What is Symmetry: Definition and 956 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. W

    The Principle of Symmetry: Universal?

    Is the principle of symmetry is universal? i.e every particle has an anti particle,similarly maxwell derive his equations by using symmetry.
  2. Z

    Particle-hole Symmetry: Definition & Resources

    Hi I've heard this term a few times and I couldn't find a definition in textbooks.. What is the definition of Particle-hole symmetry? I gather it's something like taking c -> c+ , but is there a definition of an symmetry operator that commutes with the hamiltonian or something? What does it...
  3. R

    Does Noether theorem apply to gauge symmetry?

    Basically, the title says it all. I've never heard of Noether charge corresponding to gauge symmetry of the Lagrangian. Is it because gauge symmetry isn't the "right type" of symmetry (one parameter continuous symmetry) so the Noether theorem doesn't apply to it?
  4. tom.stoer

    Top-quark condensate and el.-weak symmetry breaking

    Does anybody know a good (short) reference which explains how a top-quark condensate acting like a "bound state Higgs" generates both fermion and W- / Z-masses?
  5. T

    Custodial SU(2) approximate symmetry

    what is meant by the custodial SU(2) approximate symmetry as a 5, a 3? it is always mentioned in the Higgs triplet, charged higgs context.
  6. E

    Electroweak symmetry breaking without Higgs boson?

    I saw this paper listed, http://arxiv.org/abs/1012.5529 Asymptotically safe weak interactions Xavier Calmet (Submitted on 26 Dec 2010) "We emphasize that the electroweak interactions without a Higgs boson are very similar to quantum general relativity. The Higgs field could just be a...
  7. L

    Understanding Symmetry in Double Integrals

    Homework Statement Let D be the triangular domain given by 0\leq y \leq3, (y/3)-1 \leq 1-(y/3). Then \int\int (e-x^{5}e^(sqrt(1+y^2)) Homework Equations The Attempt at a Solution There is a quick way to solve it by breaking apart the double integral and then, apparently the x^5...
  8. P

    Polar Coordinate Symmetry with Double Angles

    Homework Statement Given the equation r²=25sin2Θ Asked to find symmetry with respect to line Θ = pi/2 Homework Equations w.r.t. Θ = pi/2: (r,Θ) - (r, pi-Θ) and (r, Θ) - (-r,-Θ) The Attempt at a Solution For the first case, I plugged in (pi-Θ) for Θ, but I'm confused about what to do...
  9. J

    What Does SU(2) and SU(3) Symmetry Mean in Particle Physics?

    I keep seeing these things being mentioned called SU(2) and SU(3) symmetry in particle physics literature. However, I don't know what they mean, and googling around just brings up pages of weird looking mathematics that I don't have the time to sift through and learn right now. Can anyone give...
  10. U

    Symmetry of Cyclohexane: How Many Vibrations in Its Spectrum?

    Homework Statement Determine the point group of the chair conformer of cyclohexane. How many Raman active vibrations and how many infrared active vibrations might you expect to detect in its spectrum? Homework Equations (see link below) The Attempt at a Solution...
  11. FlexGunship

    The Sock Toe-Hole Symmetry Breaking Problem

    I love my nice argyle socks (which I've collected from Christmases passed). But I've noticed a weird inequality in their aging behavior. Toe holes do not form evenly on both sides of the sock. My socks are not "footed" or "handed." That is to say, I do not have a left-sock, or a right-sock...
  12. E

    Primer on conformal / dual conformal symmetry

    Hey guys, i am looking for some primer on conformal, dual conformal symmetry, respectively. I have to read a lot of stuff about scattering amplitudes for uni and in recent papers people talk a lot about these symmetries... unfortunately i am not so familiar with them, so does any of you know...
  13. arivero

    Witten of the arguments about B-L symmetry

    I have found this small review by Witten of the arguments about B-L symmetry and its role in neutrino masses. http://arxiv.org/abs/hep-ph/0006332 I have been always amazed about the mismatch between the role of this symmetry in any attempt to unify interactions, including Weinberg-Salam, and...
  14. K

    Symmetry factors (Srednicki, figure 9.11)

    In Srednicki's QFT book on page 63, figure 9.11, the diagram in the middle of the second row is a Feynman diagram with four external lines, two vertices, one internal line and one loop placed on one external line. It has symmetry factor 4. Does the symmetry facor stand for the 4 possibilities...
  15. nomadreid

    Is the Many-Worlds Interpretation Symmetrical?

