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. C

    Question about symmetry of length contraction

    Say we have two inertial observers Bob and Alice moving relative to each other at a significant fraction of the speed of light c (say 0.5c). Bob is moving to the left relative to Alice and Alice to the right relative to Bob. When their origins cross, a pulse of light is emitted to the right...
  2. J

    Solving Volume and Symmetry: Find Integral from Calculator

    Homework Statement Your supposed to set up the integral and do it from the calculator. y = , y = (cosx)^2, -pi/2 <= x <= pi/2 a. x axis b. y axis Homework Equations I = ∏∫(cosx)^4 dx = 3.70110 and for part b I = ∏∫((1)-(cosx)^2)^2 dx = 3.70110 The Attempt at a Solution Did...
  3. shounakbhatta

    Symmetry and models of Symmetry

    Hello, I am quiet new to this subject. I am reading over grand unified theory and found that there are quiet a number of Symmetries, like U(1) and SU(2)..... Can anybody help me in finding all the types of symmetries and how it evolved and what are they basically are? Thanks
  4. D

    Unraveling the Mystery of Symmetry Groups in Physics

    Hello, PF have helped me a lot understanding a lot of important things in physics, I hope you guys can help me with this too :). I have problems understand the symmetry groups. I know there are groups like SU(2), O(3).. etc. But I have no idea how they represent certain particles.So particles...
  5. B

    Error in proof for symmetry groups?

    \renewcommand{\vec}[1]{\mathbf{#1}} Here is an excerpt from the text: "[...]Theorem 12.5 The only finite symmetry groups in ℝ^2 are \mathbb{Z}_n and D_n. PROOF. Any finite symmetry group G in \mathbb{R}^2 must be a finite subgroup of O(2); otherwise, G would have an element in E(2) of...
  6. J

    Mirror symmetry in String Theory?

    From looking at the Wikipedia entry on string theory I gather that it is found that any given physical model implies two Calabi-Yau spaces. Perhaps one space gives rise to a sector of particles with left-handed weak interactions and the other gives rise to a sector with right-handed weak...
  7. F

    Does the CC depend on symmetry breaking?

    I wonder if symmetry breaking of the U(1)SU(2)SU(3) symmetries of the standard model have anything to do with the calculation of the cosmological constant. Do we assume that the symmetries are broken or unbroken in the current calculation of the CC? As I recall, one way symmetry is broken in...
  8. M

    Symmetry violation in the early universe - a book

    Hi there, I've done some searching around on the forums and in the library, but I haven't found what I was looking for - some information of symmetry violation in the early universe. I know some small pieces of information but I'm currently trying to consolidate that so that I have an actual...
  9. M

    Symmetry violation in the early universe - a book

    Hi there, I've done some searching around on the forums and in the library, but I haven't found what I was looking for - some information of symmetry violation in the early universe. I know some small pieces of information but I'm currently trying to consolidate that so that I have an actual...
  10. T

    Skew Symmetry: Inner Product of Rows & Determinant

    I am entranced. I mean There are so many thing which seem to deal with skew symmetry, like the skew anti-symmetric matrices of Electromagnetic 4-tensor, I have this thing, a question. And it is stated as: " if you take the inner product of the rows of a skew symmetric matrix would it be equal to...
  11. S

    Time-reversal symmetry protection

    Hi there! I'm a third-grade physics student and I'm trying to understand the physics of topological insulators, I have found this thread, where somebody else has already asked this question, but in that thread it wasn't really answered in details, they concentrated on other issues. My...
  12. B

    Find Symmetry in Molecules: NMR Spectra & 3D Structures

    What is the general method for finding symmetry in molecules which would allow you to find which nuclei are equivalent in an NMR spectrum? I know it sounds vague but it seems inevitable. Any good guides on the Internet would be great. My main issue is with larger molecules whose structures are...
  13. S

    Why there is parity Symmetry ?

    Greetings, Can someone give a detailed explanation of why the expectation value of z coordinate in the ground state of hydrogen atom is zero due to parity symmetry? In addition how do you represent parity inversion in spherical coordinates and how do spherical harmonics behave under this...
  14. C

    Self energy logarithmic divergence due to chiral symmetry.

