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. WaveJumper

    A challenge to the symmetry of laws of physics

    "It's the planet that really shouldn't exist – or at least not for long. It is 10 times the size of Jupiter, orbits its own star in under 24 hours and should soon be spiralling into the surface of its searingly-hot sun..." Full story...
  2. haushofer

    Quick question on the Schrodinger symmetry group

    Hi, I'm reading the article "Galilean Conformal Algebra's and AdS/CFT", 0902.1385v2, and have a quick question about the Schrodinger symmetry group. The symmetry group consists of the usual Galilean group G(d,1) with rotations, boosts and (space and time) translations. On top of that we have...
  3. P

    Permutations of Subscripts for Unchanged Value in Polynomial Symmetry

    Homework Statement (x_1 - x_2)(x_3 - x_4) Find permutations of subscripts that leave value unchanged Homework Equations The Attempt at a Solution Okay so I know that it's asking how I should rearrange things and still not change the value. Switching 1 with 2 or 3 with 4 would work but I know...
  4. sweetser

    Exact Gauge Symmetry of the Standard Model

    Hello: The gauge symmetry of the standard model is written in authoritative places like wikipedia :-) as U(1)xSU(2)xSU(3). This would have 12 elements in its Lie algebra corresponding to one photon, W+, W- and W0 or Z, and the 8 gluons. I recall reading discussions that such a...
  5. A

    Local symmetry and forces, what book to read?

    I would like some tips about what book I should read if I want to properly understand the relation between local symmetry and forces in gauge theories. And with properly uinderstand I mean a combination of mathematics and intuition/visualization. On the topic of QFT I have the books by Zee (...
  6. J

    Beers Law with Spherical Symmetry

    In essence, Beers law describes the behavior of a quantity where the probability of a unit of that quantity over a distance changing follows an exponential distribution. This can be for instance, the probability of a particle being absorbed or scattered over a distance x. Problems of spherical...
  7. K

    Spontaneous Symmetry breaking,phase factor

    Book: Maggiore-A modern Introduction to QFT Section:11.1 He says that if a symmetry transformation multiplies the vacuum state by a constant phase factor only, the symmetry is not broken.. Section:11.2 U(1) symmetry is spontaneously broken...multiplication by exp(i theta) takes the...
  8. L

    Wave equation, general solution, cylindrical symmetry

    I was interrested in the general solutions to the wave equation depending on only one spatial coordinate. For one linear coordinate, the general solution is: a f(x-ct) + b g(x+ct) For one radial spherical coordinate, the general solution is: a f(r-ct)/r + b g(r+ct)/r I thought that...
  9. R

    Symmetry Restoration in QFT: Exploring V_{eff}(\phi)

    In Zee's book on QFT he derives this equation for the effective potential in \phi^4 theory: V_{eff}(\phi)=\frac{1}{4!}\lambda(M)\phi^4+\frac{\lambda(M)^2}{(16 \pi)^2}\phi^4[log\frac{\phi^2}{M^2}-\frac{25}{6}]+O(\lambda(M)^3) The effective potential is basically the potential with quantum...
  10. L

    Symmetry and range of interaction

    I have just read a book. It said that: "if symmetry is exact, interaction is a long range". Could you explain me more detailed? Thanks!
  11. G

    Chiral symmetry, quark condensate and self-energy

    Why in QCD chiral symmetry breaking study only the light quarks are taken into account? And why are their masses usually set to zero, Goldstone bosons are found, and then their masses are corrected by letting the quarks have non-zero mass? What happens if one study this symmetry breaking with...
  12. B

    Chiral symmetry breaking and approximate flavour symmetry

    I have 2 questions: 1. When there are no fermion mass terms, the Dirac part of the Lagrangian posseses an SU(N) left X SU(N) right flavour symmetry for N flavours of fermions. This can be "re-arranged" as an SU(N) vector X SU(N) axial symmetry. The axial part is spontaneously broken by the...
  13. 0

    Are Eigenfunctions of a Hamiltonian on a lattice always Bloch functions?

