What is Symmetry: Definition and 955 Discussions

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.

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  1. amjad-sh

    A What is inversion symmetry in solids and why does it break at the surface?

    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...
  2. J

    I Other ways to break the Higgs symmetry group

    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?
  3. ajbroadbent

    Curved Mesh on Symmetry Boundary in ANSYS Maxwell 3D

    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...
  4. L

    MHB What is the axis of symmetry of quadratic function f(x)=-2x^2-(1/2)

    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
  5. Ventrella

    A Binary fractal tree with equidistant leaves on a circle

    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...
  6. JTC

    A Example of how a rotation matrix preserves symmetry of PDE

    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...
  7. L

    A Tensor symmetries and the symmetric groups

    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...
  8. H

    B Question about Unitary Operators and symmetry

    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...
  9. Sahar ali

    I Exploring the Symmetry Behind 14 Bravais Lattices

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

    Triangle altitude's concurrency by symmetry

    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...
  11. A

    I Understanding Gauge Symmetry: A Review of the Schrödinger Equation

    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...
  12. W

    I Why this system has a rotational symmetry in Dirac equation?

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

    Contractions of the Euclidean Group ISO(3) = E(3)

    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...
  14. Milsomonk

    Spontaneous symmetry breaking scalar field masses

    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}...
  15. F

    Magnetic field outside a conducting hollow cylinder

    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...
  16. S

    A Symmetries in particle physics

    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...
  17. S

    I Can a Hermitian matrix have complex eigenvalues?

    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...
  18. G

    I Symmetry in differential equations

    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
  19. P

    Rotational Symmetry in MCNPX core design

    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...
  20. C

    B Electroweak spontaneous symmetry breaking

    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...
  21. K

    A Ed Witten on Symmetry and Emergence

    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...
  22. J

    A Breaking of a local symmetry is impossible, so what about global symmetry....

    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...
  23. T

    A Asking about lattice translation as a discrete symmetry

    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.
  24. L

    B Unlocking Symmetry: The Ultimate Guide to Intuitive Reasoning

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

    A Symmetry/Conservation Violated in Quantum Anomaly

    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...
  26. A

    Implementing symmetry boundary condition for the diffusion equation

    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 =...
  27. Eslam100

    Intro Physics Textbooks on symmetries and physics

    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...
  28. J

    A How can gauge symmetry be broken?

    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!
  29. N

    A Symmetry factors in cluster expansions

    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...
  30. i_hate_math

    I The symmetry argument and expectation value

    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...
  31. Mohamed_Wael

    Can I use symmetry in modal analysis in FEA

    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
  32. M

    MHB Is y = | x | - 2 Symmetric About the x-axis, y-axis, or Origin?

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

    B Muon Time Dilation: Earth vs Muon Perspective

    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...
  34. M

    I Symmetry on the partition function

    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##...
  35. H

    A Azimuthal Symmetry in fluid flow

    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?
  36. ShaddollDa9u

    Electrostatics and symmetry

    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...
  37. ScrollPortals

    Respecting Time Symmetry when programming

    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...
  38. L

    B Is Inversion Symmetry Found in Nature or Technology?

    what is inversion symmetry?
  39. DaveC426913

    B Achieving Rotational Symmetry with Tetrahedral Universal Joints

    I'm building a widget that requires tetrahedral arrangement of universal joints. Currently, I'm only concerning myself with half of the u-joint - the half attached at the tetrahedron. (essentially just the one bar) I want the arrangement of the U-joints to be as symmetrical as possible around...
  40. A

    I Understanding ISSS from Minkowski Space to Poincaré Group

    I try to understand where the intrinsic spin symmetry of spacetime (ISSS) is established. I read articles but still do not understand how to put together all the information to make a clear picture of where ISSS comes from. Minkowski space - Lorentz group O(1,3) - Covering SO(1,3) with SL(2)c -...
  41. rumborak

    In the list of "conservation of X due to symmetry Y" ....

    That is, with Noether's theorem, it feels to me the conservation of angular momentum somewhat stands out because the measure is more of a derived one. That is, rotation of something is really more of an interplay between inertia of the constituent particles and the forces that hold them...
  42. Marcus95

    Fourier Series Coefficient Symmetries

    Homework Statement Let ## f(x) = \frac{a_0}{2} + \sum_{n=1}^{\infty} (a_n \cos nx + b_n \sin nx) ## What can be said about the coefficients ##a_n## and ##b_n## in the following cases? a) f(x) = f(-x) b) f(x) = - f(-x) c) f(x) = f(π/2+x) d) f(x) = f(π/2-x) e) f(x) = f(2x) f) f(x) = f(-x) =...
  43. Chris Miller

    B Relativistic simultaneity and symmetry problem

    With both their clocks synced at 00:00 (12 AM), spaceships A and B leave Earth in oposite directions, each at 17308257.5 m/sec (.57735027c), So the Lorentz factor of their relative velocity 259627884.49 m/sec (.866025404c) is 2. They travel in opposite directions at this velocity for 2 hours...
  44. F

    I Direct product of a symmetry group with itself

    In group theory, what is the direct product of a symmetry group with itself? Say T*T or O*O?
  45. Konte

    Computing molecular symmetry group for non rigid molecules

    Hi everybody, My post today is about Molecular Symmetry group (MS) for non-rigid molecules. I read from this excellent work (Longuet-Higgins), that MS is obtained by selecting only feasible operation from Complete Nuclear Permutation Inversion Group (CNPI). My question is, As I have a quite...
  46. Azura

    About electric fields (Symmetry)

    1) Imagine you have a clock but in each number you have a charge "q". If I have a test charge Q at the center, then by simetry, the net force on Q is zero. I imagined like, 1 cancels 7, 2 cancels 8, etc... But then, if I have a polygon with 13 sides, with a test charge Q, the net force also...
  47. P

    I Symmetry of Liénard-Wiechert Potentials

    According to responses at: http://physics.stackexchange.com/questions/93390/field-of-moving-charge-lorentzlienard-wiechert The Lorentz contraction of the electric field of a charge with uniform velocity is supposed to be symmetric across the plane pi/2 radians from the velocity vector of the...
  48. M

    A Show Spherical Symmetry of Schwarzschild Metric

    In one of the lectures I was watching it was stated without proof that the Schwarzschild metric is spherically symmetric. I thought it would be a good exercise in getting acquainted with the machinery of GR to show this for at least one of the vector fields in the algebra. The Schwarzschild...
  49. Konte

    Molecular symmetry group of non-rigid molecules

    Hello everybody, I have read some very interesting book (Molecular symmetry and Spectroscopy - Bunker and Jensen) that talk about how to find the Molecular Symmetry group (MS) of a molecule by using the concept of "feasible" operation from the Complete Nuclear Permutation Inversion (CNPI)...
  50. K

    I How does spin relate to the symmetry of a particle?

    Why are particle with half integer spins anti-symmetric while integer spin particles are symmetric? Or in other words, how does spin relate to the symmetry of indentical particles?
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