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.

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

    Find Out the Symmetry of Polonium Unit Cell

    For inorganic chemistry, I am being asked to draw the solid state structure of polonium which i know how to do. However it asks what the symmetry of the unit cell is, and I don't know how to answer. I know what a unit cell is, I'm just not sure what the question means, or what it is looking for...
  2. F

    How to assign symmetry to water molecule using D4h symmetry?

    Could you explain why an H2O that attacks Ni(CN)4 ^(2-) (in square planar) (which has D4h symmetry) at one of the axial sites would have A2u symmetry? I know that the "HOMO" for the p orbital of the H2O would be a p orbital. I also tried to link that electron pair to an irreducible...
  3. zdroide

    B H boson is 125 GeV, super symmetry, multiverse not possible?

    What other theories this number make impossible or improbable. When final number was given I hear some older physicist saying for one " 40 years of works gone" second grinding "only 30 for me!" We are ask to follow establish science. Seem to me that lots of theories was built on other's ones and...
  4. Logic Cloud

    I Symmetry in Physics: Books/Papers for Physical Theories

    I am looking for books/papers pertaining to symmetry principles in physics. I am particularly interested in literature aimed at deriving physical theories from their underlying symmetries, but all recommendations are welcome. I already know of the books Symmetries in Fundamental Physics by...
  5. M

    Quantum Mechanics-Spin State for Identical Particles

    Consider a system of two identical spin-1 particles. Find the spin states for this system that are symmetric or antisymmetric with respect to exchange of the two particles. (Problem 13.3, QUANTUM MECHANICS, David H. McIntyre) I know that for bosons, the total wavefunction should be symmetric...
  6. S

    A classical example of spontaneous symmetry breaking

    Homework Statement A simple classical example that demonstrates spontaneous symmetry breaking is described by the Lagrangian for a scalar with a negative mass term: ##\mathcal{L}=-\frac{1}{2}\phi\Box\phi + \frac{1}{2}m^{2}\phi^{2}-\frac{\lambda}{4!}\phi^{4}##. (a) How many constants ##c##...
  7. N

    MHB Symmetry in the algebraic expressions

    Hello! I read about the symmetry of the following product $(x+a+b)(x+b+c)(x+c+a)$ my book says that a, b and c occur symmetrically. Why is that?
  8. S

    Conserved Noether charges for Lorentz symmetry of the action

    Homework Statement Consider the infinitesimal form of the Lorentz tranformation: ##x^{\mu} \rightarrow x^{\mu}+{\omega^{\mu}}_{\nu}x^{\nu}##. Show that a scalar field transforms as ##\phi(x) \rightarrow \phi'(x) = \phi(x)-{\omega^{\mu}}_{\nu}x^{\nu}\partial_{\mu}\phi(x)## and hence show that...
  9. S

    Conserved Noether current under SO(3) symmetry of some Lagrangian

    Homework Statement Verify that the Lagrangian density ##\mathcal{L}=\frac{1}{2}\partial_{\mu}\phi_{a}\partial^{\mu}\phi_{a}-\frac{1}{2}m^{2}\phi_{a}\phi_{a}## for a triplet of real fields ##\phi_{a} (a=1,2,3)## is invariant under the infinitesimal ##SO(3)## rotation by ##\theta##, i.e...
  10. S

    Conserved Noether current under U(1) symmetry of some Lagrangian

    Homework Statement The motion of a complex field ##\psi(x)## is governed by the Lagrangian ##\mathcal{L} = \partial_{\mu}\psi^{*}\partial^{\mu}\psi-m^{2}\psi^{*}\psi-\frac{\lambda}{2}(\psi^{*}\psi)^{2}##. Write down the Euler-Lagrange field equations for this system. Verify that the...
  11. V

    Volumes in Charge symmetry anf distribution problems

    Hi everyone, I am self-studying Electricity and Magnetism. I have a good grasp in Calculus, but still I am confused on how to figure out volumes of arbitrary figures(rest is easy). I know it's a bit silly. I mean how do we know how to choose a figure (like in case of hemisphere, you imagine...
  12. S

    A Symmetry considerations between observer and observed in QM

    The following is taken from page 101 of Warren Siegel's textbook 'Fields.' Another example is quantum mechanics, where the arbitrariness of the phase of the wave function can be considered a symmetry: Although quantum mechanics can be reformulated in terms of phase-invariant probabilities...
  13. C

