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.

View More On Wikipedia.org
Recent contents Top users
  1. J

    Why should there be CPT symmetry?

    A few of the books and magazines I have read talk about maintaining CPT symmetry, but I can't see why it should be the case. What is the evidence, theoretical or experimental, of CPT symmetry?
  2. sweetser

    Gauge symmetry in EM by inspection

    Hello: I was under the impression that gauge symmetry was a property of the Lagrange density. Here is the Lagrangian for EM written out in its components: \begin{align*} \mathcal{L}_{EM} &= J\cdot A +\frac{1}{2}\left(B^2-E^2\right) \quad eq.~1\\ &=\rho \phi - Jx Ax - Jy Ay - Jz Az \\...
  3. B

    Linear Algebra/Tensor Algebra: Symmetry of a (1,1) tensor.

    Homework Statement Let M be a differentiable manifold, p \in M. Suppose A \in T_{1,p}^1(M) is symmetric with respect to its indices (i.e. A^i_j = A^j_i) with respect to every basis. Show that A^i_j = \lambda \delta^i_j, where \lambda \in \mathbb{R}. Homework Equations The Attempt at a...
  4. P

    Symmetry and Causality: are the two connected?

    I've been reading an <URL=http://www.nybooks.com/articles/archives/2011/oct/27/symmetry-key-natures-secrets/> article </URL> by Steven Weinberg on symmetry, written for laymen, in the New York Review of Books. Weinberg describes as simply as he can how symmetry lies at the heart of the Standard...
  5. G

    Greiner Mueller's QM II Symmetry

    Is anyone in PF reading the titled book? For me, it is slow work because I have not done physics for a while - decades! I am retired and read some old physics books just for challenge. Mueller gives me that, but also reward. From time to time, I find little stumbling blocks, sometimes a...
  6. N

    How do 6 quarks manifest hiden SU(2) symmetry(together SU(3) symmetry)?

    Please teach me this: It seem to me that lepton manifests broken symmetry SU(2) with couple electron and neutrino(electron is a state with mass,neutrino is a state with nearly zero mass).Similarly for 2 other families of lepton,we have a state with mass and a state with nearly zero mass.But I...
  7. B

    Orthogonal change of basis preserves symmetry

    Homework Statement Prove that symmetric and antisymmetric matrices remain symmetric and antisymmetric, respectively, under any orthogonal coordinate transformation (orthogonal change of basis): Directly using the definitions of symmetric and antisymmetric matrices and using the orthogonal...
  8. A

    Transistors: Collector vs Emitter (where does the symmetry get broken)

    I thought I had a good understanding of transistors, but I have seen articles on how to tell the collector from the emitter. I had always pictured transistors as a perfectly symmetrical device. Either side could be the collector, and the opposite side was the emitter. Clearly, there is some...
  9. Telemachus

    Azimuthal Symmetry: Difference Between and Cylindrical Symmetry

    Hi there. I have this simple conceptual question, I'm studing electrostatics, and the book speaks about azimuthal symmetry. The doubt I have is, what's the difference between azimuthal symmetry and cylindrical symmetry? I mean there is any difference between those symmetries? it looks like the...
  10. B

    Using Gauss' theorem ande exploiting the cylindrical symmetry of the system, show

    Homework Statement A wire of length L and negligible transverse dimensions, made of an insulating material, is placed on the x-axis between the origin and the point (L,0). The wire has a uniform line charge density lambda. using Gauss' theorem and exploiting the cylindrical symmetry of...
  11. T

    Goldstone bosons in Models with global symmetry, broken by Orbifolding

    Hi, I am interested in grand unification with extra dimensions. Especially the case when extra dimensions are broken by orbifolding. Now I am trying to understand how the Goldstonebosons appear in the spectrum of a theory with global (for example SU(N)) symmetry. From the...
  12. P

    The physical meaning of a symmetry

    I know that the physical meaning of SU3 and SU2 - you can change the places of the quarks or/and leptons and you will get the same results. What is the physical meaning of U1, and O3,1 (Lorentz group if I am not wrong)? I know U1 is connect with the Polarization of the light. Thanks...
  13. R