    It is common knowledge in Physics that eigenstates share the symmetries of the Hamiltonian. And it is trivial to show that this is true for the eigenspaces. Let g be an element of a symmetry group of Hamiltonian H, M_g its representation, \left| \phi \right> an eigenvector and \lambda the...
  14. Jim Kata

    Conformal symmetry group for R(1,3)

    I'm trying to derive the lie algebra for the conformal symmetry group and was curious if anyone could help? I'll go through what I have and highlight the parts I"m unsure of ds^2 = \bar g_{\alpha \beta } (\bar x)d\bar x^\alpha d\bar x^\beta = g_{\alpha \beta } (x)dx^\alpha dx^\beta...
  15. T

    Broken Symmetry: Examining Lagrangian with $\Phi$

    As an exemple of borken symmetry the teacher showed what happens with this lagrangian: \Lambda=\frac{1}{2}\partial_\mu \Phi^{+}\partial^{\mu}\Phi - \left( \frac{m^2}{2} \partial_\mu \Phi^{+}\partial^{\mu}\Phi +\frac{g^2}{4}(\partial_\mu \Phi^{+}\partial^{\mu}\Phi )^2 ) \right) where...
  16. A

    Rotational Symmetry: Deriving Delta X & Delta Y

    I've been following along with Lenny Susskinds lectures on modern classical mechanics on youtube. at 34:30 he writes a few translation formulas on the board: delta X = - epsilon Y delta Y = epsilon X It's not obvious to me why these equations are true. I can't seem to find a...
  17. malawi_glenn

    Z_3 symmetry in NMSSM superpotential

    Hello I am trying to learn more about NMSSM, and in the Lecture Notes by Jack Gunion, held at SUSY08 conference in Seoul 2008 ( http://susy08.kias.re.kr/slide/pl/Gunion.pdf ) there is in slide #20 arguments for a Z_3 symmetry of the NMSSM superpotential. My questions are what/which is this...
  18. T

    Symmetry in Statistical Mechanics

    I have of late been reflecting on something. Generally as a rough approximation we may divide physics into classical mechanics, quantum mechanics, classical field theory (like E/M, fluid mechanics...), quantum field theory, and then statistical mechanics. All the classical and quantum...
  19. A

    How does a system consisting of two nuclei have rotational symmetry?

    I don't see it. Can someone explain? The Wikipedia article (http://en.wikipedia.org/wiki/Rotational_symmetry) defines an object with rotational symmetry as an object that looks the same after a certain amount of rotation. But this seems vacuous; doesn't *everything* look the same after a...
  20. B

    IR spectra and point group symmetry

    Hello I'm currently studying the reaction of anisole with hexacarbonylchromium, and experiment shows the displacement of 2 of the carbonyl ligands with the anisole group, forming a 2-η ligand with the chromium ion. After refluxing to obtain the crystals, IR and nmr spectra of the sample...
  21. C

    CP symmetry violation and matter antimatter asymmetry

    anyone know what research is being done in CP symmetry violations and Matter Antimatter Asymmetry currently?
  22. K

    Finding a Rotational Symmetry Group

    Homework Statement Glue two dodecahedra together along a pentagonal face and find the rotational symmetry group of this solid. What is its full symmetry group? Homework Equations The Attempt at a Solution Since this clearly is a finite subgroup of SO3, it must be isomorphic to a...
  23. W

    Symmetry and Electrostatics

    Homework Statement Past exam question: Briefly explain the roles of symmetry, uniqueness and superposition in solving electrostatics problems. Homework Equations N/A The Attempt at a Solution I know the definition of these words and could cobble together an answer from that - but...
  24. O

    Symmetry Groups and Group Actions

    Homework Statement I would like to find the number of distinct elements in S17 that are made up of two 4-cycles and three 3-cycles. Homework Equations The Attempt at a Solution This seems like a very simple question but since the group is so huge it's hard to figure out. I have...
  25. W

