Symmetry Definition and 967 Threads

Homework Statement Hi everyone! Just wondering if there's a way to prove the symmetry property of the Riemann curvature tensor $$ R_{abcd} = R_{cdab}$$ without using the anti-symmetry property $$ R_{abcd} = -R_{bacd} = -R_{abdc} $$? I'm only able to prove it with the anti-symmetry property and...

I'm trying to better understand how people refer to symmetry in Physics and Differential Geometry. In "Exterior Differential Systems and Euler Lagrange Partial Differential Equations," by Bryant, Griffiths and Grossman, it seems a vector field is a symmetry of a Lagrangian if the Lie derivative...

Homework Statement Exact spin symmetry in the Dirac equation occurs when there is both a scalar and a vector potential, and they are equal to each other. What physical effect is absent in this case, that does exist in the Dirac solution for the hydrogen atom (vector potential = Coulomb and...

1-As you know classical electrodynamics has conformal symmetry. But does this symmetry survive renormalization? if not, can anyone give an explanation on why? 2-What is the situation with QCD? Does it have conformal symmetry at a classical level? If yes, does it survive renormalization? Thanks

Hi, Just curious. One of the requirements for a data set to be normally-distributed is that of symmetry. Question: Is there or could one define a statistic to this effect, meaning to determine the level of symmetry on the data set and use that to determine at certain confidence level if the...

I'm curious to know what Lorentz symmetry is, and how it works. The wiki description is a bit too difficult for me to understand. And how does it differ from a computer's cubic symmetry? I understand that in cubic symmetry, the laws of physics or physical things look different depending on what...

Hello! The time reversal operator, ##\hat{\Theta}## transforms a Bloch state as follows: ##\hat{\Theta} \psi_{nk}=\psi^*_{nk}##. How does one proceed to prove the condition that ##\psi_{nk}## and ##\psi^*_{nk}## must satisfy in order for our system to be time reversal invariant? Thanks in advance!

Hello guys! I have to solve a problem about crystal symmetry, but I am very lost, so I wonder if anyone could guide me. The problem is the following: Using semiclassical transport theory the conductivity tensor can be defined as: σ(k)=e^2·t·v_a(k)·v_b(k) Where e is the electron charge, t...

Homework Statement Homework EquationsThe Attempt at a Solution I am trying to solve this question by symmetry .If I draw a line perpendicular to the line joining AB then points C and D are symmetric . Now I am unsure how to proceed further .

Why is it that bosons (particles having symmetric wave functions) have integral spins and fermions (particles having antisymmetric wave functions) have half integral spins? A lot of books state this without specifying the reason. I was wondering if this is a theoretical deduction. Or is it an...

Hello everyone :) Not too long ago, I was thinking about planetary motion around a sun, both with circular orbits and elliptic orbits. However, when thinking a little longer about these two cases in a broader sense, I spotted a big difference which I found quite odd (assume purely classical...

Hi, The article below states that they made a material that blocks the motion of molecules in only one way but passing the other way is possible. See the article. https://physicsworld.com/a/blocking-the-symmetry-of-motion/ This seems to me in contrast with the second law. You can for example...

Hello Can somebody explain for me what is the meaning of inversion symmetry in solids? and why does it breaks at the surface? and also why this inversion symmetry breaking leads to SOC(spin orbit coupling)? If somebody also know a document that explain this in full details(from A to Z) please...

Our standard model breaks the Higgs Su(2) electroweak symmetry via the Higgs mechanism. In official beyond the standard models. May I know the different lists of models where the Higgs field can be part of larger symmetry group like SU(10) and different ways to break it?

I figured this would be the best place to ask as there doesn't seem to be a FEM/Simulation specific sub-forum here, but I am looking for some help regarding mesh generation in ANSYS Maxwell. I have an array of "micro-needles" that I am applying a voltage to in order to determine the electric...

The problem is: f(x)=-2x^2-(1/2) Determine if this statement is true of false: The axis of symmetry is x=-2. What is the axis of symmetry? How can you figure out the axis of symmetry without a b value, since the formula for it is x=-b/2a

Does there exist a binary fractal tree… (reference: http://ecademy.agnesscott.edu/~lriddle/ifs/pythagorean/symbinarytree.htm ) …whose leaves (endpoints) lie on a circle and are equidistant? Consider a binary fractal tree with branches decreasing in length by a scaling factor r (0 < r < 1) for...

Good Day I have been having a hellish time connection Lie Algebra, Lie Groups, Differential Geometry, etc. But I am making a lot of progress. There is, however, one issue that continues to elude me. I often read how Lie developed Lie Groups to study symmetries of PDE's May I ask if someone...

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...

We know that for every symmetry transformation, we can define a linear, unitary operator (or antiunitary, anti linear operator) that takes a physical state into another state. My question is if there exists unitary operators that act in this way that do not correspond to any symmetry? Would a...

what limits a large number of bravais lattice to only 14? Is it because of symmetry operations?

Homework Statement in the proof of triangle altitudes concurrency , i have found the equation of the Altitude AD, x(x2-x3)+y(y2-y3)-x1(x2-x3)-y1(y2-y3) Homework EquationsThe Attempt at a Solution In the book other altitude equations are written by symmetry, how is the idea of symmetry is used...

I have reviewed the various posts on gauge symmetry in particular this one which is now closed. In this post there is the following link:http://www.vttoth.com/CMS/physics-notes/124-the-principle-of-gauge-invariance. This is a good read. However, there is some clarification I need. The...

why system has a rotational symmetry in dirac equation? is that a general property of all systems?

