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. K

    Gauge symmetry of cylindrical rod

    A twisted cylindrial rod has the cross sectional symmetry so that it's not posible to tell whether it is twisted or not without knowing if there is any torsional energy. now drawing a line on the surface of it can tell us whether or not it's twisted. It might not be a straight line.. there are...
  2. K

    Shape of a Bending Beam with P Applied at the Axis of Symmetry

    Homework Statement A beam (e.g. a steel liner) of a length L is bent between two supports, as shown in fig (a). According to the Euler column, the shape is a half period of a sine. Now, a force P is applied at the axis of symmetry - fig (b). What is the shape of the liner? y=f(x) Instead of the...
  3. P

    Symmetry factor of a Wick diagram

    Hello ! In the book Quantum Field for mathematician, there is this Wick diagram as an example to understand how to compute the symmetry factor (I am sorry, I draw it with paint...) This is about a hermitian field interacting with a complex field. The book says it has a symmetry factor of 2...
  4. binbagsss

    Basic Decay Equations possible? - Parity, symmetry concepts

    The question is to determine which decays are possible for: i) ##P^0## ## ->\prod## ##^+## ## \prod## ##^-## ii)##P^0## ## ->\prod## ##^0## ## \prod## ##^0## where ##J^p = 0^-, 1^- ## respectively for ## \prod## ##^+##, ## \prod## ##^-## , ## \prod## ##^0## and ##P^0## respectively. For...
  5. T

    Exchange symmetry and addition of angular momentum

    In case it's relevant, the context of my question is finding the allowed states of an atom. For example, given a nitrogen atom with (1s)2(2s)22p3, how do we find the possible states in terms of total orbital angular momentum L, total spin S, and total angular momentum J = L + S. It seems that...
  6. S

    Spontaneous symmetry breaking in SHO

    Spontaneous symmetry breaking refers to the solution of a system loses some symmetry in its Lagrangian. Consider a Simple Harmonic Oscillator, its lagrangian is time translationally invariant but its solution is periodic in time, thus not time-translational invariant. Is this Spontaneous...
  7. G

    Internal vector symmetry of Dirac Lagrangian

    Homework Statement Find the conserved Noether current j^\mu of the Dirac Lagrangian L = \bar{\psi} ( i \partial_\mu \gamma^\mu - m ) \psi under the transformation: \psi \rightarrow e^{i \alpha} \psi \,\,\,\,\,\,\,\,\,\, \bar{\psi} \rightarrow e^{-i \alpha} \bar{\psi} Homework Equations...
  8. G

    Field Theory: Prove transformations are a symmetry

    Homework Statement Consider the lagrangian L=\delta_\mu \phi \delta^\mu \phi^* - m^2 \phi \phi^* Show that the transformation: \phi \rightarrow \phi + a \,\,\,\,\,\,\,\,\,\, \phi^* \rightarrow \phi^* + a^* is symmetry when m=0. The attempt at a solution Substituting the transformation...
  9. Breo

    Order of the symmetry group of Feynman Diagrams

    Hello, I am learning Feynman diagrams and I still do not understad quite well the symmetry factor idea. The equation is: $$ \frac{1}{O(G)} = \frac{M}{n!(4!)^n} $$ I was trying the next example: If I am not wrong it is O(G) = 10 taking care of the asymmetry of each pair of internal lines...
  10. G

    Show symmetry in a (x,y) | 3a=f(x,y) set

    Homework Statement Let S = { (x,y) in Z | 5x+7y is divisible by 3 } Show that S is symmetrical. Homework Equations None apart from basic algebraic knowledge. The Attempt at a Solution [/B] The only thing I can think of is starting with 3a = 5x+7y and putting x (or y) into the...
  11. P

    Quarter period symmetry in Fourier series

    Suppose we have some function f(x) with period L. My book states that if it is even around the point x=L/4, it satisfies f(L/4-x)=-f(x-L/4), whilst if it is odd it satisfies f(L/4-x)=f(x-L/4). Then we define s=x-L/4 so we have for the function to be odd or even about L/4 that f(s)=±f(-s)...
  12. S

    CFD:Symmetry in Lagrangian

    Hi guys, have a very tricky question on my HW to find compact group of global symmetry to this Lagrangian of 2 complex scalar fields L={\partial_\mu \phi_1^*}{\partial_\mu \phi_1}+{\partial_\mu \phi_2^*}{\partial_\mu \phi_2}-\lambda(\phi_1^* \phi_1 - \phi_2^* \phi_2 - v^2)^2 and I can't figure...
  13. A

    Exploring Azimuthal Symmetry: What is its Physical Meaning?

