Symmetry (from Greek συμμετρία symmetria "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definition, and is usually used to refer to an object that is invariant under some transformations; including translation, reflection, rotation or scaling. Although these two meanings of "symmetry" can sometimes be told apart, they are intricately related, and hence are discussed together in this article.
Mathematical symmetry may be observed with respect to the passage of time; as a spatial relationship; through geometric transformations; through other kinds of functional transformations; and as an aspect of abstract objects, including theoretic models, language, and music.This article describes symmetry from three perspectives: in mathematics, including geometry, the most familiar type of symmetry for many people; in science and nature; and in the arts, covering architecture, art and music.
The opposite of symmetry is asymmetry, which refers to the absence or a violation of symmetry.
Firstly I have found the eigenstates for both the original well and the new well as the following
$$\psi_{n,\frac{L}{2}} = \begin{cases} \sqrt{\frac{2}{L}} \cos{\frac{n \pi x}{L}} \; \; \; \; \; n \text{ odd} \\ \sqrt{\frac{2}{L}} \sin{\frac{n \pi x}{L}} \; \; \; \; \; n \text{ even}...
Hello everyone,
I hope somebody can assist me with this. I am working on a calculation for a planet gear with 4 sun wheels and 1 planet wheel. The aim is to determine the forces on the sun wheel. Initially, I have 3 equations and 4 unknowns. By making an assumption based on symmetry, I now have...
Hi All,
Is it true that in order to form the ##H_2## molecule from two hydrogen atoms one needs a third body so that the energy difference between initial and final states can be released?
Best Regards,
DaTario
Hello everyone,
I've been studying Morin's book and the case for time dilation makes sense, a clock in the rest frame of the moving body counts to ##T_A##, and a clock in the lab frame counts to ##T_B## and we find ##T_B = {\gamma}{T_A}##
What I might be failing to do is understand what the...
Hello everyone,
Suppose there is an airplane that is taking off from an airport but before it takes off it synchronizes it's clock to zero with the clock at the airport.
In the rest frame of the plane the airport is moving, so you could argue ##T_{plane} = \gamma*T_{airport}##
In the rest...
A homework thread, https://www.physicsforums.com/threads/point-charge-with-very-thin-metal-sheet-along-a-spherical-surface.1057702/, references https://arxiv.org/pdf/1007.2175.pdf.
There is an uncharged conductor and a point charge. In the paper referenced, ##\bar\phi_y(x)## is defined as the...
Hi, as we know SM is symmetric under SU(3) X SU(2) X U(1) , But my question is , how can we check the invariance of terms in Lagrangian under these symmetries - thanks
Why are the coordinates seemingly used when the symmetry is around ##z## axis? Any particular reason why not ##x## or ##y##. In transforming from Cartesian to cylindrical form; I can see that ##z## is not considered when determining ##r##.
Can we also use ##x## and ##z## assuming that the...
I have been learning emma noether’s theorem where every symmetry results in conservstion law of something, sometimes momentum, sometimes angular momentum, sometimes energy or sometimes some kind of quantity.
Every explanation that I have listened to or learned from talks about homogeneity of...
Emmy Nöther proved that mathematically, if a certain quantity is conserved, there must be a corresponding symmetry somewhere. Momentum conservation stems from spatial symmetry, charge conservation stems from complex phase symmetry at the quantum level and energy conservation stems from time...
I found some interesting discussions in this site (e.g: https://www.physicsforums.com/threads/smolin-lessons-from-einsteins-discovery.849464/; https://www.physicsforums.com/threads/relatismo-to-the-max.83885/) which are related to Lee Smolin's ideas that laws are not immutable and can therefore...
According to Sabine Hossenfelder in the extremely early Universe nothing had mass because the electroweak symmetry was not yet broken so there was no Higgs field. Am I correct in thinking this is not controversial?
https://youtu.be/9-jIplX6Wjw?t=638
In the picture below we have two identical orbitals A and B and the system has left-right symmetry. I use the notation ##|n_{A \uparrow}, n_{A \downarrow},n_{B \uparrow},n_{B \downarrow}>## which for example ##n_{A \uparrow}## indicates the number of spin-up electrons in the orbital A. I would...
Hello everyone,
I'm reading "Special Relativity For the Enthusiastic Beginner" (by David Morin) and so far I really like the book, but I have a little bit of a hiccup in understanding terminology regarding stated symmetries or the lack there of in reference to the Galilean transformation when...
