Symmetry Definition and 958 Threads

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. K

    Time reversal symmetry breaking in EM

    I have come across a problem I am trying to understand, and hoping someone here has some insight. Basically, when writing down different solutions for an EM field from given sources, there seems to be a problem from the standpoint of time symmetry. From my understanding, if you reverse time, the...
  2. R

    Understand the two doubly degenerate mode of D4h symmetry

    Hello all, This is not a homework problem. Just to understand the two doubly degenerate mode of D4h symmetry i wanted to make sample calculation. Pt in the middle of a square formed by 4 Cl atoms. PtCl4 has square planar structure (AB4) molecule. 1. What is the whole charge of PtCl4 ? Is this -2...
  3. R

    D4h Symmetry Group: 9 Normal Modes of Vibration

    Hello all, In a D4h symmetry group we have 5(3)-6=9 normal mode of vibrations. Normally in books they show only 7. Because 2 of that 7 doubly degenerate Eu modes. And i know the how it vibrates (picture shown in book). But does anyone know how their degenerate partners vibrate ? Is there some...
  4. T

    Conserved charge as a generator of symmetry, Peskin & Schroeder

    Hey! I am stuck at a passage in the QFT book of Peskin & Schroeder and I need your help :) It is about page 698, last break. The sentence is: "At long wavelength, the Goldstone bosons become infinitesimal symmetry rotations of the vacuum, Q |0> , where Q is the global charge associated...
  5. I

    Dihedral group D5 - Symmetry of a Pentagon - Conjugacy classes

    Hi I am struggling to get my head fully around the conjugacy classes of D5. Everywhere I have looked seems to say that there are 4 irreducible representations of D5 which implies that there are 4 conjugacy classes. However, when examining the symmetry of the pentagon I am only able to see 3...
  6. D

    Symmetry in Graphs: Conditions & Possibilities

    For a graph of any function, one of following conditions is said to exist so as for it to be symmetric: a graph is symmetric about y-axis if along with a point (x,y) a point (-x, y) exists. a graph is symmetric about x-axis if along with a point (x,y) a point (x, -y) exists. a graph is...
  7. A

    Nomenclature of high symmetry points in the bandstructure

    Can anyone help me how the high symmetry points in the bandstructure are named. I know a few rules which are as listed below: * Points (and lines) inside the Brillouin zone are denoted with Greek letters. * Points on the surface of the Brillouin zone with Roman letters. * The...
  8. Pengwuino

    Oreo-Milk Symmetry Breaking (OM-Violation)

    So I've found the strangest thing with oreos and milk. I have a glass of milk and when I just toss an oreo inside of it and let it sit, even for the longest time, it doesn't really get all saturated with milk and delicious. However, when I hold the oreo while dipping it in the milk, it becomes...
  9. Q

    Deriving the needed wavefunction transformation for gauge symmetry?

    Homework Statement Take the Schrodinger equation for a point particle in a field: i\hbar \frac{\partial \Psi}{\partial t} = \frac{1}{2m}(-i\hbar\nabla - q\vec{A})^2\Psi + q\phi\Psi I'm supposed to determine what the transformation for Psi is that corresponds to the gauge transformation...
  10. LeonhardEuler

    Enforced symmetry in multi-electron problems

    I've been thinking about how the requirement of anti-symmetry of the wavefunction is introduced in multi-electron problems and I am left puzzled over some aspects of it. Various types of symmetry come automatically in classical physics. If you are studying water flowing in a cylindrical...
  11. D

    How many supports are needed for a symmetrical and antisymmetrical truss?

    given a symmetrical truss, loaded with an assymetrical load, i can divide this truss into 2 separate symmetrical trusses, one with a symmetrical load and one with an antisymmetrical load, then to solve the truss i can solve half of each of these 2 trusses and add/subtract results accordingly...
  12. J

    Exploring the Implications of Gluon Mass and SU(3) Symmetry

    I know people have looked into what it would mean if photons had a mass. But what would it mean if gluons had a mass? ie. if there was a small violation of SU(3) symmetry. In other words, how do we know (experimentally) there is SU(3) symmetry?
  13. R

    How is broken symmetry really observed?

