What is Symmetry breaking: Definition and 119 Discussions

In physics, symmetry breaking is a phenomenon in which (infinitesimally) small fluctuations acting on a system crossing a critical point decide the system's fate, by determining which branch of a bifurcation is taken. To an outside observer unaware of the fluctuations (or "noise"), the choice will appear arbitrary. This process is called symmetry "breaking", because such transitions usually bring the system from a symmetric but disorderly state into one or more definite states. Symmetry breaking is thought to play a major role in pattern formation.
In his 1972 Science paper titled "More is different" Nobel laureate P.W. Anderson used the idea of symmetry breaking to show that even if reductionism is true, its converse, constructionism, which is the idea that scientists can easily predict complex phenomena given theories describing their components, is not.
Symmetry breaking can be distinguished into two types, explicit symmetry breaking and spontaneous symmetry breaking, characterized by whether the equations of motion fail to be invariant or the ground state fails to be invariant.

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  1. 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...
  2. E

    Crystal momentum in a lattice.

    Background information: The wave function for an electron in a crystal lattice is modeled by a Bloch wave. A Bloch wave is a function with the periodicity of the lattice multiplied times a complex exponential function. This exponential function has a wave vector k, called the crystal momentum...
  3. 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...
  4. E

    Spontaneous symmetry breaking and the photon/baryon ratio

    Hi, I am looking into symmetry breaking and how it (may have) affected the photon/baryon ratio in the primordial universe. I found this wonderful encyclopaedia of cosmology which relates the grand unified theory to an orthorhombic crystal, making analogies for symmetry, spontaneous symmetry...
  5. stevendaryl

    Understanding Inflation: Effects of Spontaneous Symmetry Breaking on Gravity

    I'm trying to understand inflation (in the cosmic sense). I know that ultimately that's a subject that involves both quantum field theory and General Relativity, but I'm wondering to what extent it can be understood from the point of view of classical (non-quantum) GR. If you have a classical...
  6. S

    Spontaneous symmetry breaking in the standard model

    In the standard model, the Lagrangian contains scalar and spinor and vector fields. But when we consider spontaneous symmetry breaking, we only account for the terms contain only scalar fields, " the scalar potential", in the Lagrangian. And if the scalar fields have vacuum expectation value...
  7. A

    Spontanous symmetry breaking

    I am bit confused by how to approach this concept with mean field theory. As I understand a symmetry break (like a acquiring a finite magnetization) can happen if at low enough temperatures the Free energy decreases when breaking the symmetry. Normally this temperature is found by calculating...
  8. W

    Spin-half mass term with symmetry breaking

    I've been thinking about chapter 11 of Griffiths' Introduction to Elementary Particles. In section 11.7, he gives the Lagrangian density \mathcal{L}=\frac{1}{2}(\partial_{\mu}\phi)(\partial^{\mu}\phi)+\frac{1}{2}\mu^{2}\phi^{2}-\frac{1}{4}\lambda^{2}\phi^{4} and shows that the minimum...
  9. 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...
  10. 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...
  11. 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...
  12. 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...
  13. 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...
  14. 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...
  15. 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...
  16. TrickyDicky

    Is the Higgs mechanism really a spontaneous symmetry breaking?

    The Higgs mechanism is often explained (both here at PF and in many physics sites including wikipedia) as an example of spontaneous symmetry breaking, but the Nobel winner physicist 't Hooft says in his "for laymen" book about particle physics, "In search of the ultimate building blocks", that...
  17. V

    Symmetry and symmetry breaking

    I am quite new to the branch of quantum physics and therefore am quite inexperienced with certain terminology and definitions. I have looked these topics up time and time again, but still cannot get a grasp on what they mean. Could someone please describe to me what the concept of "symmetry" in...
  18. alemsalem

    What happens to conserved currents after spontaneos symmetry breaking?

    should the current still be conserved? since it stills commutes with the Hamiltonian and symmetry is just hidden. but I just read that the linear-σ model was invented to demonstrate how the axial current could be partially conserved? Thanks!
  19. lpetrich

    Analogies for Symmetry Breaking and the Higgs Particle

    Any good ones? I like this one: For full symmetry, imagine a marble and a bowl with rotational symmetry. Drop the marble into the bowl. It will oscillate back and forth and settle down in the center. The bowl+marble system still has rotational symmetry. If you push the marble out of the...
  20. jfy4

    O(2) symmetry breaking trouble

    Hi, I'm going to quote a lot of a book so that I can get some help, brace yourselves... First, \phi_{a} is my field with a=0,1 as internal components and my lagrangian is L=\frac{1}{2}\partial_{\mu}\phi_a \partial^\mu \phi_a +\frac{1}{2}\mu^2 \phi_a \phi_a +\frac{1}{4}\lambda (\phi_a...
  21. N

    Symmetry breaking/ degrees of freedom

    Dear PF... Please help me with basic question more I think more I get confused... In O(n) space there are n(n-1)/2 generators... suppose I have symmetric tensor in O(n) space, it will have n(n+1)/2 independent components... and i am building invariant potential from it (quartic polynomial...
  22. S

    Yukowa potential and symmetry breaking

    Hello, I am trying to shortly explain how the Yukowa potential breaks symmetry in weak interactions. I would like to use the mexican hat potential as a specific example. Unfortunately Wikipedia does not go very in depth or explain it very well. Link. Any help on understanding the collapse of...
  23. F

    What is symmetry breaking in the Standard Model?

    I'm trying to figure out where symmetry breaking occurs in Feynman diagrams. I'm just free wheeling here, correct me where needed. But as I understand it, when you have a Feynman diagram where there is an interaction of one particle which decays to others, the incoming particle may obey one...
  24. S

    ElectroWeak symmetry breaking.