I have tried to follow "Symmetry, Uniqueness, and the Coulomb Law of Force" by Shaw (1965) in both asking and solving this question, but to no avail. Some of the mathematical arguments there are a bit too quick for me but, it suffices to say, the paper tries to make the "by symmetry" arguments...
In Problem 3.7, Ballentine says:
The unitary operator ##U(v) = exp(iv·G)## describes the instantaneous ##(t = 0)## effect of a transformation to a frame of reference moving at the velocity ##v## with respect to the original reference frame. Its effects on the velocity and position operators are...
So on this page https://www.feynmanlectures.caltech.edu/I_11.html under heading 11-2 Translations first he tries to proof that there is no origin in space. Joe writes newtons laws after measuring quantities from some origin.
$$m(d^2x/dt^2)=F_x$$
$$m(d^2y/dt^2)=F_y$$
$$m(d^2z/dt^2)=F_z$$
We need...
For this problem,
If we assume that x = 0 is where the spring connects to the wall, then the rest position of the mass-spring-electric field position is x = EQ/k and the max position is x = 2EQ/k. Is there a reason for the symmetry between the rest position and max position? (The symmetry...
Suppose that we have a system including two single (and identical) orbitals as shown in the attached image. Then, consider the states that we have two different spins on the two orbitals. It seems that because of the left right symmetry of the system the special part of teh wave function can not...
Say we have a copy of our world, but with the "parity" and "time" reversed. (For example, the mirror world from the novel "Alice Through the Looking Glass".)
If the "charge" is also reversed, then due to the CPT symmetry, the same physics law would apply to the mirror world, right?
If we...
"Spherical symmetry requires that the line element does not vary when##\theta## and##\phi## are varied,so that ##\theta##and ##\phi##only occur in the line element in the form(##d\theta^2+\sin^{2}\theta d\phi^2)##"
I wonder why:
"the line element does not vary when##\theta## and##\phi## are...
Hey all,
I just wanted to double check my understanding of (26) in the following notes: https://arxiv.org/pdf/1512.08882.pdf.
Is the reason that ##(U_{T}\cdot K) \cdot (U_{C}\cdot K) = U_{T}\cdot U_{C}^{*}## because ##K## is a unitary operators and thus ##(K\cdot U_{C}\cdot K) = U_{C}^{*}## as...
Pions are particles with spin 0 and they form an isospin triplet: π+, π0, π− (with the superscript indicating the electric charge). Their intrinsic parity is −1 and they are pseudoscalar mesons. In nature we also find other kind of mesons, like the ρ mesons, ρ+, ρ0 and ρ−. As pions, they also...
Hello,
I would like to understand a relation of this article by Volkov (eq. 4).
Let's define the Green function $$ G^{ij}_{ab} (1,2) = -i \langle T_c \Psi_a (1_i) \Psi_b (2_j) \rangle $$ where ##a,b = (1,2)## are the spin indices and ##i,j = (1,2) ## are the indices for the Keldysh contour ...
We usually plot electronic bands with the help of high symmetry points of the irreducible zone of primitive cell of particular material. But if we want to plot bands with conventional cell, we have to map the high symmetry points from primitive cell to conventional cell.
so how can we map the...
There are several "bumblebee" models [1], [2] where Lorentz invariance is violated usually resulting from a local vector or tensor field acquiring a nonzero vacuum expectation value
We do not know whether we are in the true vacuum state or in a "false"/metastable vacuum state that could decay...
In this paper [1] which considers the possibility that the Lorentz symmetry could be broken, at page 4-5 the author says:
"We now introduce a Higgs sector into the Lagrangian density such that the gravitational vacuum symmetry, which we set equal to the Lagrangian symmetry at low temperatures...
What does mean spinel structure has F d3m space group? I know F is for face centred cubic, 3 is 3-fold symmetry and m is mirror, but I don't know what means "d"?
Hello,
I was wondering if it was possible to define good quantum numbers in solid state physics or chemistry when systems posses a discrete cylindrical symmetry Cnv. I know that in terms of angular momentum, L and L_z will be good quantum numbers for spherical symmetry, then only L_z is a good...
I am a beginner in GR, working my through Gravitation by the above authors. If there is a better place to ask this question, please let me know.