    Anyone can explain me what is the physical meaning of azimuthal symmetry? Based on the book, azimuthal symmetry means when m=0. However how can we determine that a system is azimuthal symmetry or not? Like for example, I have a two concentric spheres with radius a and b and hold at different...
  14. CrimsonFlash

    Exchange symmetry when adding angular momentum and in LS coupling?

    When you add two angular momentum states together, you get states which have exchange symmetry i.e. the highest total angular momentum states (L = l1 + l2) will be symmetric under the interchange of the two particles, (L = l1 + l2 - 1) would be anti-symmetric...and the symmetry under exchange...
  15. K

    Calculating Symmetry Factors for Graphs: Reasoning Behind Findings

    consider the following two graphs. I want to calculate the symmetry factors for them . I am using field contraction method for that. but I am getting 2 for the 2 vertex diagram and 1 for the zero vertex diagram where it should be 4 and two respectively. Can anyone do it for me. I am writing...
  16. J

    FEM stiffness matrix for simple frame exploiting symmetry

    Hello. I need help with the following problem: I don't know where to start. I know that the frame can be split up into one symmetric part and one symmetric+assymetric part but i forgot the theory and rules on translation and axis etc. I hope someone can help as I have to hand in the...
  17. avito009

    The Electroweak Symmetry: What Happens When It Breaks?

    I was thinking whether to ask this question or not because the mentor might not like it. Again it could be my misconception. But I think I should ask this question because it would help others who are at the same level of study as I am. So those people can just see this post of mine and clear...
  18. S

    Exploring Polyakov's Action: Diffeomorphism Symmetry?

    The Polyakov action, S=\frac{1}{4\pi\alpha^\prime}\int d^2\sigma\sqrt{-h}h^{\alpha\beta}G_{ij}(X)\partial_\alpha X^i\partial_\beta X^j has the local symmetries, diffeomorphism on world sheet and the Weyl invariance. But is diffeomorphism on the target space also a symmetry? The target space...
  19. A

    Why doesn't Graphene have a band gap?

    Is there any simple justification about graphene having no band gap? How bout its linear E-K? Why bilayer graphene has a quadratic E-K and electric field can open a band gap there? I do not completely understand the broken symmetry argument? Also Why MoS2 which has similar structure, do not...
  20. Xenosum

    Symmetry Condition for Scaling a Lagrangian?

    Homework Statement Take the action S = \int d^4x \frac{1}{2} \left( \partial_{\mu}\phi(x)\partial^{\mu}\phi(x) - m^2\phi^2(x) - g\phi(x)^p \right) , and consider the following transformations: x^{\mu} \rightarrow x^{'\mu} = \lambda x^{\mu} \phi(x) \rightarrow \phi^{'}(x) =...
  21. K

    How to calculate symmetry factor of Feynman graphs?

    I am reading Srednicki's book and I am stuck at this point of calculating symmetry factors for Feynman's Graph in the context of dealing with interacting scalar field. First of all my question is what is the standard procedure to calculate it. The way Srednicki has talked about it is that if...
  22. B

    Interpretation of induction in terms of symmetry transformations

    It just occurred to me that induction can be seen as a statement quite analogous to that of "a function whose derivative is 0 on an interval is constant on that interval". Suppose there is a property P about the natural numbers that we want to prove. Then let P: N -> {0, 1} be a function for...
  23. H

    Curie's Symmetry Principle and Heterogeneous Thermodynamic Systems

    I am trying to understand the (possible) couplings between scalar chemical reaction phenomena and vectorial phenomena such as heat conduction and mass diffusion. It is argued in the literature that I have read that the usual assumption of cross coefficients for scalar+vectorial phenomena only...
  24. B

    The breaking of the flavour permutational symmetry

    Hello,I read an article about fo generating mass for the first two generations of quarks by breaking the flavour permutation symmetry S3. In the top of the page 5 of the following article: http://arxiv.org/pdf/hep-ph/9807214v2.pdf , they mention that "Mq1 transforms as the mixed symmetry term...
  25. Safinaz