    The spherical symmetry of massive bodies

    Homework Statement Consider the study of the motion of a two bodies system interacting with only gravitational forces. If the two bodies (or even one of them) has not spherical symmetry, how will you proceed? Indeed the Earth and the moon does not have spherical symmetry mass distributions...
  14. S

    Representations of Symmetry Operators

    For spin 1/2 particles, I know how to write the representations of the symmetry operators for instance T=i\sigma^{y}K (time reversal operator) C_{3}=exp(i(\pi/3)\sigma^{z}) (three fold rotation symmetry) etc. My question is how do we generalize this to, let's say, a basis of four...
  15. N

    Uncovering the Mystery of Wave Function Symmetry

    Hello again! Say I have a potential well, between 0 and a. I also know how the wave function looks like for (t=0): \psi(x,0)= \frac {2bx} {a} for 0<x<\frac {a} {2} and \psi(x,0)= 2b(1- \frac {x} {a} ) for \frac {a} {2} <x<a Now, I wish to find the wave function of a general time...
  16. M

    High symmetry point in GaAs superlattice

    Hi I have a problem that i couldn't solve by myself with my little background. I want to plot the bandstructure for a GaAs superlattice, the z-axis is the 111 direction. The structure is non periodic in the z direction and periodic in the x and y direction. The process is totally different then...
  17. M

    High symmetry points for a GaAs superlattice

    Hi I have a problem that i couldn't solve by myself with my little background. I want to plot the bandstructure for a GaAs superlattice, the z-axis is the 111 direction. The structure is non periodic in the z direction and periodic in the x and y direction. The process is totally different then...
  18. T

    Exploring Symmetry in Extra Dimensions: SO(n,1) & SO(3,1)xG

    Hi how, in my master project I am working on extra dimensions and I am asking my self why is it common to start most of the theories with a space time symmetry given by SO(n,1) (n>4) and then compactify the obtained spectrum to SO(3,1)xG (where G is an abitrary symmetry group). Because...
  19. T

    Calculating the killing vector fields for axial symmetry

    hi, i need to calculate the killing vector fields for axial symmetry for a project so i can study the galaxy rotation curves. i am assuming the galaxy to be a flat disk, in addition to being axially symmetric. so i figured that the killing vector fields with respect to which the metric...
  20. TrickyDicky

    Exploring FRW Symmetry to Geometrical Patterns in FRW Metrics

    Does anybody know what kind of geometrical symmetry FRW metrics present? I know it's not spherically symmetric, but I think I recall having read it shows radial symmetry.
  21. A

    Extending the Symmetry Group: Even/Odd Z2 Symmetry?

    I am extending the standard model symmetry group by introducing discrete symmetry (Z2). The group could be (I, G) or (I, -G). Is that called even and odd Z2 symmetry? What is the difference of considering either of them?
  22. J

    Spontaneous symmetry breaking, Higgs mech, and particles getting masses?

    I'm trying to get a basic picture in my head of particles having mass. I always seem to come across the ridiculously vague statement that "the Higgs mechanism gives particles mass", and a passing mention of "spontaneous symmetry breaking". There is a lot of stuff confusing me at the minute so...
  23. B

    How does symmetry affect the shell theorem?

    Gauss' shell theorem states that if given a spherical shell of charge such that the charge is uniformly distributed on the surface, the net electric field anywhere inside the sphere is zero. But I'm wondering (and turns out this was on a past exam), what happens if the charge is not uniformly...
  24. K

    Exploring Time Dilation Symmetry: A Case Study of a Rocket Traveling at 0.8c

    Homework Statement Hi, I have a problem connected with time dilation symmetry, which is supposed to be explained in a following example: A rocket traveling at 0.8c starts from station P and is directed to station Q 864 million km away. Time taken to travel as measured by space station clocks...
  25. R

