What is Symmerty: Definition and 16 Discussions

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  1. mathgirlie

    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. S

    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. Rafaelmado

    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. Samama Fahim

    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. W

    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. lmmoreira

    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. S

    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. L

    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. D

    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. Cryo

    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

    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. It's me

    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. dextercioby

    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. Q

    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. AlanKirby

    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. Michele Zappano

    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?