Symmetry Definition and 907 Threads

Hey. Let's say you have an infinitely wide and long disk with a thickness h. Inside the disk, there is a constant charge density ρ0. Why would the electric field lines be perpendicular to the disk? Can somebody explain how symmetry and such generally affect electric field distribution of a...

If we have a metric connection with no other restrictions (torsion may be non-zero), do the connection coefficients {\Gamma^{\alpha}}_{\mu\nu} have any symmetries among the indeces? I'm thinking not. Or.. for a Levi-Civita connection, the only fixed symmetry condition is...

Hi! So I'm a bit confused: first off, does Fermi liquid theory have "order". I suppose it depends on how you define order. But in case it does, is it described by symmetry breaking? From what I read, I think it does have order which is not described by symmetry breaking. But then I have...

Homework Statement State whether the following are true or false. If false, give a counter-example: 1. ≽ is not symmetric \Rightarrow ≽ is not asymmetric 2. ≽ is not symmetric \Rightarrow ≽ is not antisymmetric 3. ≽ is not antisymmetric \Rightarrow ≽ is not asymmetric Homework...

\oint E\cdot dA=|E|\int_{0}^{2\pi}\int_{0}^{\pi}(1+1/2sin6\theta\sin5\phi)^2sin\phi d\phi d\theta =|E|\int_{0}^{2\pi}(\frac{25}{99}sin^2(6\theta)+2) d\theta =|E|\frac{421\pi}{99}= \frac{\rho_{q}}{\varepsilon o}\int_{0}^{2\pi }\int_{0}^{\pi }\int_{0}^{(1+\frac{1}{2}sin6\theta sin5\phi...

Both Rho^0 and Pi^0 are bosons so require an overall symmetric wavefn. However, they are in different spin states: the Pi is in the anti-symmetric S=0 state and the Rho is in one of the symmetric S=1 states. Which other part of the overall wavefn (color, flavor, spatial) differs between the two...

Homework Statement Find the point in respect to these ellipses are symmetrical x2 + 3y2 - 2x -2 = 0 x2 + 3y2 +6x + 12y +18 = 0 Homework Equations x = 2a - x' y = 2b - y' The Attempt at a Solution I have applied the equations of symmetry to the first equation then I've equaled the...

Hello everyone, I read in Edmond's 'Angular momentum in Quantum Mechanics' that the symmetry group of the 9j symbol is isomorphic to the group S_3 \times S_3 \times S_2. Why is this? Can anyone shed some light on this?

Hi, I'm an undergraduate taking the basic quantum classes and on my own, I'm trying to wrap my mind around how symmetry and group theory applies in Q.M. and theoretical physics in general; it's coming along slowly but surely! Can someone please explain why the ammonia molecule is said to...

Is there a reason why we have to expand a field ψ about the true vacuum |Ω>? Can't we just do field theory about ψ=0 instead of about ψ=<Ω|ψ|Ω>? Also, I'm a bit confused about other fields. For the E&M potential, under the true vacuum, wouldn't we need to expand about A=<Ω|A|Ω> instead of...

Spontaneous symmetry breaking: the vacuum be infinitly degenerate? In classical field theories, it is with no difficulty to imagine a system to have a continuum of ground states, but how can this be in the quantum case? Suppose a continuous symmetry with charge Q is spontaneously broken, that...

As we know, spin is an internal symmetry. but it seems a bit different from other internal symmetry, e.g. electrical charge, color, flavor... because it can be coupled with orbital angular momentum and in some aspects be linked to space-time. further more, we can classify all the particles into...

Hi everyone, I read in 'Angular momentum in Quantum Mechanics' by A.R Edmonds that the symmetry group of the 6j symbol is isomorphic to the symmetry group of a regular tetahedron. Is there an easy way of seeing this? I've tried working out what the symmetry relations of the 6j symbol do...

I understand that one is able to derive the inhomogenuous pair of Maxwell's equations from varying the field strength tensor Lagrangian. Now implying the U(1) gauge invariance, how is one led to the Maxwell's equations?

How should I think about symmetry currents?... in particular, when there are no fields to "carry the charge", eg in a pure Maxwell theory or, maybe, in a CFT of free scalars? Perhaps it would help if someone elucidated the connection between the "charge" in Noether's theorem and the "charge" in...

