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Weinberg's spontaneously broken symmetries

Steven Weinberg in his second volume of QFT's book (in section about spontaneously broken symmetries, in subsection about Goldstone bosons) writes following: if we have linear transformation of ...
3
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2answers
59 views

Simplest example of spontaneous breaking of time reversal symmetry

Consider a two-dimensional fluid flow, confined to a square, where the bottom is held at a higher temperature than the top. With appropriate choices of the parameters, this will form a single ...
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29 views

Still confused about $ T_i $ generators (Spontaneous Breakdown) [on hold]

If the Langrangian density is $$L=\frac{1}{2}(\partial_\mu \Phi)\cdot(\partial^\mu \Phi)-V(\Phi \cdot \Phi)$$ where $V(\Phi \cdot \Phi)=\frac{1}{2}\mu^2 \Phi \cdot \Phi + \frac{1}{4}|\lambda|(\Phi ...
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1answer
41 views

Why Levi-Civita term signal the breaking of parity and time reversal?

For example, referring to Zee's QFT book, in Chern-Simons matter theory, after writing a term $$\gamma {\varepsilon ^{\mu \nu \lambda }}{a_\mu }{\partial _\nu}{a_\lambda }$$ he said The ...
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39 views

Lorentz violation in String theory

First of all, why are there so many researches to find Lorentz violation? Are there some models of (super-)string theory that include Lorentz violation at some scale?
3
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151 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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0answers
31 views

Weinberg's QFT and superconductors

In the beginning of subparagraph about superconductors (which corresponds to paragraph about spontaneously symmetry breaking) Weingberg states that in superconductors EM gauge invariance is ...
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0answers
36 views

Understading triplet Majoron model

In the Higgs triplet Majoron model, the spontaneous breakdown of ungauged lepton number gives rise to two Numbu-Goldstone bosons. But isn’t the SU(2) symmetry also broken? I mean when the neutrak ...
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1answer
56 views

Problem with determining number of goldstone bosons

Consider a theory $$\mathcal{L}=(\partial_\mu\Phi^\dagger)(\partial^\mu\Phi)-\mu^2(\Phi^\dagger\Phi)-\lambda(\Phi^\dagger\Phi)^2$$ where $\Phi=\begin{pmatrix}\phi_1+i\phi_2\\ ...
4
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1answer
105 views

Does the Lorentz invariance of equation of motion guarantee the Lorentz invariance of the solutions?

If I have a Lorentz invariant equation of motion, like Klein-Gordon equation, is the solution automatically guaranteed to be Lorentz invariant? I ask this question because of the discussion from Mark ...
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0answers
67 views

Where do pions go in the spontaneous symmetry breaking of the linear sigma model?

I have a few questions to figure out Peskin 4.3 problem which is Linear sigma model about the interactions of pions at low energy. This model consist of N scalar fields governed by the Hamiltonian ($ ...
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0answers
38 views

Where does the $\gamma_5$ here come from?

If we have that $$\delta \psi_L = i \epsilon_L^aT_a\psi_L$$ and $$\delta \psi_R = i \epsilon_R^aT_a\psi_R$$ And then we say that the above can be written in terms of $\epsilon^a$ and $\epsilon^a_5$ ...
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1answer
42 views

Relation between gauge symmetry and mass difference

Usually (like in Georgi's Lie Algebra book) people argue the reason why Gellmann $SU(3)$ flavor symmetry (u,d,s) can't extend to $SU(4)$ (u,d,c,s) or higher flavour symmetry is the their mass ...
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0answers
33 views

Trilinear term in SUSY soft-breaking

In MSSM soft-SUSY breaking, there are such term called 'A-triliear term'. But, some papers, e.g Riva-Biggio-Pomarol, do not have trilinear term. What is the use of introducing trilinear term?
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0answers
114 views

A naive question on the “continuously” degenerate ground states of 1d phonons?

In general, the gapless Goldstone mode is related to the "continuously" degenerate ground states. The Mexican hat potential is an example (see the logo of this SE website), where the bottom circle is ...
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1answer
97 views

Goldstone modes of spin density wave

A spin density wave (SDW) is a phase in which a material suddenly shows a periodically modulated spin density $S_{\vec{q}}(\vec{r}) $ below a certain critical tempereature $T_C$. Obviously some kind ...
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0answers
22 views

Spatial symmetry breaking and locality

I consider a system described by a state $\Psi(\mathbf{r})$, where $\mathbf{r}$ are the spatial coordinates. The energy of the system is a functional $E[\Psi]$. An usual analysis of a phase ...
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1answer
23 views

Must a symmetric phase and a symmetry-breaking phase be different?

When I was reading this paper, it urged me to ask whether a symmetric phase and a symmetry breaking phase must be different? As I am considering quantum phase transitions, let $H(g)$ be a general ...
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2answers
166 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.
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0answers
22 views

Charge density waves: site-centering v.s. bond-centering

Question about charge density wave (CDW): From this Ref. page 13, why bond-centering charge density wave is naturally compatible with the observed coexistence of charge ordering and ...
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0answers
22 views

Spontaneous breaking order and the Peierls order

From this this Ref, several types of orderings are considered. Question: What are the Hamiltonians which support the Peierls order? Do they necessarily break translational symmetry or break the ...
5
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1answer
152 views

Why do we need spontaneous symmetry breaking in Lagrangian formalism?

I have always struggled with the concept of spontaneous symmetry breaking. It seems to me that many others don't find it very intuitive as well, but that could be just me having difficulties with the ...
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133 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 ...
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1answer
82 views

Is this an example of spontaneous symmetry breaking?