I understand (from section 5.7) that the stress-energy tensor is symmetric, and from equation 5.23 (p. 141), it is explicitly symmetric. But...
From Stokes we know that ##\iint_{\textbf{S}}^{}curl \textbf{F}\cdot d\textbf{S}=\int_{C}^{}\textbf{F}\cdot d\textbf{r}##.
Now, we can calculate the surface integral of the curl of F by calculating the line integral of F over the curve C.
The latter ends up being 0(I calculated it parametrizing...
Ok for (1) I would say that the order of rotational symmetry is ##8##. Would that be correct? What about ##4##?
For (2) The number of lines of symmetry is ##4##.
And if one would say infinity for both (1) and (2) would that be correct?And if you consider a kite. Would the order of...
Gauge symmetry is highly confusing, partly because many definitions differ in the literature. Strictly speaking gauge symmetry should be called gauge redundancy since you are mapping multiple representations to the same physical state.
What is your favourite definition of what "large" gauge...
Generally speaking, if the Hamiltonian has a specific symmetry defined by an operator M, that is ##[H,M]=0##, when I apply such symmetry operator to a Bloch state I would expect the state to be left unchanged up to a phase:
$$M\ket{ψ_{\mathbf k}}=e^{iϕ(\mathbf k)}\ket{ψ_{\mathbf k}}$$
For the...
[Moderator's Note: Thread spin off due to topic and level change.]
For a spherically symmetric solution, if SET components were written in terms a single one of 4 coordinates, in a way plausible for a radial coordinate, the I believe solving the EFE would require spherical symmetry of the...
Hi all,
I am somewhat familiar the Landau Ginzburg paradigm for phase transition. My understanding is that it is a phenomological model of 2nd order phase transitions by "guessing" that the free energy can be expanded a configuration integral (path integral) of a functional of a local order...
In chapter 20 of Peskin&Schroeder about spontaneous symmetry breaking, he considers and example on page 696 of spontaneous symmetry breaking of SU(3) gauge group with generators taken in adjoint representation.
Covariant derivative is defined with:
$$D_\mu\phi_a = \partial\phi_a +...
Hello everyone,
I need to solve a problem applying symmetry and superposition theorem but the problem is that the circuit is almost symetrical but has little differences in both sides (the source in the left side and the unknown impedance in the right side). I couldn't solve the problem using...
If you were to fire a single atom from a fixed point into a chamber of perfect vacuum and measure where it collides with the opposite wall. Could Spontaneous symmetry breaking in the sub atomic particles cause momentum change in the atom, changing the part of the wall the atom interacted with?
The question is to find the resistance between AF (top 2 points). Let the far right unlabelled vertex of the pentagon be B.
Why can we say that points O and C are at the same potential? I get that both points O and C appear to be at 'half the path' if you consider AOF and ABCDF, and so potential...
The given diagram looks something like this:
Electric force on nucleus from external field must balance attraction force from electron cloud and electric force from external field.
$$e\vec{E}=\frac{k(\frac{L^3}{R^3}e)}{L^2}\hat{L}$$ where ##\vec{L}## is from center of electron cloud to...
I don't know where to start with this problem. If ##\pi_a = (\mu + TS) u_a## then show that \begin{align*}
u^a \nabla_{a} (\pi_b G^b) = 0
\end{align*}where the field ##G^a## is a symmetry generator. [##S## is entropy/baryon, ##T## is temperature, ##u_a## is a one-form field corresponding to a...
The answer given states that:
The entire x-y plane is obviously at the same potential since all the fields are strictly perpendicular to it (draw a diagram if youre confused). Since we choose the sphere to be at potential zero, the point on the sphere which cuts the x-y plane is also at zero...
Recently I saw this YouTube video from Veritassium about CPT -Symmetry:
In this video an experiment of Prof. Chien-Shiung Wu is presented, which has proven that parity is not symmetric, by observing the emmition of electrons from Co60 atoms with synchronised spin. After thinking about this...
Will translation parallel to x-axis work ?
Else please suggest the symmetry?
And does symmetry here refer to the symmetry of the sheet which causes the symmetry of the field or something else?
Please be kind to help.
Hello,
Today I found this paper and this one where P.W. Anderson says that there is no broken symmetry in ferromagnetism because the ground state is an eigenstate of the spin rotation operator. And so we don't have in this system Goldstone's mode for example.
But I thought spin waves were...