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20 views

Topological terms VEVs and ghosts

Suppose we have the Standard model, and we want to calculate with VEVs of topological susceptibilities of $SU_{L}(2), U_{Y}(1)$ and $SU_{c}(3)$ fields, which have the form $$ \tag 1 \kappa \equiv ...
26
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2answers
700 views

Finding the vacuum which breaks a symmetry

I will start with an example. Consider a symmetry breaking pattern like $SU(4)\rightarrow Sp(4)$. We know that in $SU(4)$ there is the Standard Model (SM) symmetry $SU(2)_L\times U(1)_Y$ but depending ...
3
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1answer
221 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 ...
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2answers
158 views

Quantum Anomalies and Quantum Symmetries

In Quantum Field Theories (QFT) there is a well known phenomenon of anomalies, where a classical symmetry is broken in the quantum theory due to a so called anomaly. This symmetry breaking can be ...
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1answer
465 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 ...
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0answers
28 views

The nature of axion-like particle

Suppose that we have axion-like particle $\varphi$ theory, $$ \tag 1 S_{a} =\int d^{4}x\left(\frac{1}{2}(\partial_{\mu}\varphi )^{2} - \frac{m^{2}}{2}\varphi^{2} - \frac{\varphi}{f_{\varphi}}F_{\mu ...
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1answer
65 views

How do symmetries break in cosmology?

The way I understand spontaneous symmetry breaking in thermodynamic systems is that the symmetry is actually explicitly broken by an infinitesimally small field. The system chooses one of the ...
3
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1answer
61 views

Why do the conserved charges in the case of SSB of a global symmetry not exist?

Reading "From Linear SUSY to Constrained Superfields" by Komargodski and Seiberg, I got a bit confused regarding the existence of the conserved charges in a theory with spontaneous symmetry breaking ...
2
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1answer
211 views

Is $SU(2)$ really broken by the Higgs VEV or just hidden?

It's generally stated in the textbooks that whent the Higgs field acquires a certain vev the corresponding symmetry is spontaneously broken. For example in A. Zee - QFT in a Nutshell: But none of ...
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1answer
36 views

Soft SUSY breaking fermion mass terms in MSSM for matter fields

In the MSSM, the chiral fermion fields (the Higgsinos) don't have any soft SUSY breaking mass terms and trilinear interactions while their scalar superpartners have so, whereas naively it should have ...
2
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1answer
64 views

Chiral current VEV below the QCD scale

Let's have pure QCD. I know that after spontaneous symmetry breaking quark bilinear form are replaced by their averaged values: $$ \bar{q}_{i}q_{j} \to \langle \bar{q}_{i}q_{j}\rangle \approx ...
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0answers
28 views

Feynman rules complex field in polar form

I am trying to derive the Feynman rules for this field: $$L=-\partial \phi^*\partial \phi - \frac{\lambda}4 (|\phi|^2-v^2)^2 $$ With this coordinates $\phi = \frac 1 {\sqrt2}\rho \exp(i \theta)$, ...
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0answers
38 views

Difference between a Hamiltonian and its mean-field form?

In most solid state physics text books, BCS theory is introduced in the following way: The authors introduce a mean-field parameter (based on the superconduncting pair) and upon that, they reduce the ...
3
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1answer
46 views

Broken symmetries realized nonlinearly

I'm trying to understand some concepts of spontaneous symmetry breaking, I'll write first the statement that I can't understand and later my questions. STATEMENT Consider a group $G$ and a subgroup ...
3
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1answer
102 views

Doubts about spontaneous symmetry breaking

I have been exposed to the usual treatment about spontaneous symmetry breaking in the standard model but it shames me to admit that there are some loose ends I still have to tie up. For simplicity, ...
1
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1answer
113 views

Is the Higgs mechanism a gauge transformation or not? ( $U(1)$ context )

I'm trying to understand the way that the Higgs Mechanism is applied in the context of a $U(1)$ symmetry breaking scenario, meaning that I have a Higgs complex field ...
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11answers
6k 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 ...
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0answers
52 views

Magnetism in Topological Insulator?

