What is Spontaneous symmetry breaking: Definition and 41 Discussions
Spontaneous symmetry breaking is a spontaneous process of symmetry breaking, by which a physical system in a symmetric state ends up in an asymmetric state. In particular, it can describe systems where the equations of motion or the Lagrangian obey symmetries, but the lowest-energy vacuum solutions do not exhibit that same symmetry. When the system goes to one of those vacuum solutions, the symmetry is broken for perturbations around that vacuum even though the entire Lagrangian retains that symmetry.
I noticed that ##V(\phi)## has nonzero minima, therefore I found the stationary points as ##{{\partial{V}}\over{\partial\phi}}=0##, and found the solutions:
$$\phi^0_{1,2}=-{{m}\over{\sqrt{\lambda}}}\quad \phi^0_3={{2m}\over{\sqrt{\lambda}}}$$
of these, only ##\phi^0_3## is a stable minimum...
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:
$$D_\mu\phi_a = \partial\phi_a +...
If you were to fire a single atom from a fixed point into a chamber of perfect vacuum and measure where it collides with the opposite wall. Could Spontaneous symmetry breaking in the sub atomic particles cause momentum change in the atom, changing the part of the wall the atom interacted with?
Hello! This questions might not make sense and I am sorry if that is the case (I am asking from a QM class perspective). I am a bit confused about the idea of spontaneously symmetry breaking (SSB), from the point of view of QM. I am talking here about the energy plot looking like a mexican hat...
If we start with the Lagrangian
\begin{equation} \begin{split} \mathcal{L} = & \frac{1}{2}(\partial_\mu \phi)^2 + \frac{1}{2}\mu^2 \phi^2 - \frac{1}{4}\lambda^2 \phi^4\\ \end{split} \end{equation}
and give the scalar field a VEV so that we can define the field ##\eta##, where
$$\eta = \phi...
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...
Homework Statement
Determine the mass of the scalars and show that one remains zero in accordance with goldstones theorem.Homework Equations
$$L=\dfrac {1}{2} (\partial_\mu \phi_a)(\partial^\mu \phi_a)-\dfrac{1}{2} \mu^2 (\phi_a \phi_a) - \dfrac{1}{4} \lambda (\phi_a \phi_a)^2+ i\bar{\psi}...
This is a question that I have tried to pose several times without any success but, anyway, I would like to try again for the very last time.
Asume for a moment that EW-SSB (electroweak spontaneous symmetry breaking) actually happened in our early universe. Imagine that our Standard Model of...
This is spontaneous symmetry breaking problem.
1. Homework Statement
Temperature is ##T=0##.
For one component complex scalar field ##\phi##, non-relativistic Lagrangian can be written as
$$
\mathcal{L}_{NR}=\varphi^* \Big( i\partial_t + \dfrac{\nabla^2}{2m} \Big)\varphi -...
Hello,
I was reading about the Higgs mechanism and I must say that I did not really follow the argument of how the gauge symmetry is broken.
I think that my problem has to do with the more general question of how does a gauge symmetry get broken in general?
Thanks!
Hi.
I don't understand the meaning of "up to total derivatives".
It was used during a lecture on superfluid. It says as follows:
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Lagrangian for complex scalar field ##\phi## is
$$
\mathcal{L}=\frac12 (\partial_\mu \phi)^*...
Hello,
I'm trying to understand how the superfluidity is connected with the Lagrangian of the system: in some textbooks (e.g. Antony Zee qft in nutshell) it is stated, that in case, when the excitations in the fluid have energy spectrum linear with momentum , there is a critical velocity, which...
In spontaneous symmetry breaking, you expand the Lagrangian around one of the potential minima and write down the Feynman rules using this new Lagrangian.
Will it make any difference to your Feynman rules if you expand the Lagrangian around different minima of the potential?
I suppose that my questions are pretty basic, but I've been trying to find out the answers and not succeeded.
1.- Do cosmologists really think that the vacuum state suddenly changed in the early Universe? If so, would it be like a phase transition? If so, first or second orther?
2.- Does the...
The quark sector of the QCD lagrangian can be written as (restricting to two flavours) $$\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}$$
Given that the masses of the u and d quarks are...
Heisenberg model of ferromagnet is defined by
\hat{H}=-J \sum_{\langle i,j \rangle} \vec{S}_i \cdot \vec{S}_j
where ##J>0## and summation is between nearest neighbours. Hamiltonian is perfectly rotational symmetric. However, the ground state “spontaneously” chooses a particular orientation...
Homework Statement
A simple classical example that demonstrates spontaneous symmetry breaking is described by the Lagrangian for a scalar with a negative mass term:
##\mathcal{L}=-\frac{1}{2}\phi\Box\phi + \frac{1}{2}m^{2}\phi^{2}-\frac{\lambda}{4!}\phi^{4}##.
(a) How many constants ##c##...
Consider a theory with two multiplets of real scalar fields ##\phi_i## and ##\epsilon_i##, where ##i### runs
from 1 to N. The Lagrangian is given by: $$\mathcal L = \frac{1}{2} (\partial_{\mu} \phi_i) (\partial^{\mu} \phi_i) + \frac{1}{2} (\partial_{\mu} \epsilon_i) (\partial^{\mu} \epsilon_i)...
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...
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...
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...
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...
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...
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'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...
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...
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'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
Was the early spontaneous symmetry breaking caused by exponential expansion in the first instant of standard theory?
Is that the reason that the early Big Bang universe is thought to have contained equal amounts of matter and anti-matter (produced by spontaneous symmetry breaking)?
Does...
On spontaneous symmetry breaking and Higgs’s mechanism of mass production
From lectures: L. Peak and K. Varvell. The Physics of the Standard Model.
Full Lagrangian for fermion and photon
Combine the gauge-invariant Lagrangian density describing a fermion field in the presence of an...
I often have this problem when reading physics books (the kind I can understand) where, because I'm only in High school math, the author explains only in analogies, and the analogies sometimes don't make logical sense.
I'm reading Steven Weinberg's "Dreams of a Final Theory" and I got to the...
Hello. I've got a QFT final tomorrow, and one question is still bothering me.
Consider two lagrangians.
The first one is
L = \frac{1}{2} D_{\mu} \vec{\phi}.D^{\mu} \vec{\phi} + \frac{m^{2}}{2} \vec{\phi}.\vec{\phi} - \frac{\lambda}{4} \left(\vec{\phi}.\vec{\phi}\right)^{2}
The second...