In explicit symmetry breaking, the equations of motion of a physical system are variant under the broken symmetry; by contrast, for spontaneous symmetry breaking (SSB), these equations are invariant, but the entire system is not because its vacuum (background) is non-invariant. Further use for the ...

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19
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1answer
672 views

Vibrational anharmonic coupling and noise-induced spontaneous symmetry breaking in a hexagonal finite mechanical lattice

Happy holidays, everyone! The following is part question, part visual gallery, and part classical mechanics problem. Inspired by snow over the weekend I began simulating the vibrations of the ...
3
votes
1answer
50 views

Spontaneous symmetry breaking of gauge symmetry in 1+1 dimensions?

The Mermin-Wagner theorem states that continuous global symmetries cannot be broken in two or fewer spacetime dimensions; however, I have not seen this statement applied to gauge theories. Does it ...
0
votes
2answers
141 views

What happens to Goldstone bosons in the Higgs potential after symmetry breaking?

When the gauge symmetry of our Lagrangian breaks spontaneously through the Higgs mechanism, we usually find that $n$ Higgs degrees of freedom become massless through the vacuum expecation value (vev), ...
30
votes
3answers
27k views

First and second order phase transitions

Recently I've been puzzling over the definitions of first and second order phase transitions. The Wikipedia article starts by explaining that Ehrenfest's original definition was that a first-order ...
5
votes
1answer
69 views

Electric charge conservation in a superconductor

In a superconductor, $U(1)$ gauge symmetry is spontaneously broken. But $U(1)$ gauge symmetry is responsible for conservation of electric charge. Then it appears to me that the electric charge ...
0
votes
0answers
10 views

Quadrupolar interaction

In http://journals.aps.org/prb/pdf/10.1103/PhysRevB.64.195109 Eq.(4), why does the Fourier transform of the quadrupolar interaction function takes the form \begin{equation} F(\mathbf{q})=\frac{F_2}{1+...
49
votes
11answers
7k views

What is spontaneous symmetry breaking in QUANTUM systems?

Most descriptions of spontaneous symmetry breaking, even for spontaneous symmetry breaking in quantum systems, actually only give a classical picture. According to the classical picture, spontaneous ...
8
votes
2answers
199 views

Can a superpartner be less massive than its SM counterpart?

Theoretically, can a superpartner be less massive than its standard model counterpart? I realize there are experimental constraints.
6
votes
1answer
268 views

Coupling of matter field with gauge boson and Goldstone boson:

What's the fundamental difference between the way a gauge boson gets coupled to a matter field, preferably a Fermionic field and the way a Goldstone boson gets coupled to the matter field ? In ...
46
votes
3answers
6k views

Do pear-shaped nuclei really have anything to do with time travel?

Recently (in the last week or two), various articles about pear shaped nuclei have appeared, such as this one from Science Alert and this from the BBC The Science Alert article includes the quote ...
0
votes
0answers
40 views

Complex field with a chemical potential

This is probably a very basic question. I'm looking at the following Lagrangian with a single complex field $\phi$, $$\mathscr{L} = D_{\mu}\phi^*D^{\mu}\phi - m^2 \phi^* \phi - \lambda (\phi^* \phi)^...
0
votes
0answers
39 views

Why must the Vacuum Manifold contain the quotient group?

For a symmetry breaking pattern $G \rightarrow H$, the vacuum manifold must contain the quotient space $G/H$. In most cases, we take the vacuum manifold to be the quotient space. My question is, Is ...
14
votes
1answer
474 views

Does measurement, quantum in particular, always increase the total entropy?

Measurement of a quantum observable (in an appropriate, old-fashioned sense) necessarily involves coupling to a system with a macroscopically large number of degrees of freedom. Entanglement with this ...
3
votes
3answers
69 views

Why do we need $SU(2)\times U(1)$ invariant mass terms if the symmetry will be broken anyway?

In the SM we can not add fermionic mass terms like $m \overline{e}_R e_L$ to the Lagrangian since these terms are not invariant under $SU(2)\times U(1)_Y$. After introducing the Higgs in the unitary ...
7
votes
1answer
287 views

effect of a simultaneous local and a global $U(1)$ symmetry breaking

EDIT : I am trying to figure out the effect of symmetry breaking in a $U(1)_Y\times U(1)_Z$ invariant lagrangian where $U(1)_Y$ is local symmetry of the Lagrangian and $U(1)_Z$ is a global symmetry of ...
0
votes
1answer
91 views

Why is $\rm SU(2)\times SU(2)$ spontaneously broken?

Following the approach of Weinberg's book to discuss the chiral symmetry, at a certain point he says If the $\rm SU(2)\times SU(2)$ symmetry is exact and unbroken, then this would require any ...
1
vote
0answers
39 views

How does bilayer 2d materials break inversion symmetry and how does it lead to a bandgap?