I have read many papers with the statement that on the introduction of the magnetic impurity, the gap at the Dirac point opens in the surface states. I am little confused about it. If the gap is ...
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0answers
76 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), ...
3
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1answer
75 views

Spontaneous symmetry breaking of anomalous global abelian symmetries and $U(1)$ of QCD

Let me restate the $U(1)$ problem of QCD: Let us forget about the $s$ quark, and consider the $u$ and $d$ massless. This is a good approximation since $m_{u,d} \ll \Lambda_{QCD}$. Then ...
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2answers
167 views

Is my understanding of Gauge Symmetries correct?

I'm currently working on a project about Symmetry Breaking for my physics bachelor. Right now I'm trying to understand Gauge Symmetries (although I guess it's not much of a symmetry). And I've been ...
21
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1answer
2k views

Emergent symmetries

As we know, spontaneous symmetry breaking(SSB) is a very important concept in physics. Loosely speaking, zero temprature SSB says that the Hamiltonian of a quantum system has some symmetry, but the ...
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1answer
734 views

What is the difference between quantum fluctuations and thermal fluctuations?

Start with a simple scalar field Lagrangian $\mathcal{L}(\phi)$ at zero temperature $T = 0$, which has a hidden symmetry and spontaneously break it. By the standard procedure a field $\phi$ is ...
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0answers
76 views

Higgs mechanism in 1+1 spacetime dimensions

I know there are problems with Goldstone's theorem, as stated by Coleman in http://projecteuclid.org/download/pdf_1/euclid.cmp/1103859034. What about Higgs mechanism? Can I possibly think of a ...
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4answers
383 views

What role does “spontaneously symmetry breaking” played in the “Higgs Mechanism”?

In talking about Higgs mechanism, the first part is always some introduction to the concept of spontaneously symmetry breaking (SSB), some people saying that Higgs mechanism is the results of SSB of ...
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1answer
222 views

From which dimensionful constants does proton mass arise?

It is well known that the most of the proton (or any other hadron with light quarks) mass is not made up from quark masses, but it is dynamically generated by QCD mess inside. I've also heard that, ...
3
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1answer
75 views

One-point function and vacuum expectation value in $\phi^4$-theory

Why is it that the one-point function in the $\phi^4-$theory, for example calculated from the generating functional, always gives zero value in absence of external source i.e., $J=0$? If there is ...
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2answers
3k views

Norton's dome and its equation

Norton's dome is the curve $$h(r) = -\frac{2}{3g} r ^{3/2}.$$ Where $h$ is the height and $r$ is radial arc distance along the dome. The top of the dome is at $h = 0$. Via Norton's web. If we put ...
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0answers
22 views

How to compute remnant discrete charges?

When a $U(1)$ gauge symmetry is broken by Higgs field with $U(1)$ charge $g$, we have a remnant $\mathbb{Z}_q$ symmetry. How can I compute the corresponding charges under this remnant group for ...
1
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1answer
64 views

Center group and Symmetry breaking

First, I will state the definition of center, $i.e$, the center of group $C_G$ is defined a sthe part of $G$ which commutes with all generators. I want to know the procedure of breaking gauge ...
9
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1answer
1k views

What is a quark condensate?

What is a quark condensate? is it a bound state between 2 quarks? can we have 3(or more)-quarks condensate? What mediates the interaction between the constituents of the condensate? Are the ...
1
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2answers
139 views

Tachyonic field

i'm working on a paper about symmetron cosmology. symmetron is a scalar field that by its symmetry breaking can explain the dark energy. the action is: ans A , V are assumed to be: where M ...
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0answers
45 views

How can the VEV of a field be a function of spacetime?

Often in the discussion of effective action and effective potential (say, in the context of $\phi^4-$theory )the one-point function in presence of source is defined as \begin{equation} \frac{\delta ...
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1answer
109 views

Where does in GUT symmetry breaking $U(1)$ come from?

In GUTs one starts with some larger group, like $SU(5)$, which is then broken into smaller groups, for example $$SU(5) ~\longrightarrow~ SU(3) \times SU(2) \times U(1)$$ This can be seen, for ...
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0answers
108 views

Why does Wikipedia equate hidden symmetry with broken symmetry for the standard model?

