Questions tagged [symmetry-breaking]

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 SSB characteristic nonlinear realizations (Goldstone mode), and the group theoretical patterns involved.

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Were all symmetries of the universe spontaneously broken?

I can think of two distinct notions of symmetry. One in which I start with a system in state $\mathcal{S}_0$ and perform some transformation on it to get another system in state $\mathcal{S}_0'$. Now, ...
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Residual Symmetry Group after Spontaneous Symmetry Breaking

I am seeking a proof of the following: Suppose we have a theory with $n$ scalar fields $(\phi_1,...,\phi_n)$ such that the Lagrangian $L$ is invariant under the action of some group $G$. However, $G$ ...
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Do supertranslations act in a physically nontrivial way?

I'm currently reading arXiv: 1703.05448 [hep-th]. In this question, I'm interested in a statement made on page 67 of the pdf (76 of the printed book, if you prefer to check in it). There, the author ...
Níckolas Alves's user avatar
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Spontaneous Symmetry Breaking, Vacuum Degeneracy, and Goldstone Bosons applied to large gauge transformations

I am reading Strominger's lecture notes on the infrared structure of gravity and gauge theory. I am trying to understand subchapter 2.11, where the author focuses on the notions of "Spontaneous ...
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How can quantum fluctuations lead to Spontaneous Symmetry Breaking?

I'm studying Quantum field theory and I came across Spontaneous Symmetry breaking and the Weinberg-Coleman potential. My question is more conceptual. The way I understand it the Coleman-Weinberg ...
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Possible divergence of susceptibility without spontaneous symmetry breaking?

In the article Strange Metals as Ersatz Fermi Liquids , the authors mentioned in the left bottom paragraph on page 4 that Furthermore the diverging susceptibility of an order parameter at a quantum ...
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$SU(5)$ Gauge Field Theory, symmetry breaking

If I start with an $SU(5)$ gauge group and discover that the vacuum is preserved only by matrices of the form $G$ $$\begin{bmatrix} A & 0 \\ 0 & B \\ \end{bmatrix}$$ where ...
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Perturbation Theory with no symmetry breaking?

I was learing about group theory in QM and stable about symmetry breaking. I find it very interesting and search some stuff and even looked on wikipedia and found this: https://en.wikipedia.org/wiki/...
Alexandru Chirvasa's user avatar
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Existence of low temperature phase in 2-Dimensional XY-Model

I'm reading the lecture notes of David Tong on Statistical Field Theory, specifically chapter $4.4$ on the Kosterlitz-Thouless Transition. He considers the XY model in $d=2$ dimensions and states the ...
Μπαμπης Ποζουκιδης's user avatar
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Question about $E_8$ symmetry breaking and hypercharge formula

Most $E_8$ gauge theories follow this breaking chain: $$E_8 \rightarrow E_6 \times SU(3)_{Gen}.$$ How does the $E_6 \times SU(3)$ group break down through $SO(10)$, the Pati-Salam Model or the Minimal ...
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$SU(2)$ breakdown to $U(1)$

When we break a lagrangian symmetric with $SU(2)$ with a higgs bosons being the adjoint representation, using the following v.e.v for higgs $\phi$, $$\langle \phi \rangle = (0,0, \rho)^T.$$ Two ...
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Before spontaneous symmetry breaking, what is the difference between the fermion generations?

Before spontaneous symmetry breaking (SSB), all fermions have the same mass (0). Across the 3 different fermion generations, all the (left) quarks doublets have the same weak isospin, and all the up ...
TrentKent6's user avatar
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What is the (non-broken) Peccei-Quinn symmetry?

In the references I read, it's always said that the Peccei-Quinn (PQ) symmetry is a $U(1)$ symmetry, and the PQ Lagrangian has a potential term that, for a certain temperature, assumes a mexican-hat ...
Mauro Giliberti's user avatar
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Is the weak quark mixing a consequence of electroweak symmetry breaking?

Because of the CKM matrix, the quark doublets that are changed by $W^{+}$ and $W^{-}$ include a linear combination of quark flavours, instead of the pure quark flavours. I was wondering if, before ...
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Are all of the characteristics of elementary particles essentially symmetry differences?

