Symmetric Definition and 539 Threads

Compute the order of each of the elements in the symmetric group ##S_4##. Is the best way to do this just to write out each element's cycle decomposition, or is there a more efficient way?

What is the condition for a spherically symmetric solution represents a black hole? ##ds^2=\exp(\nu(r))dt^2-\mu(r)^{-1}dr^2-r^2 d\Omega^2## it is enough that it is fulfilled that ##\nu## and ##\mu## are nulled in the same value of r??. There are other conditions?

Hello, I'm a new ANSYS user and could someone give me some help about this tutorial: https://confluence.cornell.edu/display/SIMULATION/ANSYS+-+Semi-monocoque+shell+-+Problem+Specification I'm trying to replicate it but can't get the same answear in the end. Any advice about what i could do...

Hello, My understanding is that, for a multi-particle system, the overall wavefunction HAS to be either symmetric or antisymmetric. A wavefunction that is neither symmetric or antisymmetric must be converted into one that is one of the two types depending on the type of particles. For example...

First, I'll give a little background so you guys know why I've arrived at this issue. I'm writing my BSc thesis right now, and the point of the thesis is to predict the bound states of two-nucleon systems (one bound, others not) by treating the problem as a simple QM two body problem. With a...

If space-time is isotropic does this imply it is spherically symmetric? why doesn't it need to be both isotropic and homogeneous?

Assume that ##P## is a polynomial over a commutative ring ##R##. Then there exists a ring ##\tilde R## extending ##R## where ##P## splits into linear factor (not necessarily uniquely). This theorem, whose proof is given below, is difficult to find in the literature (if someone know a source, it...

In one General Relativity paper, the author states the following (we can assume tensor in question are tensors in a vector space ##V##, i.e., they are elements of some tensor power of ##V##) To discuss general properties of tensor symmetries, we shall use the representation theory of the...

When we use Ampere's law, the most basic case that of an infinite current carrying wire is taken whose magnetic field is evaluated at a distance r from the wire. However there's nothing wrong in using the law for non symmetric scenarios. If this is the case how do you explain the B field at a...

Hello all, If A and B are both squared invertible matrices and A is also symmetric and: \[AB^{-1}AA^{T}=I\] Can I say that \[B=A^{3}\] ? In every iteration of the solution, I have multiplied both sides by a different matrix. At first by the inverse of A, then the inverse of the transpose...

This is a homework problem in a course in particle physics at Cornell University. Assume the Left Right Symmetric (LRS) model for leptons. The gauge group is GLR = SU(2)L×SU(2)R×U(1)X. The Standard Model group SU(2)L×U(1)Y has to be included in the LRS group. Namely, U(1)Y ⊂ SU(2)R×U(1)X. Find...

Any physical quantity ##K(t,x,x')## on a maximally symmetric spacetime only depends on the geodesic distance between the points ##x## and ##x'##. Why is this so? N.B.: This statement is different from the statement that The geodesic distance on any spacetime is invariant under an arbitrary...

Is calculating the Euler angles analitically possible? I am trying to obtain the angles to transform the body-fixed reference frame to the inertial reference frame. I can get them without problems with numerical methods. But I would to validate them analitically, if possible. I followed the...

Hi people! First of all, sorry for my poor english. I read in many places and I did the calculus and I agree that the field of a moving charge have this aspect: (Taked from Feynman´s Lectures on Physics chapter 26th.) But my problem is in that my intuition says me that it must be something...

Homework Statement Need to prove that the derivative of a rotation matrix is a skew symmetric matrix muktiplied by that rotation matrix. Specifically applying it on the Rodrigues’ formula.Homework EquationsThe Attempt at a Solution I have shown that the cubed of the skew symmetric matrix is...

Is the potential energy of a symmetric planar (x,y) charge distribution lower than any non symmetric distribution ? from the discussion on Gauss's law and symmetric charge distributions I would think so because the electric field could only be normal to the (x,y) plane in the symmetry case but...

I have a question regarding the FLRW metric used for cosmological analysis in S & G Relativity. Let the coordinates of a point in the space time be ##(t,r,\theta,\varphi)##. For constant ##t, \theta## and ##\varphi## we have the metric $$d \tau^2 = \frac{dr^2}{1 - kr^2}$$ My doubt is about this...

Isn't, if we have xRy and yRx then xRx will also make transitive? Because if I am right {(x,x),(y,y)} on set {x,y} is symmetric and transitive. Isn't the above similar to, if xRy and yRz then xRz is transitive relation? Thanks.

