Group Definition and 1000 Threads

Hi, My question is short and very simple: Is the loss of a leaving group primarily a random event? What is the actual mechanism that initiates that a specific leaving group.. leaves? Thanks in advance :)

Hi, I'm studying transformer and am a bit confused. Say for vector group: Dy11, I guess it's the line voltage of LV leads the Line voltage of HV by 30 degrees. Book says phase angle. The phase angle is line voltage right, since the phase voltage of HV and LV will always be in phase with each...

Homework Statement Homework Equations Probability = number of favourable events / all possible events The Attempt at a Solution Group X Y Total people Indians 10 8 18 (total 18 Indians in both group) Total People 25 20 45 (total 45 people in both...

So, we know that if g is a Lie algebra, we can take the cartan subalgebra h ⊂ g and diagonalize the adjoint representation of h, ad(h). This generates the Cartan-Weyl basis for g. Now, let G be the Lie group with Lie algebra g. Is there a way to diagonalize the adjoint representation Ad(T) of...

The Galilean transformations are simple. x'=x-vt y'=y z'=z t'=t. Then why is there so much jargon and complication involved in proving that Galilean transformations satisfy the four group properties (Closure, Associative, Identity, Inverse)? Why talk of 10 generators? Why talk of rotation as...

Hi guys for my group project this year my team needs to apply two computational methods to a real system. The two methods are transfer matrix and finite difference and we have chosen to apply them to a resonant tunnelling diode. Can any of you guys recommend any resources which may be useful to...

Homework Statement For the following sets, with the given binary operation, determine whether or not it forms a group, by checking the group axioms. Homework Equations (R,◦), where x◦y=2xy+1 (R*,◦), where x◦y=πxy and R* = R - {0} The Attempt at a Solution For question 1, I found a G2...

How can I collapse macroscopic absorption cross-section of 4 groups into two ? Assuming that the first two groups are fast groups and the other twos are thermal . I am suffering with the following : 1- Do I have to assume that the groups are directly coupled ? 2-Does what apply on the two...

Dear All, I am looking for tools and even online platform able to host a study group in physics. My goal would be the creation of a general relativity group. It will be a study group for graduated in physics (then not for amateurs) that for the simple pleasure of science would like to...

Homework Statement I know that for a dispersive wave packet, the group velocity equals the phase velocity, which is given by v=w/k. But how do I calculate the group velocity of a non-dispersive wave packet? I'm supposed to be giving an example with any functional form. Homework Equations...

I understand that in group theory, a group consists of a set and a binary operation for the elements in the set, and of course all the group axioms. But if we move away from set theory into category theory, is a group defined on a category?

Hello! I am not sure I understand why ##SO(2)## is the isotropy group for ##x \in R^3##. If I understood it well, the isotropy group contains all the elements such that ##gx=x##. But this is not the case for ##SO(2)## as this group represents rotations in a plane, so unless x is the axis of...

Homework Statement No problem statement. Homework EquationsThe Attempt at a Solution Suppose that ##R## is a ring and ##f : R \to R## is an additive group homomorphism. Is the following a way of extending ##f## to a ring homomorphism? Let ##\varphi : R \to R## and define ##\varphi(r) =...

Hi, so I have just a small question about cyclic groups. Say I am trying to show that a group is cyclic. If I find that there is more than one element in that group that generates the whole group, is that fine? Essentially what I am asking is that can a cyclic group have more than one generator...

Let ##M## and ##N## be connected n-manifolds, n>2. Prove that the fundamental group of ##M#N## (the connected sum of ##M## and ##N##) is isomorphic to ##\pi(M)* \pi(N)## (the free group of the fundamental groups of ##M## and ##N##) This is not for homework, I was hoping to get some insight...

This space is homotopy equivalent to the complement of the three coordinate axes in ##R^3##. This is in the chapter about the Seifert-Van Kampen Theorem, so I'm expecting to invoke that theorem. The thing is, how should we choose our open sets such that the intersection is path connected and...

"Quantity in a group" If you have 6 apples and you subtract 4, then you have 2 apples left "in the group". "Quantity in an Indexed group" I'm a computer programmer - I manipulate arrays of data (a.k.a. matrix) In a math formula format: x1, x2, x3... xn (as a side note - in a computer format...