    Discovering Z Symmetry: Understanding its Role in Physics

    Hi all, Have anyone heard about a symmetry called " Z symmetry " . It's considered a discrete symmetry, in which terms at a Lagrangian for example can take "Z charges" 0, 1 or +1 to be invariant or non-invariant under this symmetry .. I heard about before, but I try to find any reference...
  26. N

    Maximizing Symmetry in Lagrangian for a Particle in 3D Cylindrical Coordinates

    Homework Statement the question is that there is a particle in 3 spatial Euclidean dimensions in cylindrical coordinates. I want to find a symmetry for the lagrangian if the potential energy is function of r and k.theta+z V=V(r,k.theta+z) Homework Equations k is constant L=T-V...
  27. S

    Symmetry of Riemann Tensor: Investigating Rabmv

    We know how objects such as the metric tensor and the Cristoffel symbol have symmetry to them (which is why g12 = g21 or \Gamma112 = \Gamma121) Well I was wondering if the Riemann tensor Rabmv had any such symmetry. Are there any two or more particular indices that I could interchange and...
  28. M

    Top, Higgs, Higgs VEV relation from conformal symmetry?

    http://arxiv.org/abs/1409.0492 Is the Standard Model saved asymptotically by conformal symmetry? A.Gorsky, A.Mironov, A.Morozov, T.N.Tomaras (Submitted on 1 Sep 2014) It is pointed out that the top-quark and Higgs masses and the Higgs VEV satisfy with great accuracy the relations...
  29. D

    High symmetry directions in a two-dimensional oblique crystal

    What are the high symmetry directions for a two-dimensional oblique crystal? Please provide a figure of the corresponding Brillouin zone with high symmetry points labelled.
  30. Safinaz

    Understanding Supersymmetry and Symmetry Breaking in the Higgs Sector

    Hi guys, I have a question about symmetry breaking in Susy, I hope it won't be so naive that I just started to study supersymmetry .. The question is that there are two Higgs doublets in Susy, H_u and H_d, how these two doublets first break supersymmetry at high energy scale and then make...
  31. stevendaryl

    Is Choice of Spinor Representation a Gauge Symmetry?

    In the Dirac equation, the only thing about the gamma matrices that is "fixed" is the anticommutation rule: \gamma^\mu \gamma^\nu + \gamma^\nu \gamma^\mu = 2 \eta^{\mu \nu} We can get an equivalent equation by taking a unitary matrix U and defining new spinors and gamma-matrices via...
  32. B

    Cyclic symmetry - harmonic load components

    I have a homework problem where I have to solve for the displacements of the attached system using cyclic symmetry. To do this, I know that I have to find the harmonic load components of the system. One thing that my professor did not make clear (or if he did, I missed it) is how to determine...
  33. Q

    From local symmetry to General Relativity

    First I want to consider an example of 1D motion. Lagrange equation: $$ \frac{d}{dt} \frac{\partial L}{\partial \dot x} - \frac{\partial L}{\partial x} = 0 $$ If we transform $$L \rightarrow L+a$$ with a is constant, the equation of motion remains unchanged. This is global symmetry. To obtain...
  34. M

    Pauli exclusion, symmetry, and electric repulsion

    I have a few questions about the Pauli exclusion principle: 1. Why do physicists believe that the symmetry in the wavefunction we assign to particles (indistinguishability) is due to an actual restriction in the physical state space that the particles can occupy (the attributes following from...
  35. C

    Srednicki 58: EM current conservation & Gauge Symmetry

    Hi I am re-reading Srednicki's QFT. In chapter 58, he points out that the Noether current $$ j^\mu=e\bar{\Psi}\gamma^\mu\Psi$$ is only conserved when the fields are stationary, which is obvious from the derivation of the conservation law. Meanwhile he assumes that $$\partial _\mu...
  36. B

    When you measure an entangled particle is it obeying a symmetry law?

    Why is it so important to the universe that if you measure the spin of an entangled pair and its up then the other particle must be down. It seems to have no practical use so why does the universe enforce this rule, how would reality differ if it wasn't true. And is it a law of symmetry...
  37. B

    What is the symmetry axis of a hyperbola and how can it be calculated?