Some (?) monolayer 2d materials have inversion symmetry, however bilayer materials don't (?). This opens up a bandgap in bilayer graphene. 1) How does bilayer break inversion symmetry? In which cases ...
3
votes
0answers
58 views

Higgs mechanism in quantum GLSM

My question is regarding the following Gauged Linear Sigma Model (GLSM) in two dimensions. $$\tag{1} S=\int d^2x\Big(-D_{\mu}\overline{\phi} D^{\mu}\phi +\frac{D^2}{2e'^2} +D(|\phi|^2-r)\Big).$$ ...
0
votes
0answers
47 views

What is Hastatic order?

I've looked around for a proper definition and defining terms for this property. Can anyone explain Hastatic order? Is there a proper theory as to why it occurs? (Also, I don't have points to create a ...
1
vote
2answers
61 views

Why $U(1)_Y$ hypercharge rather than $U(1)_\text{em}$ electromagnetism?

In the Standard Model we have $SU(2)_I\times U(1)_Y$, where $U(1)_Y$ is weak hypercharge and $SU(2)_I$ is the symmetry group of weak isospin. Why do we introduce $U(1)_Y$ of weak hypercharge rather ...
-1
votes
1answer
57 views

Understanding standard model and symmetry

I just want to know whether my understanding regarding standard model and symmetry is correct or utter nonsense. The standard model is the (yet incomplete) Lagrangian of the universe. The ...
1
vote
0answers
75 views

“Constant Fermion”

I was talking to a professor in my institution which works in Lorentz Violation of various QF theories. While we talk about a SUSY lagrangian, I asked him if we could have a fermion acquiring VEV and ...
1
vote
1answer
48 views

How does a $\Theta$ function arise in this correlator?

I am currently reading the paper by Coleman on Symmetry breaking in 2d, which can be found here. On page 262 (4th page in the document), he is evaluating the following distribution: $$ F_{\mu}(k)=\...
2
votes
0answers
40 views

Massless excitations without SSB

Is there possible the situation when there are massless excitations in spectrum of states in a theory with phase transition but without spontaneous symmetry breaking? The motivation for this question ...
3
votes
2answers
382 views

Why are there gapless excitations in the anti-ferromagnetic Heisenberg model while the true ground state is a singlet?

The true ground state of the anti ferromagnetic quantum Heisenberg Model (nearest neighbor only)is known to be a singlet (I think this is Liebs theorem.) Since a singlet is invariant under rotations, ...
3
votes
0answers
141 views

Are symmetries of a degenerate ground-state manifold always broken?

If a Hamiltonian has a global symmetry and a degenerate ground state, then in the thermodynamic limit, the ground states $| \psi \rangle$ that are eigenstates of the symmetry operator typically become ...
2
votes
1answer
152 views

What is the minimal symmetry required for a spin Hamiltonian to describe a spin-liquid ground state?

Let's restrict to the case of spin-1/2 system. As we know, a spin-liquid (SL) state is the ground state of a lattice spin Hamiltonian with no spontaneous broken symmetries (sometime it may ...
0
votes
0answers
32 views

Symmetry breaking with adjoint matter, departing from vacuum in different way

$$L=-\frac{1}{4}TrF_{\mu\nu}F^{\mu\nu}+\frac{1}{2}D_\mu\phi D^\mu \phi -\lambda V(\phi)$$ Say we have a potential $V(\phi)=(|\phi|^2-v^2)^2$, and 3-component real scalar field $\phi=(\phi_1, \phi_2, \...
3
votes
1answer
68 views

Can a symmetry breaking VEV lie far above the “symmetry breaking scale?”

The scale where some symmetry gets broken can be computed using the renormalization group equations for the gauge couplings. If there is only one Higgs VEV responsible for some breaking, can this VEV ...
1
vote
0answers
26 views

What are the Higgs masses for $SU(2) \times U(1)$ goes to $U(1)$ symmetry breaking with a complex triplet?

Consider an $SU(2)\times U(1)_Y\rightarrow U(1)_{EM}$ theory that is broken via a complex triplet with hypercharge 2. The potential is of the form \begin{align} V(\Phi) = -m^2\Phi^\dagger\Phi + \...
5
votes
1answer
96 views

Spontaneous symmetry breaking of a spinor / vector field [duplicate]

Why does SSB deal only with scalar fields and not with fermion or vector fields? My professor told me that it's closely related to the Lorentz invariance of the theory, but I don't understand at all ...
5
votes
3answers
1k views

Why cannot fermions have non-zero vacuum expectation value?