Homework Statement The lecture notes states that if ##T_{ij}=T_{ji}## (symmetric tensor) in frame S, then ##T'_{ij}=T'_{ji}## in frame S'. The proof is shown as $$T'_{ij}=l_{ip}l_{jq}T_{pq}=l_{iq}l_{jp}T_{qp}=l_{jp}l_{iq}T_{pq}=T'_{ji}$$ where relabeling of p<->q was used in the second...

Restricting to finite dimensional QP, suppose a system is in a state S1, an experiment is done, and state S2 is one of the eigenstates (assume all eigenvalues are distinct). The probability that the system transitions from S1 to S2 is p = Trace( S1*S2), using state operator notation. On the...

Hello, If a composite system is formed by particles that are all fermions, the overall wavefunction must be antisymmetric. If the particles are all bosons, the wavefunction must be symmetric. What if the particles are not all identical particles (all electrons) but are all fermions? Does the...

I have a few questions about interpretations that use retrocausality. I only know of 2. 1. TIQM - Transactional Interpretation of QM by John Cramer 1986 https://en.wikipedia.org/wiki/Transactional_interpretation 2. TSQM - Time Symmetric QM by Huw Price...

I know the seesaw mechanism is a model used to explain both neutrinos having mass and why their dirac mass/yukawa coupling is so much smaller than for the other fermions. The seesaw mechanism needs the right handed neutrino to exist. How does the seesaw mechanism for the vMSM differ from that...

Case 1) Two rockets (no Earth involved) have an exactly the same acceleration profile/flight-plan during round trip but they dispatched to opposite directions. At the start both rockets are docked to the same space station...both rockets have an identical engine operation plan during the round...

Homework Statement Hi guys, having problem trying to understand what this question wants. the question I am stuck with is 7.3. Homework EquationsThe Attempt at a Solution So for a) I converted to spherical co-ordinates: ##log(r^2sin^\theta cos^2\phi+r^2sin^2\theta sin^2\phi+r^2...

Hello. Im trying to learn more about different extensions of the standard model. Are the Left Right Symmetric Extension of the Standard model and the Neutrino Minimal Standard Model different extensions? I know both add 3 right handed neutrinos. Do these neutrinos differ in any way, also are...

Hello all, For each of the following statements, I need to say if it is true or not, to prove if it is true or to contradict if not. 1) \[A\bigtriangleup (B\cap C)=(A\bigtriangleup B)\cap (A\bigtriangleup C)\] 2) \[A\cup (B\bigtriangleup C)=(A\cup B)\bigtriangleup (A\cup C)\] Where...

Homework Statement Prove that if ##1 \leq d \leq n##, then ##S_n## contains elements of order d. Homework EquationsThe Attempt at a Solution Here is my idea. The order of the identity permutation is 1. Written in cycle notation, the order of (1,2) is 2, the order of (1,2,3) is 3, the order of...

Homework Statement Here's the question : 1x1+ 2x2 +0x3 + 0x4 = 1 2x1+ 9x2 +1x3 + 0x4 = 6 0x1+ 1x2 +9x3 + 4x4 = 2 0x1+ 0x2 +4x3 + 3x4 = 8 I' m asked to solve this question using Choelsky method ( We need the symmetric positive definite matrix when we are using this method) Homework...

The sum of the $k$ th power of n variables $\sum_{i=1}^{i=n} x_i^k$ is a symmetric polynomial, so it can be written as a sum of the elementary symmetric polynomials. I do know about the Newton's identities, but just with the algorithm of proving the symmetric function theorem, what should we do...

Homework Statement For the circled beam , we can see that for both cases , the load are loaded in the same way ... Why the M / EI diagram for the first case is different from the second case ? Why for the first case , it's symmetric loading ? For the second case , it's antisymmetric loading ...

Let U be a universal set, and let C be any subset of U. Let R be the relation on P(U) defined by A R B if $A \cap C = B \cap C$. Determine whether the relation is reflexive, symmetric, and/or transitive. Prove you answer.

I split off this question from the thread here: https://www.physicsforums.com/threads/error-in-landau-lifshitz-mechanics.901356/ In that thread, I was told that a symmetric matrix ##\mathbf{A}## with real positive definite eigenvalues ##\{\lambda_i\} \in \mathbb{R}^+## is always real. I feel...