Consider a pencil standing in a (ideally) perfectly vertical position. The gravitational field will the same no matter the (angular) direction it will fall in. But it will end up falling in a ...
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1answer
98 views

Terminology of Higgs boson and Goldstone boson

I know, the from the Higgs Mechanism, or Spontaneous symmetry breaking, the massless Goldstone boson becomes massive. So in some sense Goldstone bosons are eaten by gauge "boson". Here I got ...
3
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1answer
68 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, ...
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0answers
31 views

Non-minimal coupling (Pauli Coupling) of gauge field with a non-relativistic scalar field

I am wondering if it makes any sense to non-minimally (say, Pauli-like) couple an external gauge field with a non-relativistic scalar field: \begin{equation} p_\mu \rightarrow p_\mu - e A_\mu + ...
2
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1answer
66 views

Spontaneous symmetry breaking of SHO

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 ...
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0answers
35 views

Symmetry breaking and band gaps?

Can the discontinuity in the E-K dispersion relation of a periodic lattice (at the boundary of a Brillouin zone) be understood as a consequence of breaking continuous translation symmetry into ...
6
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1answer
158 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 ...
2
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2answers
167 views

masslessness of Goldstone boson, Effective action, and functional-integral measure

I have difficulty in understanding the path-integral formalism of SSB, and that of Effective Action. Let's say a complex scalar field theory has the global $U(1)$ SSB, $$L(\phi)=(\partial^\mu ...
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1answer
43 views

Explicit Symmetry Breaking: Where do the additional d.o.f. come from?

Massless vector bosons have only two independent degrees of freedom, while massive ones have three. In spontaneous symmetry breaking, the massless vector belonging to the broken group becomes massive ...
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3answers
113 views

Spontaneous symmetry breaking to subspace not giving massless bosons

I'm currently trying to understand spontaneously broken in general and have stumbled upon a weird result which doesn't seem to correspond to my knowledge about broken gauge symmetries. Suppose we ...
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2answers
75 views

Unification of the electroweak theory

Can the electroweak theory be described by the spontaneous symmetry breaking of $SU(3)$ to $SU(2)\times U(1)$?
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0answers
72 views

Simple questions on the symmetric eigenstate and time-reversal (TR) breaking eigenstate?

Followings are two independent questions as implied by the title: (1) Considering a quantum Hamiltonian $H$ possesses some symmetries described by a symmetry group $G=\left \{ g_1,g_2,...,g_n \right ...
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0answers
36 views

Conductivity Matrix (Symmetry Information)

I'm trying to understand the symmetry content of the conductivity matrix: one information is, presence of time-reversal symmetry causes the off-diagonal terms to vanish. When this is broken (e.g. in ...
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0answers
41 views

Discrete Symmetries: Breaking and Preserving

This is not a question, let's list down all the effects resulting from breaking or preserving of various discrete symmetries, on various observables, be it in condensed matter or in high energy. ...
4
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1answer
153 views

Why doesn't topological phase transition break any symmetry? Hidden symmetry?

This question may be superficial. However why all people saying this without a proof? Just like the "hidden variables" assumption in quantum mechanics, can one disproof that there is no hidden ...
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0answers
28 views

Mean-field approach to quantum phase transitions in Fermi systems

I have a basic confusion concerning the mean-field theory of quantum phase transitions in Fermi systems. Consider as an example the BCS theory of superconductivity in a Dirac fermion system, ...
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2answers
98 views

What are spin and valley symmetries in graphene?

I have been assigned a presentation on a part of a paper (http://arxiv.org/abs/1303.6942). My task is to present on the spin and valley symmetries in graphene, and relate it back to the paper above. ...
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0answers
53 views

What is the relation between pseudogap and time reversal symmetry breaking?

Some papers concerning high-$T_c$ superconductor discuss the pseudogap and time reversal symmetry breaking. My questions are: What is the characteristic of order-parameter in pseudogap? How to ...
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0answers
25 views

Hamiltonian governing liquid to a solid transition

What is the Hamiltonian 'H' (at the atomic or molecular level) that governs the phase transition from a liquid to a solid state? Actually, I want to explicitly verify the Hamiltonian 'H' admits the ...
3
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2answers
143 views

Origin of quark masses

Does all the mass of the quarks in the standard model come from the Higgs sector or is there also a contribution to quark masses due to QCD chiral symmetry breaking?
2
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1answer
131 views

Dilaton field and Scale symmetry breaking

I have read at some places that a dilaton field is associated with the spontaneous breaking of scale symmetry in a theory. (While others would be difficult to trace right now, the most easily ...
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0answers
100 views

Why doesn't Graphene have a band gap?

Is there any simple justification about graphene having no band gap? How bout its linear E-K? Why bilayer graphene has a quadratic E-K and electric field can open a band gap there? I do not ...
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1answer
172 views

Intuitive explanation of how hadron mass emerges from the strong force

I'm not familiar with QCD, but I'm looking for intuitive explanation of this phenomenon (it could be that easy explanation does not exist). What I've read is that large part of hadron masses arises ...
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vote
1answer
65 views

Ambiguous points in spontaneous symmetry breaking of discrete symmetry

For a discrete symmetry: At the minimum value of the potential, $V$, in the Lagrangian density, why do we take $\phi= \langle v\rangle + \eta$? Aren't we deliberately breaking the symmetry? If we ...
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2answers
593 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.
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0answers
19 views

Symmetry breaking under isothermal expansion

Is there any example of a symmetry breaking phase transition in a system of particles under isothermal expansion?
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1answer
117 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 ...