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. LCSphysicist

    What is the Fermion's mass in this Lagrangian?

    We have a Lagrangian of the form: $$ \mathcal{L} = \overline{\psi} i \gamma_{\mu} \partial^{\mu} \psi - g \left( \overline{\psi}_L \psi_R \phi + \overline{\psi}_R \psi_L \phi^* \right) + \mathcal{L}_{\phi} - V(|\phi|^2) $$ Essentially, what we are studying is spontaneous symmetry breaking...
  2. codebpr

    A Symmetry breaking in the AdS small/large black hole phase transition

    I am trying to reproduce the results from this paper where they find out the expression for the Landau functional to be $$\psi(x,t,p)=\frac{1}{4}(\frac{1}{x}+6x+px^3-4tx^2)$$ We plot the Landau functional v/s the order parameter($x$) at $p=0.5$ and obtain the Figure 4. from the paper as Now...
  3. S

    I No symmetries in the Universe at the Big Bang...?

    I apologize in advance if this is a stupid question but... According to some scenarios about the beginning of the universe (namely cosmological inflation), in layman's terms, everything was born out of a quantum fluctuation which caused a violent expansion. In this case, since an expanding...
  4. H

    I Was Electroweak Symmetry Breaking in the Early Universe Controversial?

    According to Sabine Hossenfelder in the extremely early Universe nothing had mass because the electroweak symmetry was not yet broken so there was no Higgs field. Am I correct in thinking this is not controversial? https://youtu.be/9-jIplX6Wjw?t=638
  5. S

    I Would infinite entropy break all symmetries?

    If the Universe could somehow reach a state of infinite entropy (or at least a state of extremely high entropy), would all fundamental symmetries of the physical laws (gauge symmetries, Lorentz symmetry, CPT symmetry, symmetries linked to conservation principles...etc) fail to hold or be...
  6. S

    A Vacuum Transitions and Lorentz Symmetry Breaking

    There are several "bumblebee" models [1], [2] where Lorentz invariance is violated usually resulting from a local vector or tensor field acquiring a nonzero vacuum expectation value We do not know whether we are in the true vacuum state or in a "false"/metastable vacuum state that could decay...
  7. S

    I Could the Lorentz symmetry be theoretically broken in vacuum?

    In this paper [1] which considers the possibility that the Lorentz symmetry could be broken, at page 4-5 the author says: "We now introduce a Higgs sector into the Lagrangian density such that the gravitational vacuum symmetry, which we set equal to the Lagrangian symmetry at low temperatures...
  8. mollwollfumble

    I Has anyone done a PPN formalism on Dark Matter? Or other non-GR?

    This thought surprisingly came from thinking about the definition of temperature and the symmetry breaking that separated time from temperature. Which led to thoughts about symmetry breaking that separated QM from GR. Which led to to the symmetry breaking that separated dark energy from baryonic...
  9. P

    A Order parameter, symmetry breaking Landau style

    Hi all, I am somewhat familiar the Landau Ginzburg paradigm for phase transition. My understanding is that it is a phenomological model of 2nd order phase transitions by "guessing" that the free energy can be expanded a configuration integral (path integral) of a functional of a local order...
  10. Antarres

    A Question about S(3) spontaneous symmetry breaking in Peskin & Schroeder

    In chapter 20 of Peskin&Schroeder about spontaneous symmetry breaking, he considers and example on page 696 of spontaneous symmetry breaking of SU(3) gauge group with generators taken in adjoint representation. Covariant derivative is defined with: $$D_\mu\phi_a = \partial\phi_a +...
  11. M

    B Could Spontaneous symmetry breaking cause momentum change in an atom?

    If you were to fire a single atom from a fixed point into a chamber of perfect vacuum and measure where it collides with the opposite wall. Could Spontaneous symmetry breaking in the sub atomic particles cause momentum change in the atom, changing the part of the wall the atom interacted with?
  12. joneall

    A Justification for phi^4 potential

    My understanding is at the level of Griffiths's Introduction to quantum mechanics or Robinson's Symmetry and the standard model, i.e., using the phi^4 potential to explain the effects of global and local symmetry breaking, Goldstone and Higgs bosons. These books and others use a potential of...
  13. joneall

    I Gauge theory symmetry breaking in L&B

    I’m reading Lancaster & Blundell, Quantum field theory for the gifted amateur (even tho I”m only an amateur...) and have a problem with their explanation of symmetry breaking from page 242. They start with this Lagrangian: ## \mathcal{L} = (\partial_{\mu} \psi^{\dagger} - iq...
  14. S

    A What would it mean if symmetries in physics would not be fundamental?