    Continuous Charge Distribution: Symmetry & Meaning

    In the Electric field of a Continuous Charge Distribution, what is "conti.." exactly? -I know its the "distribution"! but I`m asking about, like, how would the "distribution" be continuous? -I think the word "symmetry" should be used? -why is the word "continuous" used?
  26. D

    Symmetry Breaking and the Metric

    Hello, im a first year phd student, and I am reading http://arxiv.org/abs/0901.1847 right now in an attempt to figure out something cool to do with lie 3 algebras. In the paper they mention that turning on a B field in the 1,2 dimensions breaks the SO(4) symmetry the theory has to...
  27. T

    Custodial Symmetry: Understanding the Transformation Law

    I have never really understood the approximate 'Custodial symmetry' in the Standard Model. I've seen it being described in many texts, but I can't seem to be able to put my finger on it. Would somebody please write down the transformation law for the Higgs fields under a 'custodial SU(2)...
  28. W

    PDE Cylindrical and Spherical Symmetry

    Homework Statement Show that the solution u(r,theta) of Laplace's equation (nabla^2)*u=0 in the semi-circular region r<a, 0<theta<pi, which vanishes on theta=0 and takes the constant value A on theta=pi and on the curved boundary r=a, is u(r,theta)=(A/pi)[theta + 2*summation ((r/a)^n*((sin...
  29. P

    Conservation principles and symmetry; Lagrangian and general momenta problem

    Homework Statement A particle of mass m and charge e moves in the magnetic field produced by a current I flowing in an infinite straight wire that lies along the z-axis. The vector potential induced magnetic field is given by A_r=A_theta=0, A_z=(\mu0*I/2*pi)*ln r, where r , theta, and z...
  30. N

    Can the Centroid Symmetry Argument Help with Graph Coordinates?

    I am confused with the coordinates when using the symmetry argument for this graph. Is Mx=0 using the symmetry argument ?
  31. K

    Symmetry of Quantum vs Classical Physics Systems

    I read a introductory book on symmetry of physics system. The author says symmetry of quantum mechanical system is VERY different from that of classical system. I just wonder what's the main difference?
  32. N

    Cylindrical Symmetry - Gauss's Law

    I am having trouble understanding the concept of cylindrical symmetry in an infinitely long line. Please picture a finite Gaussian cylinder enclosing a portion of the length of the line, parallel to the line. My book states that there cannot be any component of E perpendicular to the...
  33. T

    Understanding Z2 Symmetry in Models

    Can someone explain what's Z2 symmetry ? Is it necessary to have it in a model, even SM ?
  34. D

    'Frame' symmetry breaking - when did it happen?

    In any place of our universe we can define a 'preferred' or 'rest' frame based on the observation of the Cosmic Microwave Background. Of course, in different places of our universe these frames are different, but the idea is the same. If instead of the CMB we define this frame based on the an...
  35. M

    Spherical symmetry implies zero angular momentum?

    why does the spherical symmetry of the ground state orbital of hydrogen necessitate zero angular momentum? I really don't have any intuition for "quantum angular momentum"
  36. drizzle

    Group Theory to Understand Band Gap Structure of Semiconductor Oxides

    ehim ehim...hello, I wonder if anyone knows about “group theory” [= approximation method] which is helpful in describing band gap structure of semiconductor oxides, my main problem is the high symmetry points i.e. gama point which occur at k=0 [the first Brillion zone], how it varies from gama...
  37. K

    What Are Symmetry Factors in Feynman Diagrams According to Srednicki?

    I am trying to understand Feynman diagrams and especially symmetry factors. I'm learning from Srednicki's QFT book page 60 to 63, or in the online version page 72 to 74. Take formula 9.11 . (P-propagator, V-vertice, E-external source and E=2P-3V) Srednicki says: a, there are...
  38. E

    Lie symmetry method for PDE/ODE

    I was wondering if anybody has any experience with Lie Symmetry Method for solving PDE and ODE's? I have heard that the method is very general/systematic, but rather tedious and useless in practice. But recently I've noticed that Maple and Mathematica contain very nice functions, for example...
  39. J

    Symmetry Arguments-a finite cylindrical can

    Symmetry Arguments--a finite cylindrical can Homework Statement Consider a finite cylindrical can shape that has charge uniformly distributed on its surface. Symmetry does allow us to say some things about the electric field of this distribution A) at points along the can's central axis B) At...
  40. X

    Why does strong magnetic field destroy spherical symmetry of atom?