I'm currently attempting to explain the concept of Gauge Symmetry to a friend. Copied and pasted pretty much directly from MathIM, (And the same applies for any other potential field, such as gravitational potential.) Would this be correct? I've tried explaining Gauge Symmetry multiple...

I'm not sure what people meant about this. Heisenberg hamiltonian is ##O(3)## invariant. H=-J\sum_{\langle i,j \rangle} \vec{S}_i \cdot \vec{S}_j ##\langle \rangle## denotes nearest neighbors. It has ##O(3)## symmetry. If I understand well ground state is infinitely degenerate. But system...

I've tried looking all over, but haven't been able to find explanations. I was wondering if anyone could provide me links to learn more about these- what's in the picture. Or if you can explain. I have already turned this work in so I'm not looking for the answers, I want explanations. I know...

Author: Matthew B. Robinson Title: Symmetry and the Standard Model Amazon Link: https://www.amazon.com/dp/1441982663/?tag=pfamazon01-20 Prerequisities: Contents:

It seems the uncertainty principle, the commutator between operators, and the symmetry of the action integral are all related. And I wonder how universal this is. For example, the action integral is invariant with respect to time, and this leads to conserved quantity of energy. This means...

Here is a quote from Vanhees 71 in another thread on Lagrangians. I reposted here as a new thread because I fear going off-topic and redirecting a thread. In any case, in my study of Lagrangians and Hamiltonians, everywhere I go for tutelage it seems as though everyone is maniacally focused...

I'm studying chiral symmetry in QCD. I understand that in order for a spontaneous symmetry breaking to occur, there must be some state with a vacuum expectation value different from zero. My question is: can someone prove that is the chiral symmetry is an exact symmetry of the QCD then...

Hi Pf I would like to know if the standard model without symmetry breaking can describe the universe after the big bang before the moment when EW symmetry breaking occured. Had we v = c for all particles? were electrons electrically charged? were there photons or B ? Z0 were not born...

This is my first post, so hello everybody. I don't have university background and english is not my native language, so please forgive me if what I'm writing is hard to understand sometimes. I'll do my best to be clear. I've always loved physics in general, but recently came to conclusion that...

Hi all, I'm taking graduate level QM I and trying to wrap my head around the notion of gauge symmetry. For some reason I've struggled with this concept more than others. I don't really have a specific question; I'm more looking to see if someone has a succinct explanation of the relevant...

People seem to be seriously looking for "Lorentz violating" neutrino oscillations - meaning direct violation of special relativity. What is a short name for the symmetry that distinguishes general relativity from special (the symmetry between acceleration and gravity)?

what is the relationship between unstable equilibria and spontaneous symmetry breaking? Would this qualify as an example of spontaneous symmetry breaking? Take a (perfectly round and unlabeled) pencil standing upright on its eraser so there is a U(1) symmetry on its original position...

Hello, it is known that the symmetry groups on the 2d Euclidean plane are given by the point-groups (n-fold and dihedral symmetries) and the wallpaper groups. However we can create more symmetries on the plane than just those. For example we can stereographically project the 2d plane onto...

1) Since Wigner it is well known that for massless particles of spin s the physical states are labelled by helicity h = ±s; other states are absent. So e.g. for photons the physical states are labelled by |kμ, h> with kμkμ = 0 and h = ±1 and we have two d.o.f. 2) For gauge theories with...

Homework Statement Solve the energy eigenvalue problem for the finite square well without using the symmetry assumption and show that the energy eigenstates must be either even or odd. Homework Equations The finite well goes-a to a and has a potential V0 outside the box and a potential...

Hi, I have included a sketch drawing of a graph that I am not entiry sure is correct for what I am trying to do? I have found the exact values of Sin, Cos and Tan of some given values in radians, and am asked to use the symmetry of graphs of sin, cos and tan to find the exact values of some...

Why the curve E(k) in the first brillouin zoon is symmetric? For example why in the first BZ of a one-dimensional lattice we have E(k)=E(-k)?

As we know, a quadratic function can be expressed in a form of complete square by a method of completing the square. This form enables us to prove that a quadratic equation is symmetric about its stationary point. But for the cubic function, is there a similar way to prove that the cubic curve...