    Physicist Joseph Polchinski wrote an article (https://arxiv.org/pdf/1412.5704.pdf) where he considered the possibility that all symmetries in nature may not be fundamental. He says at page 36: "From more theoretical points of view, string theory appears to allow no exact global symmetries, and...
  15. S

    A High energy symmetry breaking and laws of physics?

    In some models of the beginning of the universe, like for example in chaotic inflation, space would stop expanding in some points, creating Hubble volumes that could experience different spontaneous symmetry breaking, which would result in different properties, such as different physical...
  16. TempleSweeper

    A Exploring Symmetry Breaking Phenomenon in a Physical System

    In some experiments of a complex physical mathematical system, we found some symmetry phenomenon, very similar as symmetry breaking phenomenon, say, as translatable sysmmetry etc. These symmetry (breaking) phenomenon occurs in most of the parts of the system or some parts of the system. Can you...
  17. K

    I Spontaneous symmetry breaking from a QM perspective

    Hello! This questions might not make sense and I am sorry if that is the case (I am asking from a QM class perspective). I am a bit confused about the idea of spontaneously symmetry breaking (SSB), from the point of view of QM. I am talking here about the energy plot looking like a mexican hat...
  18. HaoBoJiang

    A LT & Translation Symmetry: Problem Analysis

    As we all know, for the reference frame S' and S of relative motion, according to Lorentz transformation, we can get As we all know, for the reference frame S' and S of relative motion, according to Lorentz transformation, we can get As we all know, for the reference frame S' and S of relative...
  19. Ranku

    I Energy of massless particles before electroweak symmetry breaking

    Would it be correct to represent the energy of massless particles before electroweak symmetry breaking as ##E = cp##, just as we do with photons post-symmetry breaking?
  20. G

    A Vacuum energy density after spontaneous symmetry breaking

    If we start with the Lagrangian \begin{equation} \begin{split} \mathcal{L} = & \frac{1}{2}(\partial_\mu \phi)^2 + \frac{1}{2}\mu^2 \phi^2 - \frac{1}{4}\lambda^2 \phi^4\\ \end{split} \end{equation} and give the scalar field a VEV so that we can define the field ##\eta##, where $$\eta = \phi...
  21. fluidistic

    Why is it said that magnetism breaks time reversal symmetry?

    It is known that Maxwell equations have the time reversal symmetry. I.e. by changing t by -t, J by -J (which can be understood as the charges going in the opposite direction when time is reversed, which makes sense), E to E and B to -B, the equations are still satisfied. However, it is also...
  22. G

    A Charged particles mass before symmetry breaking

    How could electrically charged particles be massless before the symmetry breaking? Wouldn't the energy stored in the electric field contribute to particles mass?
  23. H

    I Lorentz Invarience and Spontaneous Symmetry Breaking

    Spontaneous symmetry breakingI’m not sure if I understand spontaneous symmetry breaking.In the context of the Mexican hat (and marble) example, wouldn’t the actual path of the marble down the Mexican hat from the top be determined by several small factors that one would normally not consider...
  24. C

    B What was matter like during the GUT and Electroweak Epochs?

    Hi all, I was reading about the history of the early universe today, and there were some things that I did not understand. In particular, I do not understand the concept of "spontaneous symmetry breaking." After reading the Mexican Hat analogy many times, here is my best understanding of it...
  25. Milsomonk

    Spontaneous symmetry breaking scalar field masses

    Homework Statement Determine the mass of the scalars and show that one remains zero in accordance with goldstones theorem.Homework Equations $$L=\dfrac {1}{2} (\partial_\mu \phi_a)(\partial^\mu \phi_a)-\dfrac{1}{2} \mu^2 (\phi_a \phi_a) - \dfrac{1}{4} \lambda (\phi_a \phi_a)^2+ i\bar{\psi}...
  26. C

    B Electroweak spontaneous symmetry breaking

    This is a question that I have tried to pose several times without any success but, anyway, I would like to try again for the very last time. Asume for a moment that EW-SSB (electroweak spontaneous symmetry breaking) actually happened in our early universe. Imagine that our Standard Model of...
  27. J

    A Breaking of a local symmetry is impossible, so what about global symmetry....

    Breaking of a local symmetry is impossible. It is often said that therefore the role of the Higgs mechanism in the standard model is a different one. Namely, Once a gauge is fixed, however, to remove the redundant degrees of freedom, the remaining (discrete!) global symmetry may undergo...
  28. S

    A Symmetry/Conservation Violated in Quantum Anomaly

    String theorists have apparently applied String Theory to expose a Quantum Anomaly in a physical analog system: electrons flowing in a Niobium Phosphide crystal. The electrons were found to violate symmetry in relation to Spin...
  29. Ranku

    I Electroweak symmetry breaking and quantum tunneling.

