8
votes
2answers
100 views

In what sense do Goldstone bosons live in the coset?

Goldstone's theorem says that if a group, $G$, is broken into its subgroup, $H$, then massless particles will appear. The number of massless particles are given by the dimension of the coset, $G/H$. ...
0
votes
1answer
73 views

Amplitudes involving Goldstone bosons

Does anyone know some theorem or statement about amplitudes involving only Goldstone bosons in theories with spontaneous symmetry breaking in the limit of low energies?
5
votes
1answer
71 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 ...
1
vote
1answer
74 views

The self-coupling constant for the Higgs mechanism

I have a few questions about the parameter $\lambda$ in the Higgs-Lagrangian density $$\mathcal{L}_H=(D_\mu \phi)^\dagger D_\mu \phi + \mu^2\phi^\dagger\phi-\lambda(\phi^\dagger\phi)^2$$ Is it ...
3
votes
0answers
31 views

Detecting Polarization States of Quantum Field

(Background) In the scenario where a gauge symmetry is spontaneously broken and the gauge field eats the Goldstone boson to acquire a mass, the massive gauge field acquires a longitudinal ...
16
votes
0answers
237 views

Symmetries of the Standard Model: exact, anomalous, spontaneously broken

There are a number of possible symmetries in fundamental physics, such as: Lorentz invariance (or actually, Poincaré invariance, which can itself be broken down into translation invariance and ...
5
votes
1answer
162 views

Why must SUSY be broken?

Background One usually claims that supersymmetry must be spontaneously broken. The reasoning is roughly the following: Since $M^2=P^{\mu}P_{\mu}$ is a casimir operator of the supersymmetry algebra, ...
1
vote
1answer
143 views

What to do with a $\phi$ term in a Lagrangian?

I am considering a Lagrangian that is of the following form: $$\mathcal{L}=-{1\over 2}\partial_\mu\phi\partial^\mu\phi+2\mu^2\phi^2+2\sqrt{6}{\mu^3\over \lambda}\phi + {9\mu^4\over 2\lambda} + ...
6
votes
1answer
146 views

Goldstone mode in O(N) (non-linear $\sigma$ model)

The question is does the Non-linear $\sigma$ model have a Goldstone mode? Consider a $O(N)$ mode for which the Hamiltonian is $H=J\sum_{i,j}\vec{n}_i \cdot \vec{n}_j$, where ...
4
votes
1answer
64 views

Why does the minimum energy field configuration require the fields to be constant?

I am having a hard time in understanding a well known statement always made in the context of field theory. Background Consider a classical real scalar field theory with Lagrangian density given by ...
4
votes
2answers
170 views

The Higgs vacuum

Srednicki's "Quantum Field Theory", an electronic copy of which is freely available here, seems to state on p 205 that the states eq. (32.3) which differ by a phase factor that can range through ...
4
votes
1answer
123 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 ...
4
votes
2answers
131 views

Why Goldstone Bosons? (A Question about VEVs)

I understand how the mechanism of spontaneous symmetry breaking works, and why it produces Goldstone bosons (for global symmetries) and massive gauge bosons (for local ones). However, I'm confused as ...
3
votes
0answers
159 views

Some ambiguous points on Spontaneous Symmetry Breaking (SSB)?

Almost in every textbook of condensed matter physics, the standard description of SSB could be formulated as follows: Consider the lattice Heisenberg model in an external magnetic field ...
2
votes
1answer
175 views

Symmetry Breaking and Vacuum Expectation Values

Consider a real scalar field $\phi$ in a theory with a Lagrangian $$ \mathcal{L}:=-\frac{1}{2}\partial _\mu \phi \partial ^\mu \phi -V(\phi ), $$ where $$ V(\phi ):= -\mu ^2\phi ...
2
votes
1answer
195 views

What led to the electroweak and strong forces splitting?

Is the reason for the split believed to be spontaneous symmetry breaking? If so, did SSB occur because the Universe was cooling rapidly from extremely high temperatures?
0
votes
0answers
43 views

chirality oscillations in weak interaction

As far as I have understood, the mass $m$ of a fermion causes a coupling of the both chiralities $\psi_L$ and $\psi_R$. This coupling would induce an oscillation of the chirality within a time scale ...
5
votes
2answers
236 views

In spontaneous symmetry breaking, global symmetry broken by gauged subgroup?