Well, for starters, ##\pi(T)##, the fundamental group of the torus, is ##\pi(S^1)x\pi(S^1)=## which is in turn isomorphic to the direct product of two infinite cyclic groups. Before I tackle the case of n connect tori with one point removed, I'm trying to just understand a torus with a point...

edit: fixed typo's andrewkirk pointed out, oops I can cover the projective plane with 2 open sets U,V where each of these neighborhood contains the point that is missing, and the intersection of these two neighborhoods will be simply connected. I was then hoping to invoke the Seifert-Van-Kampen...

After reading some books on Group Theory, I have two questions on group representations (Using matrix representation) with the second related to the first one: 1 - Can we always find a diagonal generator of a group? I mean, suppose we find a set of generators for a group. Is it always possible...

Why is it that all group 15 element's trihalides except Nitrogen on hydrolysis gives an acid while Nitrogen trichloride give ammonia which is a base on hydrolysis?

In Quantum Mechanics Concepts and Applications by Zettili the following formulas are used for phase and group velocities. {\rm{ }}{v_{ph}} = \frac{w}{k} = \frac{{E\left( p \right)}}{{p}}{\rm{ }}\\ {\rm{ }}{v_g} = \frac{{dw}}{{dk}}{\rm{ = }}\frac{{dE\left( p \right)}}{{dp}}{\rm{ }} In...

They seem the same to me. So I can have many paths between a and b that are continuously deformable into each other while keeping the endpoints fixed. We say these function form a equivalence class [f]. This should be regardless if the endpoints are the same or not. The fundamental group seems...

Homework Statement The n-dimentional Euclidean group ## E^{n} ## is made of an n-dimentional translation ## a: x \mapsto x+a ## (##x,a \in \mathbb{R}^{n}## ) and a ## O(n) ## rotation ## R: x \mapsto Rx ##, ##R \in O(n) ##. A general element ## (R,a) ## of ## E^{n} ## acts on ## x ## by ##...

This is not homework, it's self study material. I would rather post it here than where questions are usually posted (homework help section) because i think it's much more likely to be seen here by somebody with knowledge on the subject. Let G be a topological group acting continuously on a...

Hey there! I just want to ask if there are any books you would like to recommend that helps in studying high energy physics and HEP data analysis? Also can you recommend a good book for group theory and symmetry? I would be glad if you have links to free downloadable books. Thanks in advance!

Homework Statement The maximum no of spectral lines for a single atom during it's electron's transition is given by [∆n(∆n+1)]/2 . But I don't seem to arrive at the answer when a group of atoms are present . The question was - What is the maximum number of spectral lines possible for Balmer...

Hello! I need to show that Lorentz Group is non compact, but has 4 connected components. The way I was thinking to do it is to write the relation between the elements of the 4x4 matrices and based on that, associated it with a known topological space, based on the determinant and the value of...

Hello, let be ##G## a connected Lie group. I suppose##Ad(G) \subset Gl(T_{e}G)## is compact and the center ## Z(G)## of ##G## is discret (just to remember, forall ##g \in G##, ##Ad(g) = T_{e}i_{g}## with ##i_{g} : x \rightarrow gxg^{-1}##.). I saw without any proof that in those hypothesis...

Just out of curiosity, what would a proof of ##a^m a^n = a^{m+n}## amount to? Of course obviously if you have n of one thing and m of another you get m+n, but I am wondering if this is rigorous enough, or if you need induction.

I have a dilemma. I'm beginning a fellowship next week, and I have 3 Ph.D. offers for when it ends. I've worked in each group, and would have no issue continuing in any of them. I respect each advisor equally for different reasons. The main problem is each group requires a slightly different...

So here is a problem (more of a dilemma) I encountered in my mandatory physics class [(high school level) i say mandatory since I take an other optional calculus based one], many students are often mislead for example in kinematics the equations are very clunkily derived and when you finish...

Hello. I will be attending a course on Group theory and the book that the professor suggests is Georgi's Lie Algebras in Particle Physics. As I liked Zee's book on General Relativity, I thought that it would be a blast to also use his Group theory textbook for the course. Problem is that I don't...

Homework Statement Let p: E-->B be a covering map, let p(e_0)=b_0 and let E be path connected. Show that there is a bijection between the collection of right cosets of p*F(E,e_0) in F(B,b_0) (where p* is the homomorphism of fundamental groups induced by p and F(E,e_0),F(B,b_0) are the...

What is more cool... to be a member of the Poincare Group or Lorentz Group? What name would you choose for a school science team and why?

I was listening to this lecture: and in it, sometime around the 30:00 to 40:00 minute mark, he implies that the torus' sturcture built up from the orbits of the group under addition on the real plane is the same idea as the cylinder's structure being built up from the orbits of the group under...

