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0answers
34 views

Infinitesimal transformation by Noether's charge [on hold]

Can anybody explain me the physics of the commutation relation : $ [Q,\phi_{i}] = it_{ij}\phi_{j}$ ; where, Q is Noether's charge and $\phi_{i} (i=1,2)$ are components of an isodoublet?
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2answers
136 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 ...
3
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1answer
36 views

One-point function and VEV 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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0answers
36 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 ...
1
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1answer
123 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 ...
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1answer
351 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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1answer
91 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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3answers
156 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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0answers
86 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
133 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
40 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
votes
1answer
117 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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1answer
515 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 ...
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0answers
37 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
238 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
57 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
40 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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1answer
381 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
39 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
23 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
53 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 ...
1
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0answers
31 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
165 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
39 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
65 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
18 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
37 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 ...
0
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0answers
19 views

Can a macroscopic passive system break the time-reversal symmetry spontaneously?

I know there are many systems can break T-symmetry if the internal source ALREADY chooses a direction of T. Without any driving source inside the system, can T-symmetry be broken spontaneously?
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1answer
142 views

Is Elitzur's theorem valid only in lattice field theory?

Elitzur's theorem, stating that spontaneous breakdown of a gauge symmetry is impossible, was originally proved for a lattice gauge theory. Is it valid in continuum field theory? Any ref?
0
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0answers
27 views

Break time-reversal symmetry in photonic system without using bias magnetic field

In photonic system, e.g, photonic crystals, people usually use ferromagnetic material or so called Tellegen medium which acts as effective field bias to break the time-reversal symmetry. I just want ...
1
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1answer
61 views

Why didn't we have inflation when the theory of everything and GUTS broke symmetry?

I asked this in astronomy and they suggested I ask it here. Inflation seems to have occurred when the symmetry breaking of the electroweak occurred. But do we know of any reason why we did not have ...
2
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1answer
78 views

How to find the remaining subgroup after some Higgs field gets a VEV?

Say we have a group $G$ and a set of Higgs fields in a representation $R$ of $G$. One of the Higgs fields in $R$ gets a VEV, how can I determine the remaining subgroup after this symmetry breaking? ...
2
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0answers
77 views

Axion strings and spontaneously broken symmetry

I have two question about axion strings: Why their appearance is connected with spontaneously broken symmetry? How to demonstrate that? Why they are stable topological configurations (look to the ...
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2answers
229 views

What's the heuristic reasoning for Chiral Symmetry breaking

In Peskin and Schroeder (page 669), and other references, the heuristic reasoning for why one would expect chiral symmetry breaking at low energies is that quark masses are small and hence it's not ...
2
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0answers
74 views

Goldstone's theorem massless states

I'm currently trying to wrap my head around Goldstone's theorem proof as given by Itzykson & Zuber. The reasoning is pretty straightforward, but there's a result that's bothering me from a ...
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0answers
147 views

Categorizing solutions to Hierarchy problem

We know that no gauge symmetry can prevent a term $m_\phi^2|\phi|^2$ for a scalar field, and that, given the quadratic loop corrections, the natural scale is $m_\phi \sim M_P$. This is related to the ...
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1answer
42 views

Transformations of electroweak gauge field $W_\mu$ under $U(1)_{e.m.}$

As the vector boson field $W_\mu$ is, together with $Z^0$, the gauge field for the Standard electroweak model, I know it transforms as a connection under the $SU(2)\times U(1)_Y$ group. But, when this ...
3
votes
2answers
111 views

Functional integral in spontaneous symmetry breaking

So, functional integral is defined to be (with $\lvert\Omega\rangle$ is the vacuum state): $$\frac{\langle\Omega\rvert ... \lvert\Omega\rangle}{\langle\Omega\vert\Omega\rangle} = \int \mathcal{D} ...
1
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1answer
44 views

Why we do we consider explicit SUSY breaking in the MSSM and not an spontaneous breaking of SUSY?

Reading about the minimal supersymmetric standard model (MSSM) I have found that an explicit breaking of supersymmetry is considered, given by the term $$\cal{L}_{soft}$$ where soft supersymmetry ...
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2answers
99 views

Solutions of symmetric equations are not invariant - is symmetry spontaneously broken?

I have a system of equations: \begin{cases} f\left(x_{1}\right)+f\left(x_{2}\right)+P=0\\ \\ g\left(x_{1}\right)+g\left(x_{2}\right)=0 \end{cases} where $f$ and $g$ are some functions, $P$ is a ...
7
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1answer
335 views

If a symmetry operator S in a QFT annihilates the vacuum, why does S preserve the space of 1-particle states?

In the paper "Supersymmetry and Morse Theory", on the third page (p. 663 in the journal version), Witten says: "Now in any quantum field theory if a symmetry operator (an operator which commutes ...
2
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1answer
58 views

Poincare non-invariance in real world and field theory

This may be a very blunt question but I wonder why we always use Poincare invariant Lagrangians in field theory. After all, the entire world around us is by no means homogeneous, isotropic and so on. ...
14
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1answer
280 views

Explicit supersymmetry breaking fermion mass terms

I hope you can clear up my following confusions. In Girardello's and Grisaru's paper (Nuclear Physics B, 194, 65 (1982)) where they analysed the most general soft explicit supersymmetry breaking ...
2
votes
5answers
206 views

Which way will the pencil fall?

Let's say you had a perfect pencil, with a point which was just that one point (see this question). The pencil's mass was perfectly distributed, and there are no flaws in the craftsmanship. Let's say ...
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0answers
33 views

What are the limitations of simulating grand unification theories of elementary particles in condensed matter settings?

What are the limitations of simulating grand unification theories of elementary particles in condensed matter settings? I know that condensed matter systems can be constructed to be described by any ...
0
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0answers
27 views

How can we determine the Hypercharges in a GUT like SO(10)?

I understand how the assignment works for a symmetry breaking like $$SO(10) \rightarrow SU(3)_C \times SU(2)_L \times SU(2)_R \times U(1)_X$$ The Hypercharge can then easily computed by $$ ...
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2answers
720 views

What is (meant by) a non-compact $U(1)$ Lie group?

In John Preskill's review of monopoles he states Nowadays, we have another way of understanding why electric charge is quantized. Charge is quantized if the electromagnetic U(l)em gauge group ...
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1answer
73 views

Is sound a Nambu-Goldstone mode?

The usual sound exists in solids, liquids, and gases, as a long-wavelength excitation with linear dispersion. Can its presence be attributed to the spontaneous breaking of some symmetry? In other ...
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1answer
49 views

Can anyone explain to a novice physicist whether there is a gravitational-electromagnetic symmetry?

I am trying to understand how the four fundamental forces relate to one another and to a theory of everything. As I understand it the unified force that is thought to exist at very high energies gets ...
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2answers
946 views

How is Meissner effect explained by BCS theory?

Someone says we can derive the GL equations from BCS theory, which can explain Meissner effect, but I want a more clear physical picture of this phenomena.