My question is simple. Given a group $G$ broken to a subgroup $H$, gauging a possibly different subgroup Hg breaks explicitly the global symmetry $G$, generating what is known as pseudo-Goldstone ...
1
vote
0answers
87 views

Spontaneous symmetry breaking by axions?

I am just reading at the beginnin of this nice article, that axions could be responsible for spontaneously breaking of a symmetry in the early universe. Does anybody know which symmetry is alluded to ...
6
votes
2answers
524 views

Spontaneous symmetry breaking in classical mechanics, quantum mechanics and quantum field theory

I wondered if someone could help me understand spontaneous symmetry breaking (SSB) in classical mechanics, quantum mechanics and quantum field theory. Consider a Higgs-like potential, with a local ...
4
votes
1answer
172 views

What if EM or QCD was spontaneously broken?

Suppose that Standard Model Higgs mechanism broke electromagnetism, by e.g. veving the charged component of the doublet, so that the photon was massive with $m_\gamma\sim v$. Could such a Universe ...
4
votes
0answers
87 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 ...
-1
votes
1answer
124 views

Symmetry breaking with Lagrangian

I have been studying the spontaneous symmetry braking from Zee (Quantum Field theory ) and found in the page 224, he wrote the lagrangian as $$\mathcal{L}= \frac{1}{2}\{ λ (∂φ)^2 + μ^2φ^ 2\} − ...
2
votes
1answer
137 views

How to find the Higgs coupling with a mixing matrix?

It is known that the couplings to the Higgs are proportional to the mass for fermions; $$g_{hff}=\frac{M_f}{v}$$ where $v$ is the VEV of the Higgs field. I'm trying to figure out why this is true ...
1
vote
1answer
164 views

Multiple vacua vs. vev's in qft

Take a (possibly supersymmetric) relativistic quantum field theory: when we construct it, we suppose that there is a unique vacuum state $|0\rangle$ which is Lorentz invariant, vector of some Hilbert ...
6
votes
0answers
80 views

Does the Standard Model plasma develop a spontaneous magnetisation at finite temperature?

Reference: arXiv:1204.3604v1 [hep-ph] Long-range magnetic fields in the ground state of the Standard Model plasma. Alexey Boyarsky, Oleg Ruchayskiy, Mikhail Shaposhnikov. The authors of this paper ...
19
votes
1answer
1k 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 ...
14
votes
1answer
406 views

Spontaneous breaking of Lorentz invariance in gauge theories

I was browsing through the hep-th arXiv and came across this article: Spontaneous Lorentz Violation in Gauge Theories. A. P. Balachandran, S. Vaidya. arXiv:1302.3406 [hep-th]. (Submitted on 14 ...
4
votes
1answer
122 views

Dimensional transmutation in Gross-Neveu vs others

Firstly I don't know how generic is dimensional transmutation and if it has any general model independent definition. Is dimensional transmutation in Gross-Neveau somehow fundamentally different ...
8
votes
1answer
173 views

Chiral perturbation theory: what is the Quark Condensate? why expand in $U$ rather than Goldstone fields?

I'm studying Chiral Perturbation Theory (ChPT) from Scherer's manuscript "Introduction to Chiral Perturbation Theory", available at http://arxiv.org/abs/hep-ph/0210398 What I am currently having ...
8
votes
1answer
315 views

Dispersion of ferromagnetic ($E\propto k^2$) and antiferromagnetic ($E\propto k$) spin wave

The dispersion of ferromagnetic spin wave at low energy is $E\propto k^2$, while $E\propto k$ for antiferromagnetic case. Is there a simple/physical argument (such as symmetry) for these results? ...
4
votes
1answer
463 views

Spontaneous symmetry breaking in SU(5) GUT?

At the end of this video lecture about grand unified theories, Prof. Susskind explains that there should be some kind of an additional Higgs mechanism at work, to break the symmetry between the ...
5
votes
2answers
650 views

What is the role of the vacuum expectation value in symmetry breaking and the generation of mass?

