Symmetries Definition and 187 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. C

    Symmetries of 6-Gon: Proving D_6 isomorphic to D_3 x Z_2

    Homework Statement We were given the following argument showing that ##D_6 \cong D_3 \times \mathbb{Z}_2##. What we did was take two subgroups H and K of G such that their intersection was trivial and that ##hk = kh## for all h and k. H = {symmetries of 6-gon that preserved a triangle inside}...
  2. S

    Symmetries in Sidney Colemans QFT script

    Hello Everybody, I am learning QFT using Sidney Colemans lecture notes (and the Peskin Schroeder book). They can be found here: http://arxiv.org/abs/1110.5013 Now, in page 40, he introduces in the paragraph Symmetries and Conservation laws some definitions which I don't quite...
  3. C

    Symmetries of graphs/Graph theory

    Homework Statement Determine the number of symmetries of the graph attached. The Attempt at a Solution I know the answer, I would just like someone to look over my argument to make sure I haven't missed out anything important. I also have some questions along the way. Vertex 1 is the...
  4. M

    Notes on symmetries of the KdV equation

    I am having trouble understanding a section in http://www.mathstat.dal.ca/~francisv/publications/XXV-ICGTMP-Proceeding/dkdv.pdf: . It is on page 3. Section 3 -- Discretization of the Korteweg-de Vries equation. I don't understand why V_4=x∂_x+3t∂_t-2u∂_u generates a symmetry group of the KdV. I...
  5. N

    Do we need to refer all interactions to symmetries?

    Do we innevitably need to attach each interaction with a symmetry?Could we contruct a theory of an interaction without using any symmetry theory(example gravity interaction)? Why do we not need to demonstate QCD being renormalized,but we must demonstrate electroweak theory is renormalized(I...
  6. E

    When does a wavefunction inherit the symmetries of the hamiltonian?

    As the title suggests, I am interested in symmetries of QM systems. Assume we have a stationary nonrelativistic quantum mechanical system H\psi = E\psi where we have a unique ground state. I am interested in the conditions under which the stationary states of the system inherit the...
  7. M

    Munich Theoretical physics (group theory and symmetries)

    I'm sorry if I'm posting this question here, but for some reason i can't add a new topic in the right section (i think it should be "Advanced Physics Learning Materials") ..I'm also sorry for my english... By The Way... Just one simple question: i'm looking for the note or the webpage for...
  8. J

    Symmetries and Spin orbit interaction

    I know that the generators of the Poncaire group that are associated with *orbital* angular momentum belong to an infinite dimensional representation, i.e. \begin{equation} L = \frac{\partial}{\partial \theta} \end{equation} Also the spin generators are associated with some finite...
  9. D

    How do Lie symmetries help find canonical coordinates in ODEs?

    I'm currently reading a textbook on the application of Lie symmetries to differential equations (Symmetry Methods for Differential Equations: A Beginner's Guide Hydon, Peter. Cambridge University Press. 2000.) I'm somewhat at the beginning (pg. 22-25) where a method is being discussed to...
  10. C

    Article about symmetries (math problems)

    Hi all. When I was reading a paper (http://physics.brown.edu/physics/undergradpages/theses/SeniorThesis_tlevine1.pdf) I have had a problem. I don’t understand some equations, namely I don’t understand 2.22 and 2.36. I confused by derivative \left(\frac{\partial t’}{\partial...
  11. TrickyDicky

    Internal (gauge) symmetries and spacetime symmetries

    Internal symmetries of the SM -U(1), SU(2), SU(3)- are usually said to belong to abstract spaces unrelated to spacetime symmetries, have there been many attempts to relate internal symmetries to spacetime symmetries, and if so how far have they gotten?
  12. F

    Particle symmetries and unification

    I'm given to understand that the internal symmetries of particle physics, U(1)SU(2)SU(3), does not depend on the dimensionality or curvature of the background spacetime. If the present particle symmetry is internal, than how can there be a unification of the forces that make the forces...
  13. lpetrich

    Quark and Lepton Mass Matrices, Textures, Horizontal Symmetries

    Does anyone have any good introduction to theories of the quark and lepton mass matrices? Theories like textures and horizontal symmetry. My understanding of research into textures is that it often involves trying to make zero as many entries as possible in the mass matrices. Is that a fair...
  14. F