    The Many-Worlds interpretation tells us where the information “goes” at a measurement. Does it also tell us where the information “comes from” afterward to create the new undetermined state? If it is symmetrical, then does that mean that a measurement is the result of confluence or interference...
  16. arivero

    Which symmetry protects the yukawa couplings?

    I asked this in a thread on string theory, but the answer could well be in the standard model, so here I ask the same from the traditional point of view. Naturalness tells us, roughly, that if there is a quantity near zero, it is because a slightly broken symmetry protects it. Of the 24...
  17. E

    What if electro-weak symmetry is broken at all energies?

    The common understanding is that below around 250Gev the weak force gauge bosons have mass and appear distinct from the electromagnetic force, with its massless photons. And that to explain this required hypothesizing the Higgs field, which acts like a superconducting field, in the vaccuum...
  18. S

    Moment of Inertia (not through symmetry axis)

    Homework Statement What is the moment of inertia of a solid cylinder (of mass 8.41kg and radius 7.5cm) rotating about an axis parallel to the symmetry axis but passing through the edge of the cylinder?Homework Equations I=.5mr2, but how does this change when the axis is passing through the edge...
  19. J

    Spontaneous Symmetry Breaking of SU(3)

    Homework Statement The generators of SU(3) are the Gell Mann matrices, \lambda_a. Consider symmetry breaking of an SU(3) theory generated by a triplet of complex scalar fields \Phi = \left(\phi_1, \phi_2, \phi_3\right). Assuming the corresponding potential has a minimum at \Phi_0 =...
  20. K

    Groups & Symmetry: Exploring the Connection

    Why do groups descibe symmetry? Why does a set which has an identity and inverse element, is closed under an abstract multplication operation and whose member obey the association law, captures symmetry? Why is that? thanks
  21. bcrowell

    Inflation requires initial symmetry?

    I'm reading Roger Penrose's Cycles of Time. On p. 124 he's explaining why he thinks inflation doesn't solve the mystery of why the universe started out in a low-entropy state. He argues that a high-entropy collapsing FLRW universe would consist of "a horrendous mess of congealing black holes,"...
  22. S

    Molecular Symmetry & Characters in MO Theory & Spectroscopy

    So I'm trying to teach myself MO Theory and Spectroscopy. I was just wondering why symmetry was so important in understanding these and what characters are used to do. I know this is a broad question, but I've been reading a lot (Cotton, etc..) so I know they have to do with integrals and...
  23. B

    Given this formula, is this formula true by symmetry?

    Homework Statement I know that, \left[ {f(x),p} \right] = {\bf{i}}\hbar \frac{{df}}{{dx}} By symmetry, is it also true that, \left[ {f(p),x} \right] = {\bf{i}}\hbar \frac{{df}}{{dp}} ...since x and p are just symbols?
  24. mnb96

    Symmetry Groups in Euclidean and Hyperbolic Spaces: A Comparison

    Hello, how do symmetry groups in the Euclidean space differ from the symmetry groups in the hyperbolic space (in the Poincaré disk) ? I've been told that in the hyperbolic case one has at disposal a richer "vocabulary" to describe symmetries, but I don't see how, and maybe I misunderstood...
  25. J

    Questions about chiral symmetry breaking

    Hello everyone, I was learning about the topic "chiral symmetry breaking" recently and got couple questions. I try to describe my understandings below, then list the questions: From the QCD Lagrangian level (quark level), I can understand the exact chiral symmetry exists when we take...
  26. J