    On monopoles' symmetry and other concerns

    Ok so, I have a few question regarding the symmetry and other properties of the magnetic monopoles. I see how they actually arise from a mathematical symmetry of Maxwell equations, but my first question is: if they were discovered to exist (experimentally speaking), would there be no need in...
  26. A

    Symmetry Elements of XeF4: Meaning of 2C2 & σh

    In my lecture notes the symmetry elements for XeF4 are listed as: [PLAIN]http://img690.imageshack.us/img690/7216/syms.png but nowhere does it explain what 2C2 or σh means. What are these symmetry operations?
  27. T

    Twin Paradox: Explaining Symmetry & Age Difference

    Hi, i want to ask about the basic explanation of twin paradox. In the explanation it says one twin has to accelarate to come back and the symmetry is broken and so one twin is older than other. Could you explain this symmetry and aging relation?
  28. J

    Listing the elements of a symmetry group of a frieze pattern

    I have run into a problem where I have a frieze pattern F, the frieze pattern has horizontal refelctive symmetry, glide reflective symmetry, but does not have 180 degree rotation and does not have vertical reflective symmetry. G represents the symmetry group for F. G={reflection symmetry...
  29. H

    Nambu Modes: Necessary & Adequate Condition of Symmetry Breaking

    Dear all, I have a question regarding the usual Goldstone theorem, which states that, for a system with continuous symmetry breaking, massless bosons must appear. However, if you look at the derivations of this theorem [1], the crucial assumption seems that, the conserved quantity associated...
  30. M

    Determining Symmetry of Matrix F: ABA

    Homework Statement Let A and B be symmetric n x n matrices. Determine whether the given matrix must be symmetric or could be nonsymmetric. F=ABA Homework Equations (AB)^T=B^T A^t The Attempt at a Solution So if it's symmetric, that means (ABA)^T=ABA. I decided to make A one...
  31. J

    Symmetry of Young's Tableaux with conjugate representation

    This isn't an assigned problem, just a popular forum I was hoping someone here would be able to help or move it to where it should be... Homework Statement I was working out the Young's tableaux for two SU(3) representations where 3 \otimes 3 = 6 \oplus \bar{3}, where the 6 is symmetric...
  32. A

    How to Prove <v_x>=0 for Weakly Interacting Gas Molecules?

    The question is: for a gas of weakly interacting molecules show that <v_x>=0 where <v_x> is the average velocity in the x direction. the probability of a molecule having a velocity v is given by: p(v_{X})=\sqrt{\frac{m}{2\pi kT}}e^{-\frac{mv_{x}^{2}}{2kT}} The above is a Gaussian...
  33. D

    Particle Exchange Symmetry Question

    I am having some trouble understanding particle exchange symmetry and I'm working on the most basic problem with 2 spin-1/2 particles in a 1D infinite square well. I understand that a singlet state requires a symmetric spatial wave function and a triplet requires an antisymmetric wave...
  34. H

    Galilei, Poincare and conformal symmetry

    Reading this article: http://arxiv.org/abs/math-ph/0102011 made me wonder: 1.) So, it appears that Galilean transformations are not the most general symmetry transformations of nonrelativistic mechanics. Fine. 2.) The article states that the two additional symmetries are the nonrelativistic...
  35. N

    Which symmetry follows Ward-Takahashi identity?

    Please teach me this: It seem to me the Ward-Takahashi is validated by the renormalization, if the theory can not be renormalized the proof of Ward identity is failed.In QED the Ward identity is validated by electrical charge renormalization. The Ward-Takahashi implies a current...
  36. N

    Why are there several gauge fixing choice for gauge symmetry fields?

    Please teach me this: For gauge symmetry fields,only one of any elementary subconfiguration of the whole configuration covers the all physics of the field.So we need to cut off the redundant configuration.It seem to me,in a loose sense,there is only one way to cut off the redundancy(the gauge...
  37. F

    Symmetry, Lagrangian, Qm, and diff eqs.