I am trying to get a better conceptual grasp on the "splitting" of the fundamental forces at the beginning of the universe. The first force to separate was the gravitational force. Am I ...
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Why do the members of $SU(2)$ doublets gain different masses after spontaneous symmetry breaking?

Before spontaneous symmetry breaking (SSB) elementary particles belonging to the same $SU(2)$ doublets are indistinguishable, which clearly is not the case after SSB. I am comfortable with the idea of ...
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Anderson Higgs mechanism and superconducting phase fluctuations

In the context of superconductivity, in the Anderson Higgs mechanism (see, for instance, https://doi.org/10.1119/1.5093291 (PDF), or https://doi.org/10.21468/SciPostPhysLectNotes.11 (PDF), the gauge-...
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Proper definition of spontaneously broken symmetry

I am currently working on generalized symmetries and i was reading https://arxiv.org/abs/2301.05261. In footnote 23 the authors state: To be precise, by spontaneous symmetry breaking, we mean a phase ...
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Thermodynamics and Gibbs energy

The equation for the Gibbs free energy is: $\Delta G = \Delta H - T\Delta S.$ $\Delta H$ is the amount of energy difference between the initial state (characterized by $U_{i}$, $S_{i}$, and $V_{i}$) ...
15_7008 Phú Hữu Trần Đôn's user avatar
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Are Hamiltonians CPT invariant?

I'm confused by the CPT theorem. It states (more or less) that a Lorentz invariant quantum field theory needs to be CPT invariant. But what does it actually mean for a QFT to be CPT invariant? It ...
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Why does flowing current break time reversal symmetry?

I am reading about the Quantum Hall Effect. In a course, they wrote that How does one get a Hall effect? The key is to break time-reversal symmetry. A flowing current breaks time-reversal symmetry, ...
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Spontaneous breaking of discrete symmetry in d=1+1 at finite temperature and infinite volume

I came across the question of SSB of a discrete symmetry (say, $\mathbb{Z}_2$) symmetry in a QFT in d=1+1 dimensions, at finite temperature, and I have trouble making sense of two different viewpoints ...
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Spontaneous symmetry breaking and ergodicity

I am studying the spontaneous symmetry breaking in the mean-field Ising model and it's clear to me the necessity of taking first the thermodynamic limit and then the zero-field limit to see the phase ...
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Symmetry groups breaking for the lagrangian of two complex scalar fields

Suppose we have a generic non-interacting Lagrangian of two complex scalar fields, \begin{align} \mathcal{L} &= (\partial^\mu \Phi^\dagger)(\partial_\mu \Phi) - \Phi^\dagger\mathbb{M}^2\Phi \tag{1}...
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Spectral function of superconductor in the BEC regime: how does Higgs mechanism affect the spectrum?

Consider the standard BCS theory but assume that the interaction energy $U$ that enters the definition of gap parameter (i.e. $\Delta = (U/N)\sum_k \langle c_{-k\downarrow} c_{k\uparrow} \rangle$, ...
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Domain walls in theories of axions

I'm stuck in figuring out why some theories of axions predict the existence of domain walls. Axions are NG bosons associated with the chiral $U(1)_{PQ}$ symmetry, which was spontaneously broken at ...
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Identification of $W$ and $Z$ mass terms in SSB and Unitary Gauge

I have two questions, both relating to the SSB of Electroweak Lagrangian. My notes say that after breaking and expanding around the VEV, the masses of $W$ and $Z$ are identified by comparing to the ...
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Proof of continuous symmetry breaking

My question concerns how to show/explain the existence of spontaneous symmetry. I will lay out a seeming paradox, preporting to show no symmetry breaking is possible. I understand the resolution for a ...
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Goldstone bosons and spontaneous symmetry breaking in the complex triplet model

In the Standard model electroweak theory, the Higgs field is a complex doublet field, which couples to the $SU(2)$ gauge field. Suppose we replace the complex doublet with a complex triplet $\Sigma$: $...
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Mermin-Wagner theorem and SSB in 2D: is there sound in low dimensional solids

The Mermin-Wagner theorem states that there cannot be any spontaneous symmetry breaking happening in systems with short range interactions below dimension 3. Moreover, we know that Goldstone boson, ...
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Spontaneous Symmetry Breaking and/or Higgs Mechanism, WIthout Field Redefinition

In all explainations of spontaneous symmetry breaking that I've seen, the scalar field doing the breaking is redefined around its vacuum expectation value (VEV), and similarly for the higgs mechanism -...
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Spontaneous symmetry breaking in relativistic QFT: (possible) equivalence of two definitions

Consider a QFT invariant under a Lie group $G$. Let this symmetry be implemented on the Hilbert space by unitary operators $U=$exp$(i \epsilon^A Q^A)$. The fields $\phi_n(x)$ transform according to $$\...
Jack Euler's user avatar
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What is the reverse operation of gauging a global symmetry?