    Maxwell Tensor Symmetries Problem - Federico

    Hi community: I'm Federico and I'm new user here! I'm trying to show that the Electromegnetic Field Tensor F_{ab} = 2A(r) (e_{0})_{[a}(e_{1})_{b]} + 2B(r) (e_{2})_{[a}(e_{3})_{b]} where (e_{0},e_{1},e_{2},e_{3}) is the tetrad basis associated with the metric ds^2=...
  15. N

    Applying Symmetry in Poisson Superfish for Cylindrically Symmetric RF Problems

    Does Poisson Superfish apply median-plane symmetry to cylindrically symmetric rf problems (or can it do so)? When I was introduced to the program, I was told that this symmetry was incorporated, but I've not seen anything in the documentation supporting that assertion. On the other hand, a...
  16. N

    Breaking Symmetries: 20 Real Scalars and 24 Symmetries

    Homework Statement Suppose that there is a gauge group with 24 indepenent symmetries and we find a set of 20 real scalar fields such that the scalar potential has minima that are invariant under only 8 of these symmetries. Using the Brout-Englert-Higss mechanism, how many physical fields are...
  17. N

    Symmetries of Lagrangian and governing equations

    Hi, I have a quick question: Let's say I have a Lagrangian \mathcal{L} . From Hamilton's principle I find a governing equation for my system, call it N\phi=0 where N is some operator and \phi represents the dependent variable of the system. If \mathcal{L} has a particular symmetry, how...
  18. P

    A question about symmetries and Pauli-Villars Regularisation

    Which symmetries and restrictions does the Pauli-Villars regularisation scheme break/violate and which ones does it preserve? Consider: - Unitarity - Abelian gauge symmetry - Non-Abelian gauge symmetry - Supersymmetry I'm asking because I got confused after reading about it. Especially after...
  19. T

    Proof of symmetries in electrostatics

    I need a mathematical proof that should indicate the following: The direction of the electric field must be radial, for a spherical charge distribution to remain invariant after applying a rotation matrix to its field. Analogously how can we prove that the electric field of a infinite...
  20. N

    Must Particles Be Eigenstates of Conserved Quantities in Interactions?

    2 questions on symmetries: "conserved in interaction => eigenstate in interaction"? Hello, I'm currently taking an introductory course in elementary particles (level: Griffiths) and I have 2 questions that are severely bothering me; all help is appreciated! They are related to Griffiths'...
  21. michael879

    CPT (M?) symmetries in Kerr-Newman metric

    So the confusion I'm having here really has to do with parity inversion in spherical (or boyer-linquist) coordinates. I've been looking at the discrete symmetries of the Kerr-Newman metric, and I've noticed that depending on how you define parity-inversion, you can get very different results...
  22. G

    Question: How do symmetries and time evolution interact in quantum mechanics?

    My question is the following: when in quantum mechanics one introduces symmetry, says that a states and observables transform both, in order to mantain mean values intact (kind of like a change of coordinate system), i.e.: |\psi>\rightarrow U|\psi> and O\rightarrow UOU^\dagger...
  23. N

    Symmetries and Maxwells equations

    Hi Maxwells Equations for a time-invariant system are separable, hence we can write a solution as E(r, t) = E(r)E(t). They also mention that if the system is radially invariant, then that implies that the solution splits into a product of radial and angular functions (with 2π periodic angular...
  24. D

    Trouble understanding Symmetries

    I'm stumped on a question about symmetries: Imagine you and a friend are on two separate rocket ships. According to me - standing on spacestation Babylon 5 – the two of you are moving parallel to each other at a constant speed but in opposite directions. What test would you do to confirm that...
  25. B

    I am having trouble understanding how to find symmetries given a

    I am having trouble understanding how to find symmetries given a problem. Ex: Cylinder, infinite in z, that is a conductor in electrostatics. My reasoning is: assuming a homogenous charge distribution, the E-field should be symmetric for translations in z and phi so those derivatives are...
  26. mnb96

    Exploring Symmetries on the Riemann Sphere: A New Perspective?