Homework Statement What are the subgroups of Z2 x Z2 x Z2? Homework Equations Hint: There are 16 subgroups. The Attempt at a Solution So far I only manage to get 15 and I am not even sure if these are correct. My answer: $$(0,0,0) , (Z_2,Z_2,Z_2), (1,1,1), (0,0,1), (0,1,0), (1,0,0), (0,1,1)...

AR2665 ... largest spot group for some time Canon 6D, 800mm, f11, 125th, ISO100 ( the 800mm is a 100-400mm L lens with a x2 teleconverter) With my eyesight going downhill, I have really been struggling of late to be able to get sharp manual focus Dave

Hello! :smile: On page 51 where he want to invert $$\Lambda^{\mu}_{\nu} = \tfrac{1}{2} \text{tr}( \bar{\sigma}^{\mu}A \sigma_{\nu} A^{\dagger})$$ the person says we may use $$\sigma_{\nu} A^{\dagger} \bar{\sigma}^{\nu} = 2 \text{tr}(A^{\dagger})I.$$ to do that ... how do you prove this formula...

Homework Statement Let G be a group. Let H and K be subgroups of G. Prove that if H ##\subseteq## K, then H is a subgroup of K. Homework EquationsThe Attempt at a Solution H is a subset of K and H,K are groups. if x,y, xy ##\epsilon## H, then x,y, xy ##\epsilon## K. So H is closed under...

Hello! I understand that the vector formed of the scalar and vector potential in classical EM behaves like a 4-vector (##A^\nu=\Lambda^\nu_\mu A^\mu##). Does this means that the if we make a vector with the 3 components of B field and 3 of E field, so a 6 components vector V, will it transform...

Hi! Is there a way to end up with the algebra i) quickly ii) starting from a group, as how one gets the CR's from the Lorentz group composition rules, as on http://www.krassnigg.org/web/physics/wp-content/uploads/hoqft12-skriptum.pdf. The other relations are quite complicated and the...

Context The following is from the book "Ideas and methods in supersymmetry and supergravity" by I.L. Buchbinder and S.M Kuzenko, pg 56-60. It is about realizing the irreducible massive representations of the Poincare group as spin tensor fields which transform under certain representations of...

Homework Statement A group of particles is traveling in a magnetic field of unknown magnitude and direction. You observe that a proton moving at 1.50 km/s in the +x-direction experiences a force of 2.25 x ##10^{-16}##N in the +y-direction, and an electron moving at 4.75 km/s in the -z-direction...

Homework Statement Prove in any finite group G, the number of elements not equal to their own inverse is an even number. Homework Equations if ab = ba = e, then a = b-1 and b = a-1 The Attempt at a Solution Let S, A, B, be subsets of G where S = A + B. Let a ∈ A s.t. there exists a unique b...

Homework Statement Assume that ##G## is an abelian transitive subgroup of ##S_A## that acts on the set ##A##. Show that ##\sigma(a) \neq a## for all ##\sigma \in G - \{1\}## and all ##a \in A##. Deduce that ##|G| = |A|##. Homework Equations A group is said to act transitively on a set if...

Hello! I read that the for the lie algebra of the Lorentz group we can parametrize the generators as an antisymmetric tensor ##J^{\mu \nu}## and the parameters as an another antisymmetric tensor ##\omega_{\mu \nu}## and a general transformation would be ##\Lambda = exp(-\frac{i}{2} \omega_{\mu...

Homework Statement Let ##\{N_i ~|~ i \in I\}## be family of normal subgroups of G such that (i) ##G = \left\langle \bigcup_{i \in I} N_i \right\rangle## (ii) for each ##k \in I##, ##N_k \cap \left\langle \bigcup_{i \neq k} N_i \right\rangle = \{e\}## Then ##G \simeq \prod_{i \in I}^w...

Homework Statement Every infinite cyclic group has non-trivial proper subgroups Homework EquationsThe Attempt at a Solution I know that if we have a finite cyclic group, it only has non-trivial proper subgroups if the order of the group is not prime. But I'm not sure how to make this argument...

Hello! I read that for a boost, for which we have a matrix ##\Lambda## we must satisfy ##\Lambda_\alpha^\mu g_{\mu \nu} \Lambda_\eta^\nu = g_{\alpha \beta}##. I am not sure I understand this. If we have a boost along the x-axis the ##\Lambda_0^0## component is ##\gamma##, but ##\gamma^2 \neq 1 =...