    Does electroweak symmetry breaking involve quantum tunneling?
  30. Ranku

    I Quantum tunneling in symmetry breaking

    Does electroweak symmetry breaking involve quantum tunneling, just like GUT symmetry breaking?
  31. S

    A Spontaneous symmetry breaking - potential minima

    In spontaneous symmetry breaking, you expand the Lagrangian around one of the potential minima and write down the Feynman rules using this new Lagrangian. Will it make any difference to your Feynman rules if you expand the Lagrangian around different minima of the potential?
  32. A

    B Does Spontaneous Symmetry Breaking Contradict Symmetry?

    Hello, I was thinking about, how symmetry can be realized, when there is SSB occurring! Dont these terms contradict?
  33. C

    A Do cosmologists take spontaneous symmetry breaking seriously?

    I suppose that my questions are pretty basic, but I've been trying to find out the answers and not succeeded. 1.- Do cosmologists really think that the vacuum state suddenly changed in the early Universe? If so, would it be like a phase transition? If so, first or second orther? 2.- Does the...
  34. C

    I Spontaneous symmetry breaking of chiral symmetry

    The quark sector of the QCD lagrangian can be written as (restricting to two flavours) $$\mathcal L = \sum_{i=u,d} \bar q_i ( i \gamma_{\mu} D^{\mu} + m) q_i .$$ Write ##q = (u d)^T## and $$M = \begin{pmatrix} m_u & 0 \\ 0 & m_d \end{pmatrix}$$ Given that the masses of the u and d quarks are...
  35. L

    A Heisenberg ferromagnet -- Spontaneous symmetry breaking

    Heisenberg model of ferromagnet is defined by \hat{H}=-J \sum_{\langle i,j \rangle} \vec{S}_i \cdot \vec{S}_j where ##J>0## and summation is between nearest neighbours. Hamiltonian is perfectly rotational symmetric. However, the ground state “spontaneously” chooses a particular orientation...
  36. 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##...
  37. 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)...
  38. 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...
  39. 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...
  40. 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...
  41. Garlic

    Gauge Symmetry Breaking: Exploring Interactions at Low Temperatures

    Can there be interactions that are symmetric under low temperatures but exhibit spontaneous symmetry breaking under extremely low temperatures? (Maybe that symmetry breaking temperature is so low that it couldn't be discovered in experiments) Does electromagnetism split into electricity and...
  42. arivero

    Puzzling Chiral Symmetry Breaking

    Thinking aloud. Most descriptions of chiral symmetry breaking nowadays present it as something happening in QCD. But it was defined well before of the quark theory, and then it was something related to isospin symmetry. It is a bit puzzling because it seems as if pion mass were originated...
  43. Vinci128

    Hi all I'm italian, i'm graduating

    Hi everyone, my name is Vincenzo, i come from puglia in Italy and I'm studying physics at th university La Sapienza in rome. I'm writing a dissertation about the discovery of the violation of CP symmetry in the neutral K mesons system. I 'd love to discuss about these themes, and i hope i'll...
  44. R

    PT symmetry breaking in optical systems

    There are very results published about PT symmetry breaking in optical systems, with effects like anysotropical transmission resonance in waveguides. But if PT symmetry is broken in a optical system and CPT symmetry must always be respected, then what C symmetry is broken in a optical system?
  45. SoumiGhosh

    Topological phase and spontaneous symmetry breaking coexist?

    As we know topological phases cannot be explained using spontaneous symmetry breaking and order parameter. But can they coexist? Suppose there is a system which is undergoing quantum phase transition to a anti-ferromagnetic phase from a disordered phase. So in the anti-ferromagnetic phase...
  46. A

    Wilson Loop and spontaneous symmetry breaking.

    I would like to ask about the case of: ##SU(2)\otimes U(1) \rightarrow U(1)\otimes U(1),## spontaneous symmetry breaking. It is given that the Wilson Loop: ##W \equiv exp[ig \oint dy H T^1]= diag(−1,−1,1).## Where ##y## is the ##S^1/Z^2## fifth/extra dimension, ##H = \frac{1}{g R}## and...
  47. A

    SU(N) symmetry breaking by non-trivial parity.

    I would like to prove the following: Suppose we have the diagonal matrix ##P = diag(1,\ldots,1, -1,\ldots, 1)##, with ##N_+## elements of ##1## and ##N_-## elements of ##-1## such as ##N_+ + N_- = N## and ##N_+, N_- \geq 1##. This matrix is a non trivial parity matrix since it is not...
  48. K

    Questions on electroweak symmetry breaking

    I have some questions or thoughts about EW symmetry breaking. (1) Higgs mechanism gives mass to SM particles after the background higgs field rolls from ##h=0## to ##h=v## and symmetry is broken. We are talking about pole mass, aren't we? So pole mass changes continuously from ##0## to ##m##...
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