Hi Guys, at the moment I got a bit confused about the notation in some QM textbooks. Some say the operators should be symmetric, some say they should be self-adjoint (or in many cases hermitian what maybe means symmetric or maybe self-adjoint). Which condition do we need for our observables...

I am currently brushing on my linear algebra skills when i read this For any Matrix A 1)A*At is symmetric , where At is A transpose ( sorry I tried using the super script option given in the editor and i couldn't figure it out ) 2)(A + At)/2 is symmetric Now my question is , why should it be...

$\tiny{s4.854.13.5.47}$ $\textsf{a. Find symmeteric equations for the line of intersection of planes}\\$ $\textsf{b. Find the angle between the planes}\\$ \begin{align}\displaystyle j+y-z&=2 \\ 3x-4y+5z &=6 \end{align} \begin{align}\displaystyle n_1&=\langle 1,1,-1\rangle\\ n_2&=\langle...

Let A,B,C be three sets . Prove Ax(BΔC)= (AxB) Δ (AxC) I tried to start with this : Let p be an arbitrary element of Ax(BΔC) then p=(x,y) such that x ∈ A and y ∈ (BΔC) x ∈ A and (y∈ B\C or y∈ C\B) (x ∈ A and y ∈ B\C) or (x ∈ A and y ∈ C\B) But I don't know how to continue or if I should even...

Homework Statement A grounded Z-axis symmetric closed conductor has a single point charge at the origin within it, inducing negative charge onto its inner surface. Given the induced charge density from the unit point charge, find the surface charge induced instead by a unit dipole at the...

Hi, I'm trying to work my way through some problems and am stuck on one for a symmetric infinite square well, of width 2a, so -a<x<+a. Since this is the symmetric case, the wavefunction should be a linear combination of the terms (a)-½ cos (nπx/2a) for odd n, (a)-½ sin (nπx/2a) for even n...

Are All symmetric matrices with real number entires Hermitian? What about the other way around-are all Hermitian matrices symmetric?

Homework Statement Same as title. Homework EquationsThe Attempt at a Solution A defining property of a diagonal matrix is that ##A_{ij} = A_{ji} ~~\forall i,j \le n##. This means that ##((A)^{t})_{ji} = A_{ji}##. Therefore, we know that ##A^t = A##. This shows that a diagonal matrix is...

If a force only depends on a radial distance "r" and it only has a radial component in the "er" then is it radially symmetric? This pertains to some homework problem I have, but part of the problem is that I'm not exactly sure what is meant by "radially symmetric". I assume its asking if the...

Hi there, I am reading something about quantum numbers, there the author introduce the quantum number by solving Schrodinger equation for Hydrogen atom. It gives me an example when the principal quantum number n=4, there are four different sub-level ##s, p, d, f##. It also depicts the sublevel...

Having read several introductory notes on Gauss's law, I have found it very frustrating that when the author comes to discussing the standard examples, in which one considers symmetric charge distributions, they do not explicitly discuss the symmetries of the situation, simply stating that, "by...

Homework Statement An electron (S=1/2) is free in a spherical symmetric harmonic potential: V(r)=\frac{1}{2}kr^2 a) Find energies and degeneracy of ground state and first excited state. b) For these states find the l^2 and l_z basis. c) How does these states split in a \vec{L} \cdot \vec{S}...

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...

A matrix is symmetric if it is equal to its own transpose, so to show $\displaystyle \begin{align*} C^T\,C \end{align*}$ is symmetric, we need to prove that $\displaystyle \begin{align*} \left( C^T\,C \right) ^T = C^T\,C \end{align*}$. $\displaystyle \begin{align*} \left( C^T\,C \right) ^T &=...

Homework Statement Hi there, I'm happy with the proof that any odd ordered matrix's determinant is equal to zero. However, I am failing to see how it can be done specifically for a 3x3 matrix using only row and column interchanging. Homework Equations I have attached the determinant as an...

Homework Statement Suppose the magnetic field line pattern is cylindrical symmetric. Explain with Stokes theorem that the field decreases like 1/r (with r the distance from the axis of the cylinder). Homework Equations Stokes theorem The Attempt at a Solution I was thinking of a circular loop...

Hi everybody. I was reading about the singlet and triplet states. It makes sense that we use an antisymmetric wavefunction for the singlet state, as we are talking about two fermions. But why are we using a symmetric wavefunction for the Sz = 0 triplet state? Doesn't this go against the...