Symmetry breaking Definition and 119 Threads

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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!

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

Dear all, I have a question regarding the usual Goldstone theorem, which states that, for a system with continuous symmetry breaking, massless bosons must appear. However, if you look at the derivations of this theorem [1], the crucial assumption seems that, the conserved quantity associated...

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...

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?

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...

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?

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...

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...

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 =...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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

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