Homework Statement Consider the contractions of the 3D Euclidean symmetry while preserving the SO(2) subgroup. In the physics point of view, explain the resulting symmetries G(2) (Galilean symmetry group) and H(3) (Heisenberg-Weyl group for quantum mechanics) and give their Lie algebras...

Homework Statement Determine the mass of the scalars and show that one remains zero in accordance with goldstones theorem.Homework Equations $$L=\dfrac {1}{2} (\partial_\mu \phi_a)(\partial^\mu \phi_a)-\dfrac{1}{2} \mu^2 (\phi_a \phi_a) - \dfrac{1}{4} \lambda (\phi_a \phi_a)^2+ i\bar{\psi}...

Homework Statement A current I flows along the surface of a hollow conducting cylinder. The radius of the cylinder section is r. By using Ampere's law, show that the magnetic field B outside the cylinder is B=\frac{\mu_0}{2 \pi} \frac{I}{r} Homework Equations Ampere's law...

We often use SO(N) and SU(N) to describe symmetries in particle physics. I am not clear which one to choose when I try to discuss a symmetry. For example, why do we use SU(3) but not SO(3) to describe the symmetry of the three colors of quarks? Similarly, why do we use SU(2) but not SO(2) to...

Hi, I have a matrix which gives the same determinant wether it is transposed or not, however, its eigenvalues have complex roots, and there are complex numbers in the matrix elements. Can this matrix be classified as non-Hermitian? If so, is there any other name to classify it, as it is not...

Before I delve into this , I just wanted to know the basic approach. Do we look for symmetries because it gives us a systematic way to find coordinate changes that change the differential equation into a separable one? Thanks jf

Designing a PWR core in MCNPX for burnup using 4 folds rotational symmetry to reduce computational time of the core, taking reflective boundary conditions on rotational symmetry planes. should the power be reduced to 1/4th of original power (3000 MWth) in burnup card or does the reflective...

This is a question that I have tried to pose several times without any success but, anyway, I would like to try again for the very last time. Asume for a moment that EW-SSB (electroweak spontaneous symmetry breaking) actually happened in our early universe. Imagine that our Standard Model of...

Ed Witten posted an interesting article on arXiv a few days ago on the fate of global symmetries in physics beyond the Standard Model. You can read it here. In particular, Witten argues that the global symmetries of the Standard Model are all approximate and emergent at low-energy, and they...

Breaking of a local symmetry is impossible. It is often said that therefore the role of the Higgs mechanism in the standard model is a different one. Namely, Once a gauge is fixed, however, to remove the redundant degrees of freedom, the remaining (discrete!) global symmetry may undergo...

I've read Modern Quantum Mechanics J.J. Sakurai 2nd Edition. In topic about lattice translation as a discrete sysmmetry(page 287) , they discuss only in case of ground state. If I want to study more in case of including excited states, where can I find this information? thanks.

Which is the best book that gives extensive intuitive reasoning on Symmetry?

String theorists have apparently applied String Theory to expose a Quantum Anomaly in a physical analog system: electrons flowing in a Niobium Phosphide crystal. The electrons were found to violate symmetry in relation to Spin...

The following lines of codes implements 1D diffusion equation on 10 m long rod with fixed temperature at right boundary and right boundary temperature varying with time. xsize = 10; % Model size, m xnum = 10; % Number of nodes xstp =...

I just started to develop an interest in symmetries after taking an introductory course in electromagnetism . The instructor explained to us how physical laws can be obtained by considering the symmetries of the physical system. It was really amazing how we can obtain such information just by...

Hello, I was reading about the Higgs mechanism and I must say that I did not really follow the argument of how the gauge symmetry is broken. I think that my problem has to do with the more general question of how does a gauge symmetry get broken in general? Thanks!

I have been going through a thermal physics book by Schroeder. In chapter 8 (Systems of Interacting Particles) he introduces the configuration integral in terms of pictorial diagrams describing sets of interacting particles in a weakly interacting gas. Each configuration has an associated...

In 1D QM: I understand that if a given potential well, U(x), is symmetric about x = L, then the expectation value for operator [x] would be <x> = L. (I am not even entirely sure why this is, guessing that the region where x<L and x>L are equally probable) Is it possible to draw conclusion...

I am doing FE analysis for symmetric shape in boundary conditions and geometry, I would like to know if I can use symmetry in my analysis or not. I have tried to run trials, the results are very similar but I am not sure if this just a coincident

Test for symmetry about the x-axis, y-axis and origin. y = | x | - 2 What are the rules for testing for symmetry?

From the reference frame of the earth, the distance between the surface of the Earth and the muon is longer, but the muon survives because time for the muon is slowed down. From the reference frame of the muon, the time experienced by the muon is not slowed down but the muon survives because...

We have a partition function ## \displaystyle Z=\frac{1}{N! \: h^{f}} \int dq\: dp \:e^{-\beta H(q,p)} ## And we obtain, for example, the pressure by ##\displaystyle p = \frac{1}{\beta} \frac{\partial\: \ln Z}{\partial V}##. So if we do the transformation ##Z \rightarrow a Z## where ##a >0##...

I am looking at evaporating droplets and I am interested in looking at when there is azimuthal symmetry, and I need to write the Navier-Stokes equations for this. I just set all \varphi terms in the spherical case equal to zero right?

Homework Statement "Find the direction and the variables which the electrostatic field depends on at all points of the plane (xOy) uniformly charged with the density of positive charges ϱ" The Attempt at a Solution So first of all, I have to study the Invariances of symmetry. I tried to...

Where can I learn to break the habit of using time steps and instead use mathematical frameworks to preserve time symmetry when programming simulations? I recently visited a site ( bugman123.com ). He's got a lot of STEM experience. He's written simulations and programs for a lot of things...

what is inversion symmetry?