    Symmetry of the Bloch Ground State

    I was reading Hasan & Kane's review on topological insulators and right in the beginning, page 3, they say that the Bloch ground state is U(N) invariant. I do not see that. Would anyone be able to show it or point to a reference? Thanks, Jan.
  27. P

    Atom position (coordinates) from symmetry

    Hi guys, I need to write down the positions of all the atom in LaFeAsO unit cell: Figure caption: "The quaternary equiatomic ZrCuSiAs-type structure is very simple, with only eight atoms in the tetragonal cell. The dashed lines represent a unit cell." I also have these informations...
  28. L

    Understanding Γ5 & Chiral Symmetry in QFT

    recently i am reading chiral symmetry in QFT. Almost all textbooks define γ5 as a chiral operator without saying some reasons. i am very confused why γ5 has something to do with chiral symmetry, can somebody explain it more intuitively and physically? who first introduce γ5 as a chiral...
  29. M

    Curves, relationships, functions and symmetry

    For the following curves i) y=x^2+4x-1 ii) y=-2+or-Square root(x+5) a) Sketch both the curves on the same sheet of graph paper- against the same axis I have done this, although I have not shown it here b) Determine with proof, whether the above curves are related. Not sure how to do this...
  30. I

    What is the origin of the 1/2 symmetry factor in Feynman diagrams?

    I was suddenly confused by the calculation of symmetry factors of Feynman diagrams. For example, in Peskin's textbook, as the attached pdf file, Below eq(4.45), he calculated the symmetry factor in detail, however, I was confused by the last 1/2 factor. I'm trying to realize this...
  31. R

    Have You Noticed the Symmetry of Primes in the Sieve of Eratosthenes?

    just got dumped out and lost my thread, so will keep this brief and add later once accepeted www.primepatterns.wordpress.com anyone noticed the symmetry of primes (well pseudoprimes if you must) starting at each p#/2 i.e. 105, 1155, 15015? they arise from the Sieve of Erathosthenes and...
  32. J

    What symmetries does the standard model lagrangian possess?

    I wanted to understand what symmetries the standard model lagrangian has, and what "effective" (don't know what to call this) symmetries our universe has due to the vacuum state breaking the symmetry. Unfortunately, I'm having trouble extracting that information from the Lagrangian of the...
  33. Delta2

    Understanding Conservation and Symmetry in Physics

    We say that conservation of linear momentum follows from the translational symmetry while conservation of angular momentum from directional (rotational) symmetry. Can anyone explain what exactly do we mean by these kind of symmetries and how they imply conservation of certain quantities?
  34. S

    Symmetry in Landen's transformation in elliptic integrals

    http://en.wikipedia.org/wiki/Landen%27s_transformation" Since both the expressions a_1 and b_1 in Landen's transformation are selected in an arbitrary manner, is it all right to define a_1 with the geometric mean and b_1 with the arithmetic mean, instead of as given in the above link? I...
  35. P

    Dynamical chiral symmetry breaking

    I don't know if it is the correct sub-forum, if I choose wrong then feel free to move the thread. I was listening to a talk today using DCSB. I think I could get a glimpse on some other parts of the talk and found some ideas intriguing. I would like to understand them better, but I cannot...
  36. S

    Symmetry of higher order partial derivatives

    Hi, As per Clariut's theorem, if the derivatives of a function up to the high order are continuous at (a,b), then we can apply mixed derivatives. I am looking at http://en.wikipedia.org/wiki/Symmetry_of_second_derivatives and I cannot understand in the example for non-symmetry, why the...
  37. L

    Maxwell–Faraday equation symmetry violation

    I still wonder about this. A simple results of this equation is: If a charge has a velocity in the positive y direction [v = (0,1,0)] and it accelerates in the positive x direction (it curls) then there will be a magnetic field in the positive z direction. There will be no magnetic field...
  38. Q

    Goldstone boson without symmetry?