    I Spontaneous Symmetry breaking of multiplet of scalar fields

    Consider a theory with two multiplets of real scalar fields ##\phi_i## and ##\epsilon_i##, where ##i### runs from 1 to N. The Lagrangian is given by: $$\mathcal L = \frac{1}{2} (\partial_{\mu} \phi_i) (\partial^{\mu} \phi_i) + \frac{1}{2} (\partial_{\mu} \epsilon_i) (\partial^{\mu} \epsilon_i)...
  14. TheJfactors

    A Boundary Value Problem Requiring Quarterwave Symmetry

    I can't seem to find an explicit or analytical solution to a boundary value problem and thought I might ask those more knowledgeable on the subject than me. If t is an independent variable and m(t) and n(t) are two dependent variables with the following 8 constraints: a) m' =0 @T=0 and...
  15. S

    I Properties of body with spherical symmetry

    I'm studing Gauss law for gravitational field flux for a mass that has spherical symmetry. Maybe it is an obvious question but what are exactly the propreties of a spherical simmetric body? Firstly does this imply that the body in question must be a sphere? Secondly is it correct to...
  16. Jimster41

    B Understanding Symmetry: Navigating Observations and Asymmetry in Closed Systems

    The part I'm confused about - in order to have two distinct observations of a system you want to check for symmetry isn't something asymmetrical is required to distinguish them... as distinct observations. If we say a system is completely closed and are restricted to refer only to that system...
  17. M

    MHB Proving the symmetry of self complementary graphs with n=4k+1

    I am trying to prove the following: Let G be a graph Let |V(G)|=n=4k+1, for k an integer Let G be isomorphic to G complement Claim: Given degree sequence for G, d1>=d2>=...>=dn, prove d(i)+d(n-i+1)=n-1 for i=1,2,...,n Now, we know for any vertex v in G, d(v)=(n-1)-D(v), where D(V) is the...
  18. Elena14

    Plane of symmetry in alphabet N

    My teacher says that "N" has no plane of symmetry(POS). But shouldn't the plane shown with blue be POS? I understand that a plane of symmetry bisects a molecule into halves that are mirror images of each other. For this reason, this plane shown here should be the POS. Where am I...
  19. S

    I Symmetry of Hamiltonian and eigenstates

    Suppose we have an electron in a hydrogen atom that satisfies the time-independent Schrodinger equation: $$-\frac{\hbar ^{2}}{2m}\nabla ^{2}\psi - \frac{e^{2}}{4\pi \epsilon_{0}r}\psi = E\psi$$ How can it be that the Hamiltonian is spherically-symmetric when the energy eigenstate isn't? I was...
  20. A. Neumaier

    A Is Poincare symmetry the real thing?

    This is a continuation of a side issue from another thread.
  21. W

    A Is CPT Symmetry Inherent in All Quantum Field Theories?

    I was looking at the wikipedia article on CPT and it starts with "Charge, Parity, and Time Reversal Symmetry is a fundamental symmetry of physical laws under the simultaneous transformations of charge conjugation (C), parity transformation (P), and time reversal (T)." What does it mean that CPT...
  22. C

    I Electroweak symmetry and unbroken generators

    I realize there has been quite a few threads on this topic lately but I wanted to ask some questions that I have here. The following are statements from my lecture notes and I have write my questions after each statement. In the gauge sector of the electroweak theory, we can write down...
  23. S

    A Exploring Chiral Symmetry in Weak Interaction

    Dear all Do we have chiral symmetry for weak interaction? I know that weak interaction is chiral. thank you
  24. wolram

    B Will super symmetry become part of cosmology

    AFAIK super symmetry as yet has no experimental evidence in cosmology, will it become part of cosmology in some useful application?
  25. H

    Infinity times zero, rotational symmetry

    To show that the Lagrangian ##L## is invariant under a rotation of ##\theta##, it is common practice to show that it is invariant under a rotation of ##\delta\theta##, an infinitesimal angle, and then use the fact that a rotation of ##\theta## is a composite of many rotations of...
  26. T

    I What breaks time reversal symmetry in ferromagnets

    I am told that in ferromagnets, time reversal symmetry is broken. However, I don't know any hamiltonian terms in solid that can break time reversal symmetry. So is there a hamiltonian term I don't know or is there any subtlety in ferromagnets?
  27. andrex904