Homework Statement When solving, say, the double delta function potential well, we fix constants using continuity. If the potential is symmetrical about the origin, can we conclude that the wave function, i.e. the solution, will also be symmetric? I found this way made the calculations much...

hi everyone, I have been trying to understand gauge theory. I am familiar with the Noether's theorem applied in the context of simpler textbook cases like poincare invariant Lagrangians. This is my question: Are there Noether currents corresponding to the local gauge symmetries too and would...

I have a problem; I am trying to show the spherical symmetry in a hydrogen atom, for a sum over the l=1 shell i.e the sum over the quadratics over three angular wave equations in l=1, |Y10|^2 + |Y11|^2 + |Y1-1.|^2 . This should equal up to a constant or a zero to yield no angular dependence...

The problem states: From the field with a radial cylindrical component only given by the following equations: E(r)= (ρ0*r3)/(4 * ε0*a2) for r<=a E(r)= (ρ0*a2)/(4*ε0*r2) for r > a obtain the corresponding charge distribution in free space in which the equation is: ρ(r) = ρ0*(r2/a2)...

Hi all, Can anyone help explaining how during a phase transition, crystal will be more symmetric at high temperature

In my abstract algebra course we learned recently of the symmetries D4. Regarding flips/reflections, of which there are 4, it seems for the 2D object that is a square, you would have to "fold it through the 3rd dimension" to obtain a flip/reflection. Couldn't you just invert the square by...

Homework Statement R is simmetric iff R=R^{-1} Homework Equations ( \forall x \forall y ((x,y) \in R \rightarrow (y,x) \in R)) \leftrightarrow R=R^{-1}The Attempt at a Solution My problem is with my formulation in [2.] of the statement I have to prove. Is that formulation right or the...

Hi, I was curious if specific symmetries (or lack thereof) in crystal structure are necessary for the formation of topological insulators. Specifically, do we require that inversion symmetry (or inversion asymmetry) be present in the lattice in order to form the TI state? Thanks, Goalie33

In deriving the Schwarzschild metric, the first assumption is that the transformation of r^2 (dθ^2 + sin^2 θ dψ) remains unchanged due to the spherical symmetry. What does that mean exactly? What is the logic behind it? Please apply any math involved in algebraic form. Thanks.

The Higgs mechanism is often explained (both here at PF and in many physics sites including wikipedia) as an example of spontaneous symmetry breaking, but the Nobel winner physicist 't Hooft says in his "for laymen" book about particle physics, "In search of the ultimate building blocks", that...

I am quite new to the branch of quantum physics and therefore am quite inexperienced with certain terminology and definitions. I have looked these topics up time and time again, but still cannot get a grasp on what they mean. Could someone please describe to me what the concept of "symmetry" in...

How can I calculate degrees of freedom of a rank (o,3) tensor, Aabc, that is mixed symmetry and antisymmetric in the first 2 indices? By mixed symmetry I mean this: Aabc+Acab+Abca=0.

I'm wondering how the spin of a particle, whether a particle is a fermion or a boson... how does this relate to the symmetry of a particle, U(1) or SU(2) or SU(3)? I'm trying to understand SUSY in relation to the other internal symmetries? Is there spin 1/2 and spin 1 particles associated with...

I have read 2 arguments that a gauge symmetry cannot be spontaneously broken. 1. Wen's textbook says a gauge symmetry is a by definition a "do nothing" transformation, so it cannot be broken. 2. Elitzur's theorem, eg.http://arxiv.org/abs/hep-ph/9810302v1 The first argument seems sound...

should the current still be conserved? since it stills commutes with the Hamiltonian and symmetry is just hidden. but I just read that the linear-σ model was invented to demonstrate how the axial current could be partially conserved? Thanks!

Homework Statement Show that ## \displaystyle B_1(u,v)=\int_a^b (p(x) u \cdot v + q(x) \frac{du}{dx} \cdot v)dx## is a bilinear functional and is NOT symmetric Homework Statement Bilinear relation ##B(\alpha u_1+\beta u_2,v)=\alpha B(u_1,v) +\beta B(u_2,v)## (1) ##B(u, \alpha v_1+...

Homework Statement In each case describe the eigenvalues of the linear operator and a base in R^3 that consist of eigenvectors of the given linear operator. Write the matrix of the operator with respect to the given base. The Orthogonal Projection on the plane 2x + y = 0 and...