    I'm looking for a summary of what invariance or symmetry of the Action in Feynman's path integral has on the equations of motion and on measurement. Do different symmetry groups of the Action integral result in different equations of motion for different particles? Is the least action principle...
  38. L

    Gauge symmetry for spin 1/2 fields

    Why is there no gauge symmetry for spin-1/2 fields? Has gauge symmetry to be related to spin-1 fields/ particles? thanks
  39. N

    Electric charge and spontaneous symmetry breaking

    Hi, If I have a Lagrangian of complex scalar field (just U(1) local invariance). And I know that phi^star describes field with -e electric charge and phi describes field with e electric charge. How do I apply "charge issue" when I write Lagrnangian after spontaneous symmetry breaking in...
  40. H

    Time reversal symmetry breaking

    We know velocity/momentum and magnetic field both are odd to time-reversal operation. Then how is the time-reversal symmetry broken in quantum Hall effect since magnetic field is always coupled with velocity/momentum?
  41. I

    Proove interchange symmetry of the Riemann curvature tensor

    Homework Statement Proove that: R_{abcd} = R_{cdab} Homework EquationsThe Attempt at a Solution I'm not sure whether to expand the following equations any further (using the definitions for the christoffel symbols) and hope that I can re-label repeated indexes at a later stage or if there is...
  42. L

    Unraveling the Mystery of Super Symmetry

    Well, I've really been getting into Quantum Relativity and Quantum physics, and one thing really just seems fuzzy to me. Super Symmetry. Wikipedia goes into too much math and history and blah blah blah... Other sites just say the history of discovering super symmetry Some sites are...
  43. M

    Understanding Symmetry in ODE Solutions

    dy/dx = (2/pi^(1/2))e^(-(x^2)) eq 1.17 My book makes a statement about the symmetry of the family of solutions to this diff eq I don't quite understand. "Symmetry. If we replace x with -x on both sides of 1.17, the right hand side is unchanged but the left hand side changes signs. So...
  44. M

    U(1) symmetry breaking within the superluid phase

    Hi With the Bose-Hubbard Hamiltonian (BHH) being invariant under a U(1)\equivO(2) symmetry transformation, it is said that the hopping-term in the BHH tends to break the U(1) symmetry as the system leaves the insulating phase. This is not clear to me. However within the mean-field...
  45. E

    Time Reversal Symmetry: Particle Motion

    Hi there! You have a particle moving to the left as time goes on. Now if you reverse the time the particle will move to the right. Does it mean that the system is not symmetric under time reversal?
  46. R

    A pencil game, strategy based on symmetry

    Homework Statement Two players A and B place in alternated way pens on the quadratic table. http://img37.imageshack.us/img37/3051/grazn.jpg (my table is not quite quadratic as it should be) The only condition is that the pens cannot come into a contact with one another. The player who can...
  47. R

    Exploring Symmetry Group of a Greek Vase

    Homework Statement Show that symmetry operations for en greek vase build up a symmetry group. Homework Equations For en greek vase we have \Gamma=[e, C_{2},\sigma, \sigma^{'}] And there are 3 conditions which must be fullfilled so that the elements will create a symmetry...
  48. P

    Covariance equations of motion and symmetry

    Homework Statement Hi, I need to proof the covariance of the equations of motion under an infinitesimal symmetry transformation. Homework Equations Equations of motion: E_i = \left(\frac{\partial L}{\partial \chi^i}\right) - \partial_{\mu} \left(\frac{\partial L}{\partial \chi^i_{\mu}}\right)...
  49. E

    What Is the Symmetry Factor of a 4-Point, 1-Loop Diagram in QCD?

    Homework Statement Calculate the symmetry factor of a 4-point, 1-loop diagram in QCD. Two legs are external, two are not Homework Equations I don't know how to include pictures here, but let's try to describe it: -It basically consists of 2 four-vertices connected by two propagators...
  50. C

    Symmetry of f(x) = x^2 - 6x: Even or Odd?

    Homework Statement How can I tell if the following equation is symmetrical and whether it is even or odd? Homework Equations f(x) = x^2 - 6x The Attempt at a Solution I would guess that it is symmetric about x = 6 but that's not what the book says.
Back
Top