    Hello, in the usual 2d Euclidean plane we know we have a limited number of symmetry groups that describe certain kinds of symmetries. Could we add richness to our "vocabulary of symmetries" by considering symmetries on the Riemann sphere, and then stereographically project onto the plane?
  27. lpetrich

    What are the proposed gauge-symmetry groups for Grand Unified Theories?

    I first thought of posting on cataloguing various Grand Unified Theory proposals, but that would be an enormous task, so I decided on something simpler: cataloguing proposed GUT gauge-symmetry groups. The unbroken Standard-Model symmetry is SU(3)C * SU(2)L * U(1)Y QCD: SU(3)C -- color...
  28. Fredrik

    What are the key theorems on the mathematics of symmetries in quantum mechanics?

    I would like to study the mathematics of symmetries in QM rigorously. Any recommendations? Let H be a Hilbert space, U the group of unitary operators on H, L the lattice of closed subspaces of H, and G a symmetry group. I'm particularly interested in theorems about the relationship between...
  29. R

    Finding all symmetries of a given Lagrangian

    Is there a systematically way of finding all space-time symmetries of a given Lagrangian? E.g. given a electromagnetic Lagrangian, can I somehow derive that the symmetries in question are conformal ones? Thanks.
  30. U

    Group Theory: Rotational Symmetries

    Homework Statement Show that the group R of rotational symmetries of a dodecahedron is simple and has order 60. The Attempt at a Solution I see how to get order 60 using the orbit stabilizer theorem. Letting R act in the natural way on the set of faces, we find the size of the orbit...
  31. J

    Listing symmetries geometrically and analytically, what do I do?

    I have found this question and not sure where to begin in terms of solving it. PLEASE HELP! Consider a double square pyramid . Introduce a coordinate P system so that the vertices of P are: A=(2,0,0) B=(0,2,0) C=(-2,0,0) D=(0,-2,0) E=(0,0,1) F=(0,0,-1) List the symmetries of P. Do...
  32. J

    Finding symmetries both geometrically and analytically. PLEASE HELP

    Finding symmetries both geometrically and analytically. PLEASE HELP! I have found this question and not sure where to begin in terms of solving it. PLEASE HELP! Consider a double square pyramid . Introduce a coordinate P system so that the vertices of P are: A=(2,0,0) B=(0,2,0)...
  33. R

    Reviewing Yang-Mills Gauge Field: Symmetries & Path Integral Methods

    Just to review a little bit: In general, for a gauge field with Yang-Mills Lagrangian \mathcal L=-\frac{1}{4}F^{c}_{\mu \nu}F^{c \mu \nu} for each c it is impossible to find the resulting free Green's function G(k) in momentum space: (g^{\mu \nu}k^2-k^{\mu}k^{\nu})G_{\nu...
  34. TrickyDicky

    Exploring FRW Metric Symmetries in Spacetime

    What are the symmetries determined by FRW spacetime? I guess they include Lorentz symmetry, rotationally and translationally symmetries, but not time symmetry. Is this right? Thanks
  35. N

    What do we mean by broken symmetries when referring to superfluid he3 phases?

    What do we mean by "broken symmetries" when referring to superfluid he3 phases? I struggle to understand the concept of broken symmetries of the superfluid phases of 3He. Any insight would be much appreciated. Thanks :)
  36. L

    Symmetries in Quantum Mechanics

    Hi, In QM symmetries can be represented by unitary operators. For example for rotations: \hat{U}_{R}\psi(\vec{x})=\psi(R^{-1}\vec{x}) , which is simple enough, as it just says that the vale of the rotated wavefunction at some point is the value of the old wavefunction at the pre-rotated...
  37. L

    Continuous symmetries (Srednicki)

    Hi, In ch22, Srednicki considers the path integral Z(J)=\int D\phi \exp{i[S+\int d^4y J_a\phi_a]} He says the value of Z(J) is unchanged if we make the change of var \phi_a(x)\rightarrow\phi_a(x)+\delta\phi_a(x), with \phi_a(x) an arbitrary infinitesimal shift that leaves the mesure...
  38. T

    Error in Schakel's 'Boulevard of broken symmetries'?