    Single particle state and symmetry

    Known that $$ [Q^a,p^\mu]=0 $$ where Q is a representation for the a-th generator of the algebra of group symmetry and p the 4-momentum, if we consider a single particle state, eigenstate of p $$ p^\mu | \psi_A (k) > = k^\mu | \psi_A (k) > $$ then also $$ Q^a | \psi_A (k) > $$ is...
  28. W

    The elasticity/stiffness tensor for an isotropic materials

    Hi PF, As you may know, is the the elasticity/stiffness tensor for isotropic and homogeneous materials characterized by two independant material parameters (λ and μ) and is given by the bellow representation. C_{ijkl} = \lambda\delta_{ij}\delta_{kl} + \mu(\delta_{ik}\delta_{jl} +...
  29. H

    Clebsch-Gordan coefficients symmetry relation

    Why are ##<j_1j_2m_1m_2|jm>## and ##<j_2j_1m_2m_1|jm>## negative of each other when ##j_1+j_2-j## is odd as given below? I would expect ##<j_1j_2m_1m_2|jm>## and ##<j_2j_1m_2m_1|jm>## to always have the same sign since nature doesn't care which particle we label as particle 1 and which as...
  30. M

    Cylindrical symmetry, Gauss's Law

    Homework Statement [/B] A semiconducting nanowire has a volume charge density ρ(r)=ρ0(r/R) where R is the radius of the nanowire. How would you calculate the electric field inside the wire? Homework Equations Gauss's Law The Attempt at a Solution [/B] I know that by symmetry the E field...
  31. Konte

    Symmetry groups of molecule - Hamiltonian

    Hello everybody, As I mentioned in the title, it is about molecular symmetry and its Hamiltonian. My question is simple: For any molecule that belong to a precise point symmetry group. Is the Hamiltonian of this molecule commute with all the symmetry element of its point symmetry group...
  32. UchihaClan13

    How can symmetry be applied in analyzing electric circuits?

    Okay guys So I was studying up some electric current and doing electric current problems I am clear with kirchhoffs rules And with series-parallel resistor combinations But I am not quite clear with the symmetric distribution of current Or symmetry in circuits, in particular Could you guys...
  33. C

    Symmetry factors of some diagrams

    I have drawn five connected diagrams that arise in ##\phi^4## theory. I was wondering if the symmetry factors I have for each of them are correct and if I have missed any graphs. I only want to consider the case of ##V=3, ## with ## J=0,...4## in turn. (V: number of vertices which i denoted by a...
  34. C

    In an infinite quantum well, why Δn=0?

    I've been reading up a bit on semiconductor quantum wells, and came across a selection rule for an infinite quantum well that says that "Δn = n' - n = 0", where n' is the quantum well index of an excited electron state in the conduction band, and n is the index of the valence band state where...
  35. ShayanJ

    SO(4) symmetry in the Coulomb potential

    In chapter 4 of "Modern Quantum Mechanics" by Sakurai, in the section where the SO(4) symmetry in Coulomb potential is discussed, the following commutation relations are given: ## [L_i,L_j]=i\hbar \varepsilon_{ijk} L_k## ## [M_i,L_j]=i\hbar \varepsilon_{ijk}M_k## ## [M_i,M_j]=-i\hbar...
  36. J

    Exploring Symmetry Breaking and Unbreaking in Physics

    Symmetry breaking separates the electromagnetic and weak force from the electroweak force. Is there an opposite procedure or symmetry unbreaking in which the em and weak force can be made to combine? What other forces or examples in physics where you can do reverse symmetry breaking or symmetry...
  37. Andrea M.

    Yang-Mills theory, confinement and chiral symmetry breaking

    I was thinking about hadrons in general Yang-Mills theory and I have some doubts that I'd like to discuss with you. Suppose that we have a Yang-Mills theory that, like QCD, tend to bind quarks into color singlet states. So far nothing strange, even QED tend to bind electromagnetic charges to...
  38. E

    Symmetry and conservation.... which is first?