    In most of quantum textbook, they say strong magnetic field destroy the spherical symmetry of an atom in zeeman effect. Total angular moment is not conserved. Can anyone explain what physical meaning is? I cannot picture it in my mind. How does strong magnetic field cause spherical symmetry...
  41. T

    Electricity and magnetism - planar symmetry question: plastic sheets

    Homework Statement Three plastic sheets that are large, parallel and uniformly charged are placed side-by-side. The electric field strength between sheets 1 and 2 is 2x105; the electric field strength between sheets 2 and 3 is 6x105. What is the ratio of the charge density on sheet 3 to that on...
  42. J

    Why can't there be spontaneous symmetry breaking in finite volume?

    Hello everyone, I'm a bit confused by something I've read as have been unable to find resources to clarify it. Here is the statement that confused me, from Binetruy's Supersymmetry textbook (p.26): It is well-known that [in the case of ordinary continuous symmetries] no possibility of...
  43. K

    Proving Symmetry of Modified Maxwell Equations

    If there were magnetic monopole, the Maxwell equations should be modified as \nabla\cdot\vec{B} = \mu_0\rho_m \nabla\times\vec{E} = - \frac{\partial \vec{B}}{\partial t} - \mu\vec{J}_m and plus the other two. I wonder how to prove these two modified equations are of correct...
  44. Fra

    Weyl's take on symmetry and the continuum

    Due to several threads, recent thinking and book readings, suggesting the the concept of "symmetry" itself, as well as the concept of "continuum" are somehow related to a key problem. I asked myself the question about the original line of reasoning of the introduction of symmetry historically...
  45. Demystifier

    Does collapse violate exchange symmetry?

    Consider a system of two bosons with spin, say photons. The wave function must be symmetric under the exchange of the two particles. For example, |psi> = |up> |down> + |down> |up> So far, so good. Now let us measure the spin of the particles, and let the outcome of the measurement be that...
  46. DaveC426913

    Applied geometry: symmetry within a 3D volume

    I've got a 3D shape that, um, inherits from a cube (i.e. it retains properties characteristic of cubes). It has high symmetry. I wish to string all its vertices (of which there are 16) with - I dunno, yarn - forming the edges (of which there are 32). I can do the entire thing with a single...
  47. A

    Exploring Symmetry Energy: What is It?

    Hi Can someone please explain me what is the symmetry energy? I know asymmetry energy in the weizsacker semiempirical mass formula which is the gap between a nucleus and it's isobar with Z=N.
  48. J

    Spontaneous symmetry breaking of gauge symmetries

    hello all gauge symmetries are redundencies of the description of a situation. Therefore they are not real symmetries. So in what sense does it mean to spontaneously break a gauge symmetry? ian
  49. B

    Find its moment of inertia about its axis of symmetry

    Homework Statement A cone of mass M has a height h and a base diameter R. Find its moment of inertia about its axis of symmetry Homework Equations I=\int R^{2}dmThe Attempt at a Solution I tried starting by finding dm. It's equal to the mass per unit volume, \frac{M}{\frac{1}{3}\pi R^{2}h}...
  50. B

    Does the Hamiltonian Symmetry Extend to All N Dimensions?

    Homework Statement I shall consider the Hamilton H(q,p)=1/2\sum{p_l^2}+1/2\sum{q_l^2}+\gamma(\sum{q_l^2})^2 all the sums if from l=1 to l=N. (gamma is bigger or equal to zero) I shall discuss the symmetry/asymmetry plus determine that the form of the qeneral solution is qualitative...
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