    I'm working through Schakel's 'Boulevard of broken symmetries' and I don't get an equation connect to the Coulomb gas problem. The equation in question is (5.77) on page 161. Luckily, you may look it up in...
  39. I

    Understanding Discrete Symmetries in Quantum Field Theory

    I don't quite understand the treatment of discrete symmetries, for example, in Peskin's QFT book: Because by definition time reversal symmetry should flip the spin and momentum, so he defined an operation to flip the spin state of a two-component spinor, i.e. \xi^{-s} \equiv...
  40. E

    How Do Symmetries Determine Expectation Values in Quantum Mechanics?

    [QM] Hamiltonian and symmetries Homework Statement Let there be the hamiltonian: H=\frac{P^2}{2m}+\frac{1}{2}m\omega^2(x^2+y^2+z^2)+kxyz+\frac{k^2}{\hbar \omega}x^2y^2z^2 Find the expectation value of the three components of \vec r in the ground state using ONLY the symmetry properties of...
  41. D

    Fundemental relation between group symmetries and periodicity?

    Fundemental relation between group symmetries and periodicity?? My question is simply: Is there a fundamental relation between group symmetries and periodicity? I been studying group theory within my recent studies of QFT and the Standard Model and the aforementioned question occurred to me...
  42. Z

    Noether's Theorem, Symmetries & Lorentz/Poincare Group Self-Study - help?

    Hello folks, I'm interested in getting a much deeper understanding of symmetries and how they pretty much define the universe; e.g. translation symmetry in time = Conservation of Energy?? according to Wikipedia. I'm *extremely* interested in how symmetries lead to universal laws. My level...
  43. B

    T-duality symmetries, how to count them?

    Im reading about T-duality in string theory and I am trying to understand: in a D dimensional, toroidally, compactified space, is there a symmetry for every compact dimension with itself and with every other compact dimension as well? So, I know that T-Duality implies symmetry under R^i...
  44. U

    What Are the Gauge Symmetries of This Theory?

    Homework Statement I want to derive Gauge symmetries of the following gauge theory: S=\int\;dt L=\int d^4 x \;\epsilon^{\mu\nu\rho\sigma} B_{\mu\nu\;IJ} F_{\mu\nu}^{\;\;IJ} Where B is an antisymmetric tensor of rank two and F is the curvature of a connection A i.e: F=dA+A\wedge A...
  45. N

    Exploring Symmetries and Degeneracies in Lattice Structures

    Hi all What symmetries are there usually in a lattice? Let us say for example that I look at a lattice having the form (each "x" is an atom) x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x Of course there is translational symmetry...
  46. C

    BRS: The Weyl Vacuums. I. Definition, Geometrical Properties, Symmetries

    In discussions of questions related to gtr, it is often useful to know that one can in fact "create solutions to order" in gtr, when one wishes to model specific physical scenarios. Sort of, not really--- and herein lies a tale which illustrates some of the many thorny technical and conceptual...
  47. R

    Kaluza Klein, Goldstone Bosons, symmetries obliging masslessness?

    Kaluza Klein, Goldstone Bosons, symmetries obliging masslessness? Hello physics people, I hope all is well, and that everyones feeling festive even though i don't celebrate xmas lol! Iv got some weird questions, at least for me. Iv been working on Kaluza-Klein theory and have found weird...
  48. S

    Confused about symmetries and canonical transformations

    this is a problem confusing me, which is in the book named Principles of Quantum Mechanics by R. Shankar. This problem is not about quantum mechanics, but just in the chapter of Review of Classical Mechanics. (The ******** is just to avoid to be deleted). The problem is in the attachment...
  49. MathematicalPhysicist

    Parity and Time Reversal symmetries.

    I have a question, in Time Reversal operator, does an external magnetic field would get a minus sign, I guess that yes cause it changes direction, i.e if it's directed orthogonal to the surface then after time reversal I think it will direct anti-orthogonal to the surface, in Parity I don't...
  50. M

    Distinct Cyclic Subgroups of D6 with Proper Subgroup Example

    Homework Statement (a) How many distinct cyclic subgroups of D6 are there? Write them all down explicitly. (Here, D6 is the dihedral group of order 12, i.e. it is the group of symmetries of the regular hexagon.) (b) Exhibit a proper subgroup of D6 which is not cyclic. Homework...
Back
Top