    How do I calculate the symmetry axis of a Hyperbole ? Is there a formula? If the Hyperbole is formula : f(x) = a/(x-p) +q
  38. Saladsamurai

    Cyclic Symmetry Analysis: Capturing Features

    I am wondering what kind of approaches people take to a cyclic symmetry analysis in FEM when you have multiple repeating features that don't divide to the same integer. Take the example below for example. I have a N_HOLES = 136 and I have N_SLOTS = 52. I am not sure what to do here. The...
  39. C

    Does spherical symmetry imply spherical submanifolds?

    In Carroll's "spacetime and geometry" he defines a spherical symmetrical spacetime as a spacetime ##(M,g)## for which there exists a Lie algebra homomorphism between the Lie algebra of the killing vectors of ##g## and the Lie algebra of ##SO(3)##. Now, this does imply by Frobenius theorem...
  40. C

    Symmetry of Spatial Wavefunctions

    I know about symmetry and antisymmetry and so on, but a thought that I had never considered just hit me. If we had two fermions in the triplet symmetric spin state and hence therefore an antisymmetric spatial state, for example a harmonic oscillator in the first excited state must be one in...
  41. K

    Is R on S an Equivalence Relation?

    Homework Statement Is this relation, R, on ## S= \{ 1, 2, 3 \} \\ R = \{ (1,1), (2,2) , (3,3) \}## Symmetric? It is obvious that it is reflexive.
  42. A

    Isospin breaking, charge symmetry and charge indepedence

    Hi, I'm just getting a little confused with all the definitions here and I need some confirmation on what I say is correct or not; Isospin symmetry: The property that an interaction is independent of the T_3 value? Isospin breaking: The property that it is dependent on T_3 ? Charge symmetry...
  43. R

    Electric field of a line of charge with symmetry

    Homework Statement http://imgur.com/W4Ntkfb Homework Equations E=KQ/R2 e= electric field Q = charge R = radius from point to charge K is a constant, 9x109 The Attempt at a Solution http://imgur.com/4CTEwDw If my handwriting sucks, I basically did the standard integral of...
  44. N

    How Do Symmetries Relate to Conservation Laws in Physics?

    I am trying to understand the connection between symmetry and conservation. For the electromagnetic force, the conserved quantity is charge, the corresponding symmetry is the phase of the wave and the force carrier is the photon. For the electroweak force, the conserved quantities are the...
  45. T

    Multiplication Table of C3V and P3 Symmetry Groups

    Can one set up a multiplication table for the symmetry group C3V of the equilateral triangle. Then show that it is identical to that of the permutation group P3. I need some clarification... What about a matrix representation (2x2) for these groups? → Here was thinking to use...
  46. F

    Understanding Inversion Symmetry and Space Symmetry Breaking

    1. P. Marder ever said that there is no special symmetry results in two dimensional oblique lattice. But it still possesses inversion symmetry. r → -r How to understand r → -r? 2. Many book ever states that space symmetry broken by atomic displacement can bring ferroelectricity. But why...
  47. G

    Does time reversal symmetry imply hermicity of s-matrix?

    If the probability for a state α prepared initially to be in a state β at a later time is given by: S_{\beta \alpha} S_{\beta \alpha}^* and for a state β prepared intitially to become a state α is: S_{ \alpha \beta} S_{ \alpha \beta}^* then in order for the two to be equal (by...
  48. C

    Is there a conservation law associated with C4 symmetry?

    I know--because of Noether's theorem--that continuous rotational symmetry implies conservation of angular momentum, and that continuous translational symmetry implies conservation of linear momentum. It also turns out that the discrete translational symmetry exhibited by a Bravais lattice...
  49. T

    MHB Due to a symmetry of the cosine we can just double the integral from 0 to 1

    Hello, ∫|cos(px/2)|dx between [0,2] I encountered this rule. How does this apply to other intervals of say [3,4],[7,9] etc. Are the numbers both halved? so [3,4] becomes [1.5,2] etc? Also, does this rule apply to all symmetrical functions? Thank you, Tim
  50. S

    Conserved charge from Lorentz symmetry

    I am trying to derive the conserved charge from the symmetry of the action under Lorentz transformations, but I am doing something wrong. Noether's theorem states that the current is J^\mu = \frac{\partial \cal L}{\partial(\partial_\mu \phi)} \delta\phi - T^{\mu \nu}\delta x_\nu For an...
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