    In peskin at page 319 right above equation (10.6) he writes "If the constant term in a taylor expansion of the self energy were proportional to the cutoff ##\Lambda##, the electron mass shift would also have a term proportional to ##\Lambda##. But the electron mass shift must actually be...
  15. omephy

    Symmetry factor of a general Feynman diagram

    I am studying QFT from Srednicki's book. Let me ask a question about symmetry factor from this book. Let, for specific values of V and P from eqn (9.11) we get some terms. One of them is a disconnected diagram consisted of two connected diagrams C_1 and C_2. The disconnected diagrams...
  16. S

    Symmetry in finite element

    Hello, Please help my question is really basic,but i need help I have concrete box and steel box and bolt as illustrated in picture one(quarter shape),so my questions are: the key points in symmetry for the quarter of the shape are: 1.prevent translation in the two plan...
  17. N

    Generalizing symmetry axis of constant-contour ellipses

    Hi I am looking at the contours of the following function f, which trace out an ellipse: f(x, y, z) = \exp(-x^2a)\exp(-y^2b) Here a\neq b are both positive, real constants. The axis of these ellipses is along z. Now, I am wondering how to generalize the function f such that the symmetry...
  18. K

    Solve Symmetry Continued Homework: f(x)+f(a+b-x)=2f((a+b)/2)

    Homework Statement This is the second part of a question I asked earlier. I tried to figure it out but was having trouble even with 4 of my peers. PART 1 (SOLVED) A function f is said to symmetric about a point (p,q) if whenever the point (p-x, q-y) is on the graph of f, then the point...
  19. K

    What is Symmetry about a Point (p,q) and its Relationship to Function Values?

    Homework Statement A function f is said to symmetric about a point (p,q) if whenever the point (p-x, q-y) is on the graph of f, then the point (p + x, q - y) is also on the graph. Said differently, f is symmetric about a point (p,q) if the line through the points (p,q) and (p+x, q+y) on the...
  20. I

    MHB Function of symmetry character for comparing two optimization methods

    First refer to this question:Is this function "$h$" symmetric of the plane $x=y$? - Mathematics Stack ExchangeThe main problem is to find an appropriate (objective) function (a curve) to compare the implicit filtering method and Nelder-Mead method for optimization. The backgrounds of these...
  21. N

    Electric Field Distribution of a Charged Disk: The Role of Symmetry

    Hey. Let's say you have an infinitely wide and long disk with a thickness h. Inside the disk, there is a constant charge density ρ0. Why would the electric field lines be perpendicular to the disk? Can somebody explain how symmetry and such generally affect electric field distribution of a...
  22. pellman

    Symmetry of connection coefficients? (simple question)

    If we have a metric connection with no other restrictions (torsion may be non-zero), do the connection coefficients {\Gamma^{\alpha}}_{\mu\nu} have any symmetries among the indeces? I'm thinking not. Or.. for a Levi-Civita connection, the only fixed symmetry condition is...
  23. N

    Why symmetry breaking a paradigm whilst not describing Fermi liquid?

    Hi! So I'm a bit confused: first off, does Fermi liquid theory have "order". I suppose it depends on how you define order. But in case it does, is it described by symmetry breaking? From what I read, I think it does have order which is not described by symmetry breaking. But then I have...
  24. K

    True Or False: Symmetry, anti-symmetric, asymmetry.

    Homework Statement State whether the following are true or false. If false, give a counter-example: 1. ≽ is not symmetric \Rightarrow ≽ is not asymmetric 2. ≽ is not symmetric \Rightarrow ≽ is not antisymmetric 3. ≽ is not antisymmetric \Rightarrow ≽ is not asymmetric Homework...
  25. M

    E field between 2 wrinkled spheres, radial symmetry?