Consider a theory of one complex scalar field with the following Lagrangian. $$ \mathcal{L}=\partial _\mu \phi ^*\partial ^\mu \phi +\mu ^2\phi ^*\phi -\frac{\lambda}{2}(\phi ^*\phi )^2. $$ The ...
12
votes
2answers
1k views

Self energy, 1PI, and tadpoles

I'm having a hard time reconciling the following discrepancy: Recall that in passing to the effective action via a Legendre transformation, we interpret the effective action $\Gamma[\phi_c]$ to be ...
2
votes
2answers
446 views

Effects of a non-Lorentz-invariant vacuum state

I'm here asking about real or though experiments (i.e., physical effects) where, at least in principle, one can see some consequence of a non-Lorentz-invariant vacuum state in an otherwise Poincare ...
-1
votes
1answer
186 views

What is Supersymmetry (SuSy)? [closed]

In particle physics, supersymmetry (often abbreviated SUSY) is a symmetry that relates elementary particles...etc. what is symmetry breaking? What is supersymmetry (SUSY)? What is spontaneous ...
4
votes
1answer
115 views

What kinds of inconsistencies would one get if one starts with Lorentz noninvariant Lagrangian of QFT?

What kinds of inconsistencies would one get if one starts with Lorentz noninvariant Lagrangian of QFT? The question is motivated by this preprint arXiv:1203.0609 by Murayama and Watanabe. Also, what ...
2
votes
1answer
339 views

Spontaneous symmetry breaking and 't Hooft and Polyakov monopoles

What is spontaneous symmetry breaking from a classical point of view. Could you give some examples, using classical systems.I am studying about the 't Hooft and Polyakov magnetic monopoles solutions, ...
1
vote
1answer
85 views

Can symmetry be restored in high energy scattering?

Suppose you have a field theory with a real scalar field $\phi$ and a potential term of the form $\lambda \phi^4 - \mu \phi^2$ that breaks the symmetry $\phi \to - \phi$ in the ground state. Is this ...
1
vote
0answers
106 views

What is the mean field value of a scalar field with spontaneously broken symmetry in a scattering event?

Consider you have a quantum field theory that undergoes spontaneous symmetry breaking at some critical temperature. It doesn't necessarily have to be a continuous symmetry that's broken, I don't think ...
6
votes
0answers
182 views

Breaking of Lorentz invariance

Thinking about the concept of symmetry breaking led me to the following question: Let's say that I have a theory described by a Lorentz invariant Lagrangian, and the true vacuum of the theory is not ...
5
votes
1answer
211 views

Goldstone's theorem and massless modes for $\phi^4$ theory

Consider a scalar field doublet $(\phi_1, \phi_2)$ with a Mexican hat potential $$V~=~\lambda (\phi_1^2+\phi_2^2-a^2)^2.$$ When $a=0$ this is a quartic potential and the symmetry is not ...
3
votes
0answers
118 views

Polyakov action as broken symmetry effective action

I would like to ask if it is possible to regard the Polyakov action as an effective action that describes the broken symmetric phase of a more general model. Could someone draw an analogy with O(N) ...
2
votes
1answer
106 views

Why are we forced to choose a specific value for $\pi$ field in Nambu-Goldstone phenomenon?

In the sigma-model of spontaneous symmetry breaking, we have degenerate vacuum states. But if we don't pick up a particular value of VEV, we won't have any symmetry breaking. As I read from a book, in ...
4
votes
3answers
302 views

In SUSY why does electroweak symmetry breaking only happen in the SM sector?

This is a difficult question to phrase succinctly, so I hope the title makes sense. What I want to understand is what seems like a lack of symmetry (besides SUSY-breaking) between the SM sector and ...
2
votes
1answer
831 views

Chiral anomaly and decay of the pion

I am told that if all classical symmetries were reflected as quantum symmetries, the decay of the neutral pion $$\pi^0 ~\longrightarrow~ \gamma\gamma$$ would not happen. Why would the conservation of ...
8
votes
1answer
89 views

Which is the coupling between the photon and the SU(2)xU(1) gauginos, before symmetry breaking?

The photon field is the non chiral piece of SU(2)xU(1), independently of symmetry breaking or not, isn't it? But before symmetry breaking, each gauge boson has only a chiral gaugino as ...
9
votes
3answers
504 views

Spontaneous breaking of Lorentz invariance

Is it possible to spontaneously break Lorentz invariance, i.e., have a Lagrangian that respects LI but a vacuum which does not? If it is possible, why isn't there even the slightest hint of the ...
3
votes
1answer
74 views

Experimental limits on anisotropies in the $e/m_{e}$ ratio

Currently the charge-to-mass ratio of the electron is known to 10 orders of magnitude. However, i'm curious if: Are there any experiments trying to bound the anisotropy of this ratio for different ...