    Hello, Now that there's only one week left until the LHC starts working on the collisions, I think it's a good idea for me to ease my mind and ask how will they observe superparticles and discern them from the SM particles.
  14. H

    Proving tensor symmetry under transformation

    Homework Statement Using indical notation, prove that a 2nd order symmetric tensor D remains symmetric when transformed into any other coordinate system. Homework Equations Tensor law of transformation (2nd order): D'_{pq} = a_{pr}a_{qs}D_{rs} The Attempt at a Solution I think I'm...
  15. R

    Finding Area Moment of Inertia for Axis 33 to X-Axis

    Homework Statement I have to find the area moment of inertia about an axis 33 to the x-axis http://img227.imageshack.us/img227/2392/shape.jpg Homework Equations I_\phi=\frac{1}{2}(I_{xx}+I_{yy})+\frac{1}{2}(I{xx}-I_{yy})cos2\phi - I_{xy}sin2\phi The Attempt at a Solution I found...
  16. H

    Proof of transformational symmetry

    Homework Statement Using indical notation, prove that D retains it's symmetry when transformed into any other coordinate system, i.e. D'_{pq} = D'_{qp} (where D is a symmetric 2nd order tensor) Homework Equations D'_{pq} = a_{pr}a_{qs}D_{rs} (law of transformation for 2nd order tensors)...
  17. P

    How will our world be different if supersymmetry is an unbroken symmetry?

    With all kinds of low energy superpartner particles floating around, do we get the same types of atoms and molecules that build up our world? Will the periodic table of elements be larger or smaller? Is this world friendly to the evolution of intelligent life?
  18. T

    Point symmetry group matrix representations

    Is there any book or source avaliable that clearly shows the point symmetry operation with matrix representations?
  19. P

    Symmetry Group in GR: Modeling Our World

    What is the symmetry group of manifold which models our world in general relativity. In special relativity this group is Poincare group. Its elements preserve standard lorentz inner product. What structure is preserved by elements of symmetry group in GR (sygnature of metric, maybe sth else?).
  20. V

    Symmetry factors in Feyman Diagrams

    Sorry I am spamming the forum, but I have yet another question on Feynman diagrams - Please see attached picture. Apparently the symmetry factor for this FD is 1 - I am trying to understand why. My notes explain that "the symmetry factor is 1 because: φ(x1) contracts to φ(y1) in 4 different...
  21. L

    Symmetry factors (Srednicki ch9)

    Hi, I'm not sure if I understand symmetry factors correctly or not. Looking at the second diagram in Srednicki's fig 9.1. The way I understand things is this corresponds to a number of terms in the expansion, that are algebraically different somehow, e.g perhaps one has a propagator like...
  22. B

    Gauss' Law symmetry of charge distribution

    This is a general question, I was reading my textbook and this statement confuses me: "The symmetry of the electric field must match the symmetry of the charge distribution" this is said regarding symmetry in relation to GAuss' law. I do not understand what they mean by symmetry of charge...
  23. J

    Symmetry breaking domain walls

    Symmetry breaking "domain walls" The only "spontaneously broken symmetry" that I can easily visualize, is cooling down a ferromagnetic material and having the spins randomly choose a direction to align. Since the choice is random, different regions will usually choose different directions...
  24. R

    Applying Guass' Law to Cylindrical Symmetry

    OK, having some trouble wrapping my head around this so would appreciate some clarification. Let us say I had a long, thin wall metal tube of radius R with a uniform charge per unit length. Would there be some magnitude of E of the electric field at a radial distance of R/2? I understand...
  25. S

    Symmetry and irreducible representation

    1. could anyone give sort of a qualititative explanation of how symmetry and irreducible representation are related in the context of molecular spectroscopy? like why is it so useful to count how many symmetries a molecule has and what does it have to do with irreducible represenations and...
  26. T