    \oint E\cdot dA=|E|\int_{0}^{2\pi}\int_{0}^{\pi}(1+1/2sin6\theta\sin5\phi)^2sin\phi d\phi d\theta =|E|\int_{0}^{2\pi}(\frac{25}{99}sin^2(6\theta)+2) d\theta =|E|\frac{421\pi}{99}= \frac{\rho_{q}}{\varepsilon o}\int_{0}^{2\pi }\int_{0}^{\pi }\int_{0}^{(1+\frac{1}{2}sin6\theta sin5\phi...
  26. J

    Wavefn symmetry requirement

    Both Rho^0 and Pi^0 are bosons so require an overall symmetric wavefn. However, they are in different spin states: the Pi is in the anti-symmetric S=0 state and the Rho is in one of the symmetric S=1 states. Which other part of the overall wavefn (color, flavor, spatial) differs between the two...
  27. S

    Symmetry Problem Homework: Find Point of Ellipses

    Homework Statement Find the point in respect to these ellipses are symmetrical x2 + 3y2 - 2x -2 = 0 x2 + 3y2 +6x + 12y +18 = 0 Homework Equations x = 2a - x' y = 2b - y' The Attempt at a Solution I have applied the equations of symmetry to the first equation then I've equaled the...
  28. N

    Testing symmetry properties of nonlinear governing equations

    Hi, I'm a bit uncertain about the validity of my argument/approach to the following: I'm trying to prove that the solution to a partial differential equation \frac{\partial u(x,t)}{\partial t} + N[u(x,t)] = 0, where N is some nonlinear operator, CAN BE (not necessarily is) asymmetric...
  29. Y

    Why is the Symmetry Group of the 9j Symbol Isomorphic to S_3 x S_3 x S_2?

    Hello everyone, I read in Edmond's 'Angular momentum in Quantum Mechanics' that the symmetry group of the 9j symbol is isomorphic to the group S_3 \times S_3 \times S_2. Why is this? Can anyone shed some light on this?
  30. P

    SU(2) symmetry of the ammonia molecule?

    Hi, I'm an undergraduate taking the basic quantum classes and on my own, I'm trying to wrap my mind around how symmetry and group theory applies in Q.M. and theoretical physics in general; it's coming along slowly but surely! Can someone please explain why the ammonia molecule is said to...
  31. G

    Understanding Spontaneous Symmetry Breaking in Quantum Field Theory

    Is there a reason why we have to expand a field ψ about the true vacuum |Ω>? Can't we just do field theory about ψ=0 instead of about ψ=<Ω|ψ|Ω>? Also, I'm a bit confused about other fields. For the E&M potential, under the true vacuum, wouldn't we need to expand about A=<Ω|A|Ω> instead of...
  32. Y

    Spontaneous symmetry breaking: How can the vacuum be infinitly degener

    Spontaneous symmetry breaking: the vacuum be infinitly degenerate? In classical field theories, it is with no difficulty to imagine a system to have a continuum of ground states, but how can this be in the quantum case? Suppose a continuous symmetry with charge Q is spontaneously broken, that...
  33. J

    About spin being an internal symmetry

    As we know, spin is an internal symmetry. but it seems a bit different from other internal symmetry, e.g. electrical charge, color, flavor... because it can be coupled with orbital angular momentum and in some aspects be linked to space-time. further more, we can classify all the particles into...
  34. Y

    Isomorphism symmetry group of 6j symbol

    Hi everyone, I read in 'Angular momentum in Quantum Mechanics' by A.R Edmonds that the symmetry group of the 6j symbol is isomorphic to the symmetry group of a regular tetahedron. Is there an easy way of seeing this? I've tried working out what the symmetry relations of the 6j symbol do...
  35. T

    Maxwell's equations from U(1) symmetry

    I understand that one is able to derive the inhomogenuous pair of Maxwell's equations from varying the field strength tensor Lagrangian. Now implying the U(1) gauge invariance, how is one led to the Maxwell's equations?
  36. E

    Intuition for symmetry currents

    How should I think about symmetry currents?... in particular, when there are no fields to "carry the charge", eg in a pure Maxwell theory or, maybe, in a CFT of free scalars? Perhaps it would help if someone elucidated the connection between the "charge" in Noether's theorem and the "charge" in...
  37. Whovian

    Trouble explaining Gauge Symmetry

    I'm currently attempting to explain the concept of Gauge Symmetry to a friend. Copied and pasted pretty much directly from MathIM, (And the same applies for any other potential field, such as gravitational potential.) Would this be correct? I've tried explaining Gauge Symmetry multiple...
  38. L

    Spontaneous symmetry breaking. Ferromagnet.