    Hello, new member here. I've been fascinated reading some of the threads and decided I had to register to ask a question that's always been a bit confusing to me. From what I've learned The Big Bang theory seems the most likely explanation of the start of the universe but there's one thing in...
  25. alemsalem

    Symmetry breaking and the ground state of a quantum field theory.

    when a continuous symmetry is broken, we say that the ground state is just one of the possible ground states, and there is no energy cost in moving from one to the other.. why doesn't the state keep changing with the slightest perturbation (production of goldstone boson). why don't we have a...
  26. F

    Is electroweak symmetry breaking a reversible process?

    I can only assume it is, if a Higgs can be found anyway. I learned about hysteresis in certain physical processes. I don't have the math to guess nor Google skills to find a clear answer. If it were, would a sufficiently large and hot enough black hole be in danger of losing its mass terms...
  27. S

    Is Electroweak Symmetry Breaking a Requirement of Universal Law?

    What law of nature says that electroweak symmetry must be broken? Is it possible that in other parallel Superstrings (or others) universes.. electroweak symmetry were not broken and even after temperature of the Big Bang decreased to what is like ours, electroweak symmetry still existed in that...
  28. J

    Spontaneous symmetry breaking, Higgs mech, and particles getting masses?

    I'm trying to get a basic picture in my head of particles having mass. I always seem to come across the ridiculously vague statement that "the Higgs mechanism gives particles mass", and a passing mention of "spontaneous symmetry breaking". There is a lot of stuff confusing me at the minute so...
  29. H

    Nambu Modes: Necessary & Adequate Condition of Symmetry Breaking

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  30. N

    Electric charge and spontaneous symmetry breaking

    Hi, If I have a Lagrangian of complex scalar field (just U(1) local invariance). And I know that phi^star describes field with -e electric charge and phi describes field with e electric charge. How do I apply "charge issue" when I write Lagrnangian after spontaneous symmetry breaking in...
  31. H

    Time reversal symmetry breaking

    We know velocity/momentum and magnetic field both are odd to time-reversal operation. Then how is the time-reversal symmetry broken in quantum Hall effect since magnetic field is always coupled with velocity/momentum?
  32. M

    U(1) symmetry breaking within the superluid phase

    Hi With the Bose-Hubbard Hamiltonian (BHH) being invariant under a U(1)\equivO(2) symmetry transformation, it is said that the hopping-term in the BHH tends to break the U(1) symmetry as the system leaves the insulating phase. This is not clear to me. However within the mean-field...
  33. 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?
  34. 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...
  35. 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...
  36. 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 =...
  37. 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...
  38. 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...
  39. 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...
  40. 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...
  41. Pengwuino

    Oreo-Milk Symmetry Breaking (OM-Violation)

    So I've found the strangest thing with oreos and milk. I have a glass of milk and when I just toss an oreo inside of it and let it sit, even for the longest time, it doesn't really get all saturated with milk and delicious. However, when I hold the oreo while dipping it in the milk, it becomes...
  42. J

    Symmetry breaking domain walls

    Symmetry breaking "domain walls" The only "spontaneously broken symmetry" that I can easily visualize, is cooling down a ferromagnetic material and having the spins randomly choose a direction to align. Since the choice is random, different regions will usually choose different directions...
  43. arivero

    Kaluza Klein and gauge symmetry breaking.

    In standard, old-fashioned, Kaluza Klein theory we have new dimensionful parameters, the size of the compact dimensions, but they become dimensionless after quotient against the Plank size, so they become the adimensional coupling constants of the gauge groups associated to the symmetry of the...
  44. R

    Exploring Flavor Symmetry Breaking in Massless Quarks

    If you model the quarks as massless, there should be no flavor mixing, because flavor mixing is achieved through the CKM matrix, which is a mass matrix. However, if quarks are massless, there ought to be an axial flavor symmetry, but there isn't. So to reconcile this, we must spontaneously...
  45. B

    Chiral symmetry breaking and approximate flavour symmetry

    I have 2 questions: 1. When there are no fermion mass terms, the Dirac part of the Lagrangian posseses an SU(N) left X SU(N) right flavour symmetry for N flavours of fermions. This can be "re-arranged" as an SU(N) vector X SU(N) axial symmetry. The axial part is spontaneously broken by the...
  46. D

    Symmetry Breaking and the Metric

    Hello, im a first year phd student, and I am reading http://arxiv.org/abs/0901.1847 right now in an attempt to figure out something cool to do with lie 3 algebras. In the paper they mention that turning on a B field in the 1,2 dimensions breaks the SO(4) symmetry the theory has to...
  47. D

    'Frame' symmetry breaking - when did it happen?

    In any place of our universe we can define a 'preferred' or 'rest' frame based on the observation of the Cosmic Microwave Background. Of course, in different places of our universe these frames are different, but the idea is the same. If instead of the CMB we define this frame based on the an...
  48. J

    Why can't there be spontaneous symmetry breaking in finite volume?

    Hello everyone, I'm a bit confused by something I've read as have been unable to find resources to clarify it. Here is the statement that confused me, from Binetruy's Supersymmetry textbook (p.26): It is well-known that [in the case of ordinary continuous symmetries] no possibility of...
  49. J

    Spontaneous symmetry breaking of gauge symmetries

    hello all gauge symmetries are redundencies of the description of a situation. Therefore they are not real symmetries. So in what sense does it mean to spontaneously break a gauge symmetry? ian
  50. J

    Entropy & Time Reversal Symmetry: Breaking Symmetry?

    Does the ever increasing nature of entropy violate time reversal symmetry?
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