S_{500} \end{array} ## Is there a procedure to...

Given a simple DC generator with a single loop in the presence of a magnetic field such as the one below, typically, the analysis involves how each rectangular loop's terminal ends up on opposite sides of an armature housing each of the coils. The analysis is fairly straightforward to then...

I'm trying to find out what all the generators of the SU(5) group explicitly look like but I can't find them anywhere. I know what the first 12 look like: T^{1,2,3} = \begin{pmatrix} 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & \sigma^{1,2,3} & \\ 0 & 0 & 0 & &...

Hi, this is a rather mathematical question. The inner product between generators of a Lie algebra is commonly defined as \mathrm{Tr}[T^a T^b]=k \delta^{ab} . However, I don't understand why this trace is orthogonal, i.e. why the trace of a multiplication of two different generators is always zero.

Please help me, this is my last hope. I am an el. engineer student and i need GOOD books on electrical machinery. My proffesor is more a good repairman than a great scientist who could teach me about all the theoretical (matematical and physical) concepts which have led to modern design process...

Hi, I was wondering if anyone here could help me prove or disprove this empirical observation or explain why there seems to be a connection between automorphic generators described below and the automorphisms of these groups: Consider the p-group expansion: ##\mathbb{Z}_n^*\cong S_2\times...

I was wondering about the following Λ=I+iT T are the generators and Λ a continuous LT transformation, thus it is real. Therefore T needs to be imaginary. And we can find two sets one being the generators for SO(3) J_i and the other for boosts K_i, which are both imaginary. Now I am wondering...

Is there a method to find the minimum number of generators ##\big<a_1,a_2,\cdots,a_k\big>## needed to generate ##\mathbb{Z}_n^*## such that ##\mathop{\cap}\limits_{n=1}^k \big<a_n\big>=\{1\}## other than by just looking for them and checking orders and products of group elements? For example...

Please note, this is a question, and not a guide or instructional article. While learning about electrical-engineering, I realized that I did not really know what electricity was. So I decided to read into it, and what I found was quite confusing. A lot of articles I read conflicted with my...

I checked some common commercial high-quality lab function generators and they seem to provide frequency output upto 50 Mhz (not a big deal), but with resolution of 1 uHz ! That means, they can generate signal with 50000000 Hz and also with 50000000.000001 Hz ?? That would equate to time-period...

Based on what I have gathered so far, I don't see why a micro-scale generator wouldn't work, but then again I am a geographer with modest calculus skills. My biggest problem is not knowing how much I don't know, and I am hoping some kind and wise soul on PF can cure my ignorance. Let's say I...

Homework Statement In science class, we are supposed to explain how a generator works and functions. However, we have to incorporate coulomb's law in our explanation. Homework Equations F=kQ1Q2/r^2<-- coulomb's law The Attempt at a Solution How I understood it was that a generator consists of...

I'm doing some research into capturing a large amount of energy over a short period of time. The energy will be stored in supercapacitors but I'm finding it hard to find information on how a generator would cope with this. My project investigates the feasibility of using a regenerative braking...

Hi I am trying to get a simple grasp of the concept of a group generator and group representations. As ever wherever I look, I get very mathematical speak definitions such as: "A representation is a mapping that takes elements g in G into linear operators F that preserve the composition...

Hi just started working on a hobby project with making a wind mill. I got to the part were i have made the blades and the casing, for the wind mill. I was wondering what type of generator should i use for a 1,5m diameter blade. I really don't have anything special that i want the power to go to...

Homework Statement I hope you can see the picture clearly. Someone drew lines over it,so please try to ignore that. The problem here is to determine the current of ideal current source Ig, if following parameters are known: -E1=50V, E3=30V -R1=200Ω, R2=500Ω, R3=3kΩ, R4= 10 kΩ -C=0.7 μF...

Hello, http://www.powerequipmentdirect.com/Reliance-Controls-GPK30RV/p1893.html Reliance Controls Sidewinder™ Parallel Power RV Cables is an example of this. That one is universal. Honda makes same thing for their invertor generators, plug two 2,000 watt together to get 4,000 watts...

Hi, I want to connect multiple small dc generators in series to increase the power , it is possible ? What are the problems that i might face while doing it ?

Hi, I am trying to understand the derivation of the Lorentz generators but I am stuck. I am reading this paper at the moment: http://arxiv.org/pdf/1103.0156.pdf I don't understand the following step in equation 15 on page 3: \omega^{\alpha}_{\beta}=g^{\alpha\mu}\omega_{\mu\beta} I don't...

i believe that superconducting generators are now in use,We have hydropower plants in our country still using the conventional generators. My idea for my masters dessertation would to replace these generators with the superconducting ones, and hopefully get better efficiency. Would this make a...