# What is Symmerty: Definition and 16 Discussions

No Wikipedia entry exists for this tag
1. ### Rotating an elastic tensor from 100 to 711 axis

I have the elastic tensor for a material where C11 aligns with the 100 axis , C22 aligns with the 010 axis and C33 aligns with the 001 axis. I want to rotate it so the the new axis are for a configuration with an axis along 711. How do I come up with the rotation matrix to do this?
2. ### I No Symmetry Spacetimes/Metrics in Theory of Relativity

In the context of the Theory of Relativity are there any spacetimes or metrics with a complete absence of symmetries? I mean, consider a type of space or metric where no symmetries would hold (at least not exactly, but approximately). A space or metric where the Poincaré invariance (including...
3. ### A Symmetry & Invariance of Pions: π+, π0, π− and Other Mesons Explained

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...
4. ### I Deriving the Commutator of Exchange Operator and Hamiltonian

In the boxed equation, how would you get the right hand side from the left hand side? We know that ##H(1,2) = H(2,1)##, but we first have to apply ##H(1,2)## to ##\psi(1,2)##, and then we would apply ##\hat{P}_{12}##; the result would not be ##H(2,1) \psi(2,1)##. ##\hat{P}_{12}## is the exchange...
5. ### B Symmetry of parity: Mistake in the experiment?

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...
6. ### A Axisymmetric vs Spherical Metric Comparison

Hello. I expect this question is not repeated. I look from it in the forum but I found nothing. I am confused on how an axisymmetric spacetime (generated by a rotating object) can manifest the spherically symmetric case. The axisymmetric spacetime should describe objects with any angular...
7. ### A What would it mean if symmetries in physics would not be fundamental?

Physicist Joseph Polchinski wrote an article (https://arxiv.org/pdf/1412.5704.pdf) where he considered the possibility that all symmetries in nature may not be fundamental. He says at page 36: "From more theoretical points of view, string theory appears to allow no exact global symmetries, and...
8. ### A Unitary representations of Lie group from Lie algebra

In Quantum Mechanics, by Wigner's theorem, a symmetry can be represented either by a unitary linear or antiunitary antilinear operator on the Hilbert space of states ##\cal H##. If ##G## is then a Lie group of symmetries, for each ##T\in G## we have some ##U(T)## acting on the Hilbert space and...
9. ### I Noether's theorem for discrete symmetry

I am wondering if it existes some discret version of the Noether symmetry for potential with discrete symmetry (like $C_n$ ). The purpose is to describe the possible evolution of the phase space over the time without having to solve equations numerically (since even if the potential may have...
10. ### A Nonlinear susceptibility and group reps

Dear All short explanation: I am trying to leverage my limited understanding of representation theory to explain (to myself) how many non-vanshing components of, for example, nonlinear optical susceptibility tensor ##\chi^{(2)}_{\alpha\beta\gamma}## can one have in a crystal with known point...
11. ### I Symmetry in geometry vs physics

Hello I was reading some article on angular momentum. And at some point, the author started talking about the symmetric objects and axis of symmetry. Now I am wondering if the author means the geometrical symmetry or the symmetry in physics. For an example, if we take a uniform rod of length...
12. ### Dirac hydrogen atom vs spin symmetry

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...
13. ### U(1) invariance of classical electromagnetism

This is an interesting question that popped through my mind. Some of us should know what is meant by „gauge transformations”, „gauge invariance/symmetry” and are used to seeing these terms whenever lectures on quantum field theory are read. But the electromagnetic field in vacuum (described in a...
14. ### A Does an infinitesimal generator of acceleration exist?

I am trying to determine what types of field theories have a Lagrangian that is symmetric under an Infinitesimal acceleration coordinate transformations. Does an infinitesimal generator of acceleration exist? How could I go about constructing this matrix?
15. ### I Origin of mass and Noethers theorem

Let me set up the question briefly. Emmy Noether's theorem relates symmetry to conserved quantities, e.g. invariance under translations in time => conservation of energy. A fundamental truth revealed. Massive gauge bosons, leptons and quarks all appear to acquire mass through the spontaneous...
16. ### Fractal Symmetry & Noether's Theorem: Chaos & Conservation

I was reading a Steven Strogatz book and he said that the self similarity of fractals is a symmetry. Has any conservation law been linked to this type of symmetry using Noether's Theorem?