    Getting started with symmetry groups

    Hey guys, I've been doing a lot of reading on quantum mechanics lately and realized immediately that i am not going to get far without first understanding the meanings of lie groups, SU groups etc. Now I've loked at wiki but unfortunately wiki is not a very good tool for learning math, it's more...
  27. Z

    What Is the Symmetry Group of the Equation \( x^4 + a^2 = 0 \)?

    my question is , given the Group G of symmetries for the equation x^{4} + a^{2}=0 for some 'a' Real valued i see this equation is invariant under the changes x \rightarrow -x x \rightarrow ix x \rightarrow -ix x \rightarrow -x x \rightarrow i^{1/2}x x...
  28. J

    Is Local Poincare Symmetry Exact in All Approaches to Quantum Gravity?

    It is my understanding that in string theory, loop quantum gravity, the 'asymptotic safety' approach, and in semiclassical quantum gravity, local Poincare symmetry is exact. But there are things like DSR (does the D stand for Deformed, or Doubly? I've heard people say it either way), which...
  29. A

    How to use symmetry in resistance networks?

    how to use symmetry in resistance networks?? Hi all I m really confused in these resistor questions..In some circuits they say that some are neglected coz they are equipotential points and using symmetry in these questions..What is this method of symmetry?? How some of the pints are...
  30. V

    Space-time symmetry (Langrangian Mechanics)

    When deriving the conserved quantity in the case of space-time symmetry, a line in my notes goes from: \int{dt.(1+\epsilon\dot{\xi}).L[q(t+\epsilon\xi)+{\delta}q(t+\epsilon\xi)]} - \int{dt.L[q(t)+{\delta}q(t)]} where L is the Lagrangian and \xi is a function of time and both integrals are...
  31. N

    Validity of Direct Product Structure of Symmetry Group

    In short, if we consider the group of symmetries of a regular octahedron, we see (or at least, the author of "Groups, Graphs and Trees" saw...) that the group is isomoprhic to Z2\otimesZ2\otimesZ2\otimesS3 - particularly since if we break up the vertices into 3 groups of front-back, top-bottom...
  32. 1

    Lost in Symmetry and Super Symmetry

    Not getting symmetry at all. I keep reading over and looking for various materials on the subject, but I still can not seem to fully grasp it. Could someone explain what symmetry means in quantum mechanics in a way that a new learner can grasp? This question also applies to super-symmetry...
  33. W

    Why symmetry is not important in classical physics?

    but ultra important in quantum physics? i can see it is important in quantum physics but i can not see why it is less important in classical physics.
  34. E

    Does the superconductivity-Meissner effect break electromagnetic symmetry?

    In superconductivity, Meissner effect describes the expulsion of magnetic field. Could this be described as a breaking of the electromagnetic force in the way that the higgs field breaks electro-weak force?
  35. L

    What is the significance of symmetry in the complex plane?

    How does one express mathematically the fact that: if we complex-conjugated everything (switch i to -i (j to -j etc. in hypercomplex numbers) in all the definitions, theorems, functions, variables, exercises, jokes ;-)) in the mathematical literature the statements would still be true?
  36. D

    Broken symmetry, superconductivity and all that

    I am struggling for some time to understand the concept of broken symmetry. As I come more from the solid state side than from high energy physics. My problem is the following: I understand, how e.g. the rotational symmetry in a ferromagnet is broken. The magnetic moment is observable and I can...
  37. W

    Global symmetry of an N-component Klein-Gordon theory?