    Hi, I was wondering about the U(1)_A problem. The Lagrangian exhibits a (in the limit of vanishing quark masses) U(1)_A symmetry but due to the chiral anomaly, the current J_5^{\mu} is not conserved: \partial_{\mu}J_5^{\mu} = G\tilde{G} + 2i\bar{u}\gamma_5 u +... The G\tilde{G} term...
  39. MathematicalPhysicist

    Question regarding CP symmetry and weak interaction

    I have the next decay: B^0 \rightarrow D^+ e^- \nu_e The question is: employ CP symmetry on the particles in this process, what reaction would you get? and what would happen if CP symmetry breaks? Now if I employ CP symmetry I get: B^0 \rightarrow D^- e^+ \bar{\nu_e} But in my...
  40. U

    Special relativity: proof of symmetry concept

    Homework Statement I am given a symmetric tensor A, meaning A^{\mu\nu}=A^{\nu\mu} and I am given an asymmetric tensor B, meaning B_{\mu\nu}=-B_{\nu\mu} Now I need to show that: A^{\mu\nu}B_{\mu\nu}=0 0) Homework Equations We know that an asymmetric tensor can be written as...
  41. C

    Make sure the Lagrangian symmetry？

    Is the Lagrangian of the neutral Proca field \mathcal{L}=-\frac{1}{16\pi}\left(F^{\mu\nu}F_{\mu\nu}-2m^2 A_{\mu} A^{\mu}\right) symmetric? And How to make sure whether it's symmetric.
  42. T

    Temporal symmetry solves all quantum paradoxes?

    Excerpted from an article by U. of Hawaii Physics Professor, Victor J. Stenger: "As has been known for seventy years, quantum phenomena depend not only on the initial conditions of an experimental setup but also on the final conditions. This observation already signals that the quantum...
  43. B

    Moment of inertia and axis of symmetry

    Homework Statement Derive an expression for the moment of inertia about the axis of symmetry for a cylinder of mass M , length L and radius a, where the mass density decreases as a function of distance from the axis as 1/r Homework Equations The Attempt at a Solution 1) am i...
  44. J

    Symmetry Problem Analysis in Ansys Workbench

    Hello everybody, that´s a simple question: I have a symmetry problem to analisys using Structural Mechanic on Ansys Workbench. I´ve applied a Symmetry function on Design Modeler. Can I visualize the result on the whole geometry? Thank´s in advance
  45. C

    Why is E3 zero for cubic symmetry?

    The total electric field is given as Etotal = E0 +E1 +E2 +E3 Where E0 is the applied field, E1 is the depolarization, E2 is caused by polarization of a hypothetical sphere while E3 is the one dependent on lattice geometry... How come E3 is zero for cubic symmetry? Can I picture this as...
  46. U

    How Can You Determine Point-Rotational Symmetry of a General Function?

    Homework Statement Given f(x), find an expression to check whether f(x) has rotational symmetry about any arbitrary point (h, v).Homework Equations If f(x) = f(-x) then the function is symmetrical about the y-axis. If f(x) = -f(-x) then the function is point-rotational about the origin.The...
  47. K

    Symmetry breaking: what is the subgroup left?

    Hi... I have studied the standard model and know that spontaneous symmetry breaking by a vev breaks SU(2)xU(1) to a U(1). How do we know to what group a vev will break the original group? I have heard of Dynkin diagrams. Are they only for continuous groups? Is there any other method for...
  48. Y

    Question on Dirichlet problem in cylinder with radial symmetry.

    This is not homework. I have problem deriving the solution for cylinder with radial symmetry given: \nabla^2U(\rho,z)=R''+\frac{1}{\rho}R'+\frac{Z''}{Z}=0 Which give \rho^2 R''+ \rho R' -k\rho^2 R=0 \hbox { and } Z''+kZ=0 With given boundary conditions U(\rho,0) = U(\rho,h) =0...
  49. 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...
  50. 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...
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