I have recently started studying the basic ideas of symmetry and group representation in order to understand the basic principles behind the standard model. I do follow the difference between a global ...
1
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1answer
46 views

Is it possible to have spontaneous symmetry breaking without scalars?

I have never seen spontaneous symmetry breaking with a fermion filed, or a gauge field. Always scalars. So is it possible to have spontaneous symmetry breaking without scalars, and why?
5
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1answer
144 views

Georgi-Glashow model and the VEV of the scalar field

Consider the Georgi-Glashow model, an $SU(2)$ gauge theory with a real scalar in the adjoint (thus a 3-vector in the colour space) $\phi$. The Lagrangian is $$ L = -\frac{1}{4g^2} F_{\mu \nu}^{\, a} ...
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0answers
48 views

Given a VEV how can I compute which generators remain unbroken using tensor methods?

This is a follow up to this question. A generator $T_a$ of a given gauge group $G$ remains unbroken after some Higgs field $\Phi$ gets a vev if $$ T_a \langle\Phi\rangle =0 $$ I'm trying to ...
5
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2answers
281 views

Quantum Anomalies for Bosons

We know that there is Adler and Bell-Jackiw(ABJ) type anomalies for fermions. In some case, the ABJ anomaly affecs particle physics pheonomelogy, such as pion decays or kaon decays(in the case of ...
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2answers
72 views

Determination of the ground state of a field theory

Consider the Spontaneous symmetry breaking in the theory $$\mathcal{L}=\frac{1}{2}\partial_\mu\phi\partial^\mu\phi-\frac{\mu^2}{2}\phi^2+\frac{\lambda}{4!}\phi^4.$$ By the ground state of a ...
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0answers
54 views

Explicit Matrix Representation for 54 Higgs rerpesentation for $SO(10)\rightarrow$ Pati-Salam Breaking

Which Higgs field or linear combination of Higgs fields gets a vev if we want to break $$ SO(10) \rightarrow SU(4) \times SU(2) \times SU(2) ? $$ Formulated a bit differently, I'm looking for an ...
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0answers
48 views

Physical proceses before the breaking of $SU(2)_L\times U(1)_Y$ symmetry

The energy scale which the electromagnetic and the weak interaction were unified, there were 4 massless gauge bosons: 3 corresponding to the unbroken generators of $SU(2)_L$, say $W_{\mu}^{1,2,3}$ ...
2
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0answers
27 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 ...
2
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0answers
68 views

Books on superconductivity and its relation to spontaneous symmetry breaking

I wish to understand more about the relationship between superconductivity and spontaneous symmetry breaking. I would also appreciate sources for learning about symmetry breaking and particles in more ...
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0answers
38 views

Excitation spectrum of heisenberg model

I understand that ferromagnetic Heisenberg model (lattice of spin variables that can point in any direction) spectrum can be deduced by a $\lambda\phi^4$ theory with $\phi$ being complex. This model ...
4
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1answer
167 views

Group theoretic way to find charges after SSB

I was wondering what is the group theoretic way to find the resulting charges of matter fields after a scalar field is given a vev. In the case of the EW symmetry breaking, one can directly read the ...
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0answers
40 views

Resource for (String) Symmetry Breaking in Terms of Roots and Weights?

I'm currently searching, for quite a while now, for a paper/book that discusses symmetry breaking in terms of roots and weights. Any suggestions would be much appreciated!
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1answer
96 views

How are scale of renormalization and scale of symmetry breaking related?

If symmetry breaking, e.g. with a potential $V=-\mu^2\phi^2 + \lambda \phi^4 $ occurs at a certain energy scale, and I now evolve to another scale via the Callan-Symanzik equations, does that change ...
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0answers
21 views

Question on distinct phases through spontaneous symmetry breaking.

If I have a many-body Hamiltonian that is invariant under the representation of a certain group $G$ i.e [H,U(g)] = 0, how many phases does can exist through spontaneous symmetry breaking (SSB) of this ...
3
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0answers
43 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 ...