    The Lagrangian is given by, \sum_{a=1}^N \left[(\partial^{\mu}\phi_{a}^{\ast})(\partial_{\mu}\phi_{a})-m^{2}\phi_{a}^{\ast}\phi_{a}\right]. Is the symmetry SO(2N), SU(N) or U(N)? It seemed quite obvious to me and some of my friends that such theory has an SO(2N) symmetry. If we view...
  38. W

    Prove Symmetry Group of Regular Polygon Has 1 & 2 Dim Irreducible Reps

    how to prove that the symmetry group of a regular polygon has only 1 and 2 dim irreducible representations?
  39. K

    Exploring the Meaning of Gauge Symmetry

    I would like to hear an original explanation of gauge symmetry. What gauge symmetry really means and why it is needed to describe nature. I am more or less familiar with the standard treatment of electromagnetism and Yang Mills theories from QFT texts, but feel still unsatisfied since I have...
  40. arivero

    11D and enhanced gauged symmetry when alpha=R2

    First of all, who discovered the enhancement of symmetry in compactified theories, when the radius of the compact dimension equals the square root of the string tension? Polchinski gives an expanded example, and GSW already mentions the effect, but without references in any of the books. It...
  41. N

    Clarifying Symmetry in Le Bellac's Quantum Physics

    I was going through Le Bellac's Quantum Physics book.In the "symmetry" chapter 1st page(Classical physics), he makes the following comments a part of which look a bit weired to me...Each statement starts with "Invariance of the potential energy".Do you think this is meaningful? *Invariance...
  42. A

    COMSOL - 2D axial symmetry for Light Diffraction

    Hello, I would be grateful if someone could comment on my problem. I am trying to simulate diffraction of optical wavelength on a sub-wavelength aperture (aperture diameter/wavelength < 0.1). What I want to achieve is: - simulate a geometrical model with an aperture of 15um diameter -...
  43. U

    Symmetry elements and reciprocal lattices.

    Hi, There are some points I really want to clear up in this topic...I promise to finish my chain of doubts as quicly as possible! I'll put in my first questions... 1. Rotoinversion is a combination of inversion and rotation-- often it ends up as having the same effect on the crystal as...
  44. J

    What is the equivalent property for magnetic fields and how is it formulated?

    It is well known, that a point charge q\delta^3(\boldsymbol{x}-\boldsymbol{x}') creates the same electric field \boldsymbol{E}(\boldsymbol{x}) as any spherically symmetric charge density \rho(\boldsymbol{x}) around the point \boldsymbol{x}', with the right total charge, for the points...
  45. G

    Symmetry Argument: Resolving the Twin Paradox Contradiction

    This is pretty much like the twin paradox question: if person A and person B were moving with a velocity v relative to each other and away from each other, then person B would observe a time dilation in person A's reference frame while person A would observe a time dilation in person B's...
  46. J

    DFT: What is the physical meaning of the symmetry about the nyquist frequency?

    When I take the fft of a set of data and plot it, there is a reflection around the nyquist. Everybody knows this, but I would like to know what the physical meaning of the second half (the reflected half) is. The real component is the same as the first half, and the imaginary component has...
  47. M

    Determining Inner Product for P2: Non-Negativity, Symmetry & Linearity

    Hi, I was wondering how would i determine if <p,q> = p(0)q(0)+ p(1)q(1) is an inner product for P2. I know, we have to check for non-negativity, symmetry and linearity. Just not sure how. thanks!
  48. S

    Centroids Simplifying by symmetry

    If you have a 3d shape how do you simplify the problem using symmetry. eg with a sphere is symmetric along any axis therefore the centroid must be in the middle of it eg2 A cone sitting on the xy plane, where the pointy bit is points up the z axis. -nb it is sitting on point (0,0,0) where the...
  49. arivero

    Kaluza Klein and gauge symmetry breaking.

    In standard, old-fashioned, Kaluza Klein theory we have new dimensionful parameters, the size of the compact dimensions, but they become dimensionless after quotient against the Plank size, so they become the adimensional coupling constants of the gauge groups associated to the symmetry of the...
  50. K

    Spontaneous Symmetry breaking-weinberg's chair

    In Weinberg's book, Quantum theory of fields-II, he talks about a chair in the chapter on spontaneous symmetry breaking. He says that, for a chair, a state with a definite l value is not stable but a state with a definite orientation is. I do not understand what he means. An l state can...
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