    I have a question. According to Noether's theorem, "For each symmetry of the Lagrangian, there is a conserved quantity." But soon I thought that I can also prove "For each conserved quantiry, there is a symmetry of the Lagrangian." Actually I can prove the second statement if I start prove...
  39. S

    'Symmetry argument' for eigenstate superposition

    Homework Statement For an infinite potential well of length [0 ; L], I am asked to write the following function ##\Psi## (at t=0) as a superposition of eigenstates (##\psi_n##): $$\Psi (x, t=0)=Ax(L-x) $$ for ## 0<x<L##, and ##0## everywhere else. The attempt at a solution I have first...
  40. B

    Exploring Polyflow Terms: Plane of Symmetry, Zero Velocity Wall & Free Surface

    What is the "plane of symmetry", "zero velocity wall" and "free surface" terms which I have seen in Polyflow? It says in Vnormal=Fs=0 for plane of symmetry and Vnormal= Vs= 0 for zero velocity Wall. Now I get when Vs=Vn=0 it means that the wall isn't moving and it's in a static state but didnt...
  41. Martin V.

    Electric Field Symmetry in a Circular Charge Distribution

    Homework Statement Problem statement: In the attached figure, two curved plastic rods, one of charge q and the other of charge q, form a circle of radius R 8.50 cm in an xy plane. The x-axis passes through both of the connecting points, and the charge is distributed uniformly on both rods. If q...
  42. T

    Why is gauge symmetry not a true symmetry?

    A symmetry of a physical system is a physical or mathematical feature of the system that is preserved or remains unchanged under some transformation. For example, the speed of light is an example of symmetry and its value will always will always remain the same no matter where and what...
  43. N

    Does H = XX+YY spontaneously break symmetry in 1D?

    Hello, I am working in 1D here. For the ferromagnetic Ising model ##H = -\sum_k X_k X_{k+1}## (or ##H = -YY##) we know that the ground state is gapped and has a twofold degeneracy due to SSB (spontaneous symmetry breaking) of the spin flip symmetry ##P = Z_1 Z_2 Z_3 \cdots##. I am now...
  44. W

    Double Integral in Polar Coordinates Symmetry Issue

    Homework Statement Find the volume of the solid lying inside both the sphere x^2 + y^2 + z^2 = 4a^2 and the cylinder x^2 + y^2 = 2ay above the xy plane. Homework Equations Polar coordinates: r^2 = x^2 + y^2 x = r\cos(\theta) y = r\sin(\theta) The Attempt at a Solution So I tried this...
  45. T

    Understanding Symmetry Breaking to Everyday Examples

    I don't really understand what this really means. To understand how a symmetry can be "broken", we descend from the land of abstraction back to everyday world. Imagine you are on a train, zipping through the countryside. E.g. Let's make it a super modern train, using magnetic levitation to...
  46. E

    Why must the Higgs' gauge symmetry be broken?

    The part I understand: I understand that the spontaneous symmetry breaking of the Higgs produces the 'Mexican hat' potential, with two non-zero stable equilibria. I understand that as the Higgs is a complex field, there exists a phase component of the field. Under gauge transformations of...
  47. B3NR4Y

    Proving things for an arbitrary rigid body with an axis of symmetry

    Homework Statement Consider an arbitrary rigid body with an axis of rotational symmetry, which we'll call ## \hat z ## a.) Prove that the axis of symmetry is a principal axis. (b) Prove that any two directions ##\hat x## and ##\hat y ## perpendicular to ##\hat z ## and each other are also...
  48. Buzz Bloom

    Question about time and/or temperature of GUT symmetry breaking

    I understand there are quite a few GUT candidates. I also understand that among these candidates some are considered by the theoretical physics community to be more likely to be correct than others. I am curious about what each of the various GUT candidates predicts as the time (relative to...
  49. F

    MHB Half wave symmetry and integrals

    If I have a periodic wave x(t) with half-wave symmetry, it means that: x(t + T0/2) = -x(t) where T0 is the period of the wave. Would this automatically lead to the conclusion that X(t + T0/2) = -X(t) where X'(t) = x(t), i.e X(t) is the integral of x(t). ?
  50. BiGyElLoWhAt

    Is There a Flaw in the Symmetry Proof for Homology Classes?

    The source I'm using is: http://inperc.com/wiki/index.php?title=Homology_classes And they say Symmetry: A∼B⇒B∼A . If path q connects A to B then p connects B to A ; just pick p(t)=q(1−t),∀t . Transitivity: A∼B , B∼C⇒A∼C . If path q connects A to B and path p connects B to C then...
Back
Top