In quantum field theory, scalar can take non-zero vacuum expectation value (vev). And this way they break symmetry of the Lagrangian. Now my question is what will happen if the fermions in the theory ...
2
votes
0answers
57 views

Physical meaning of the chiral condensate in QCD

Considering the QCD Lagrangian in the chiral limit, where all the quarks masses are set to zero. Then the Lagrangian has the following chiral symmetry: $$ SU(L)_{V} \times SU(L)_{A} \times U(1)_{V} \...
1
vote
1answer
51 views

Left-right topology

Are there non-trivial topological solutions (in particular 't Hooft-Polyakov magnetic monopoles) associated with the (local) breaking \begin{equation} SU(2)_R \times SU(2)_L \times U(1)_{B-L} \to SU(...
3
votes
1answer
83 views

Symmetry breaking to a special subalgebra?

This is a follow-up to my question here. For regular subalgebras of some group's Lie algebra the root system of the subalgebra is a subset of the root system of the original's group algebra. In ...
11
votes
5answers
280 views

How is the ground state chosen in a spontaneous symmetry breaking process?

This question is about how the ground state is chosen in a spontaneous symmetry breaking process. Say we have a Mexican Hat potential (e.g. the one for the Higgs field) and are sitting at the unstable ...
0
votes
0answers
16 views

how to construct a model with fully broken SU(2) gauge symmetry, in which the masses of all three vector bosons are different

When we do the spontaneous symmetry breaking of SU(2) local gauge symmetry, the three vector fields acquire mass which is equal for all three of them. Now how do I construct a model in which the ...
1
vote
1answer
46 views

How does the surface of a material always break inversion symmetry?

I am trying to visualize this for an HCP structure. Take the profile view as such: just working in 2d. So my understanding is if we can take a point (x,y) -> (-x,-y) and get the same crystal than ...
1
vote
0answers
28 views

Spontaneous symmetry breaking of scalar multiplet theory

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) (\...
0
votes
0answers
32 views

Spontaneous Symmetry Breaking in global $U(1)$ symmetry

I was reading SSB from Ashok Das - Lectures on Quantum Field Theory. I have a couple of questions. First Question Equation (7.65) reads $$\delta\sigma(x)=-i\epsilon[Q,\sigma(x)]=\epsilon\chi(x)...
0
votes
0answers
26 views

What is the difference between the generation of mass for Fermions compared with Bosons in the standard model?

I've seen a few questions asking how the Higgs mechanism generates mass for particles of the standard model. However, I haven't seen any which specify the differences between Bosons and Fermions in ...
2
votes
0answers
29 views

Gauge mediated SUSY breaking

I have seen it claimed that in SUSY gauge mediated breaking there can be no flavour changing terms because the mediation is flavour blind. What does this mean and how does it work?
3
votes
1answer
47 views

Symmetry responsible for equality of masses of particles

During my studies of basic particle physics the following question came up. What symmetry is responsible for equality of masses of particles and their antiparticles? In particular, is this symmetry ...
7
votes
2answers
132 views

Lie groups with same algebra

I had a problem when considering symmetry breaking in an SO(4) gauge theory: $\mathcal{L} = \left| D_\mu\phi \right|^2$ where $D_\mu$ is the SO(4) covariant derivative. Then assuming there is some ...
2
votes
0answers
47 views

Are the pions really all that light?

I'm studying the sigma model where the pions are identified as the (pseudo) Nambu-Goldstone bosons of chiral symmetry breaking ("pseudo" from mild isospin symmetry violation). This argument usually ...
5
votes
1answer
55 views

Is there a spontaneous $U(1)$ symmetry breaking in atomic BECs?

In the theory of Bose-Einstein condensation, one way to define the order parameter is by using the concept of spontaneous symmetry breaking. One says that, below the critical temperature, the ...
0
votes
0answers
44 views

Equation for Electric and Magnetic field from the equation for a “massive photon”

I was reading the Quantum Field Theory book by Maggiore. There he says that in side a superconductor the photon satisfies the equation $$(\Box+m^2)A_\mu=0$$ Then he adds that the electric field and ...
3
votes
1answer
84 views

How to find the remaining subgroup after some linear combination of Higgs fields gets a VEV?

This is a follow-up question to this question. How can I compute which generators remain unbroken when a linear combination of Higgs fields $a \Phi_1+ b\Phi_2$ get a vev? If I compute the unbroken ...
4
votes
1answer
93 views

Superposition of distinct vevs in spontaneous symmetry breaking

The simplest account of spontaneous symmetry breaking goes like this. Take a potential $V(\phi)$ with symmetric minima that are not at $\phi = 0$, like the Mexican hat potential shown in this site's ...
1
vote
1answer
84 views

Meaning of counterterms and quantum corrections

When one talks about the “classical Lagrangian” of a field, does one mean the tree-level Lagrangian with physical masses and physical couplings? If yes, does it therefore mean that the bare Lagrangian ...