    I'm not sure what people meant about this. Heisenberg hamiltonian is ##O(3)## invariant. H=-J\sum_{\langle i,j \rangle} \vec{S}_i \cdot \vec{S}_j ##\langle \rangle## denotes nearest neighbors. It has ##O(3)## symmetry. If I understand well ground state is infinitely degenerate. But system...
  39. M

    Symmetry of a graph. SymmT(A)?

    I've tried looking all over, but haven't been able to find explanations. I was wondering if anyone could provide me links to learn more about these- what's in the picture. Or if you can explain. I have already turned this work in so I'm not looking for the answers, I want explanations. I know...
  40. M

    Thermodynamics, a model of the symmetry restoration in the universe

    Homework Statement The energy density (u=E/V) of a thermodynamic system (used as a model of symmetry restoration in the early universe) is given by: u(T)=aT^4 + \Lambda(T) where \Lambda =0, T \leq T_0 or \Lambda =\Lambda_0, T>T_0 k_B T_0 = 10^{14} GeV a) Calculate the Helmholtz...
  41. Greg Bernhardt

    Particle Symmetry and the Standard Model by Matthew B. Robinson

    Author: Matthew B. Robinson Title: Symmetry and the Standard Model Amazon Link: https://www.amazon.com/dp/1441982663/?tag=pfamazon01-20 Prerequisities: Contents:
  42. F

    Uncertainty, Symmetry, and Commutators

    It seems the uncertainty principle, the commutator between operators, and the symmetry of the action integral are all related. And I wonder how universal this is. For example, the action integral is invariant with respect to time, and this leads to conserved quantity of energy. This means...
  43. DiracPool

    How Does Symmetry Underpin Conservation Laws in Physics?

    Here is a quote from Vanhees 71 in another thread on Lagrangians. I reposted here as a new thread because I fear going off-topic and redirecting a thread. In any case, in my study of Lagrangians and Hamiltonians, everywhere I go for tutelage it seems as though everyone is maniacally focused...
  44. Einj

    Chiral symmetry and quark condensate

    I'm studying chiral symmetry in QCD. I understand that in order for a spontaneous symmetry breaking to occur, there must be some state with a vacuum expectation value different from zero. My question is: can someone prove that is the chiral symmetry is an exact symmetry of the QCD then...
  45. naima

    What about physics before electroweak symmetry breaking?

    Hi Pf I would like to know if the standard model without symmetry breaking can describe the universe after the big bang before the moment when EW symmetry breaking occured. Had we v = c for all particles? were electrons electrically charged? were there photons or B ? Z0 were not born...
  46. H

    How do conservation laws arise from symmetries in classical mechanics?

    This is my first post, so hello everybody. I don't have university background and english is not my native language, so please forgive me if what I'm writing is hard to understand sometimes. I'll do my best to be clear. I've always loved physics in general, but recently came to conclusion that...
  47. T

    Gauge Symmetry in Quantum Mechanics (QM I) Explained

    Hi all, I'm taking graduate level QM I and trying to wrap my head around the notion of gauge symmetry. For some reason I've struggled with this concept more than others. I don't really have a specific question; I'm more looking to see if someone has a succinct explanation of the relevant...
  48. S

    Name of general relativity symmetry

    People seem to be seriously looking for "Lorentz violating" neutrino oscillations - meaning direct violation of special relativity. What is a short name for the symmetry that distinguishes general relativity from special (the symmetry between acceleration and gravity)?
  49. BWV

    Spontaneous Symmetry Breaking -Conceptual Question

    what is the relationship between unstable equilibria and spontaneous symmetry breaking? Would this qualify as an example of spontaneous symmetry breaking? Take a (perfectly round and unlabeled) pencil standing upright on its eraser so there is a U(1) symmetry on its original position...
  50. mnb96

    Symmetry groups on the plane

    Hello, it is known that the symmetry groups on the 2d Euclidean plane are given by the point-groups (n-fold and dihedral symmetries) and the wallpaper groups. However we can create more symmetries on the plane than just those. For example we can stereographically project the 2d plane onto...
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