As far as I understand, gauging a global symmetry means taking a model with a global symmetry and transforming it into a model such that the previous symmetry group is now the gauge symmetry of your ...
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Infinite conductivity, goldstone bosons and generalized voltage

Weinberg [1] has put forth an elegant argument (summarized in [2, Section 3.3] and at the bottom of the question), which suggests that the broken symmetry phase of any $U(1)$ gauge theory will be ...
phonon's user avatar
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Introductory material for effective potential in thermal QFT?

I'm looking for materials that systematically deal with both thermal and quantum corrections to the effective potential to all loop orders at a beginner-friendly level with prerequisites of QFT before ...
1 vote
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What is a symmetry defect?

I found that it is a normal concept appearing in condensed matter physics and especially topological order field. I have been aware of the topological defect. But what is a symmetry defect? Could ...
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What is the topology of sine-Gordon equation?

In one pdf on solitons, I am finding the following written For the sine-Gordon theory, it is much better to think of $\phi$ as a field modulo $2\pi$, i.e. as a function $\phi: R \rightarrow S_{1}$. ...
Arkaprava Sil's user avatar
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Electroweak Interaction and SSB

I read that above unification energy, on the order of 100 GeV, electromagnetic force and weak force would merge into a single electroweak force. I do not really understand how and when exactly two ...
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The difference between High energy SUSY and low energy SUSY

In the literature and comments, I have met two pieces of jargon: Low energy SUSY, High energy SUSY I'm confused about the technical and well-defined conceptual differences between the two type of ...
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Why does isospin symmetry survive chiral symmetry breaking?

In QCD there is a breaking of chiral symmetry such that, for the lightest quarks only, we have $$\langle \overline{u} u \rangle = \langle \overline{d} d \rangle = \mathrm{const.}$$ where the constant ...
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Lattice $SU(2)$ Higgs model in unitary gauge

I'm currently reading the book Quantum Fields on a Lattice by I. Montvay and G.Münster, and in section 6.1 they describe lattice actions for various higgs models. And I got confused at the moment ...
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Comparing "gauge theory" and "(global) spontaneous symmetry breaking"

To construct an effective field theory with spontaneously broken global symmetries, we need building blocks for the Lagrangian (such as covariant derivatives) that seem similar to gauge theory ...
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Do we have an analytic calculation to derive $\frac{F^2}{4}\,\text{Tr}\left\{\partial_\mu U\partial^\mu U^{\dagger}\right\}$ from the QCD Lagrangian?

I have studied the quark condensate and chiral perturbation theory. However, I am not sure where the "kinetic term" of the pion $$\frac{F^2}{4}\operatorname{Tr}\left\{\partial_\mu U\partial^...
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Notion of $4$-vectors in Lorentz symmetry violating case

$4$-vectors can be defined in various ways. One very common way among them is by saying if $A^{\mu}$ is some $4$-vector, then it will transform via the Lorentz transformation rule and will obey the ...
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Calculating the vacuum in an $O(2)$ spontaneous symmetry breaking

Consider the Lagrangian (we ignore the quantum correction here) $$\mathcal{L}=-\frac{1}{2} \partial_\mu \phi_1 \partial^\mu \phi_1-\frac{1}{2} \partial_\mu \phi_2 \partial^\mu \phi_2-\frac{\mu^2}{2} \...
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What symmetry has to be broken to result in the hyperfine structure splitting?

In Quantum Mechanics, symmetry operators $\mathcal{S}$ are associated with degeneracies if the Hamiltonian $H$ is conserved under the symmetry operation in question $$\mathcal{S}^{\dagger}H\mathcal{S} ...
grav.field's user avatar
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Relating phase transition with symmetry-breaking according to Landau Theory

I am trying to reproduce the results from this paper where they find out the expression for the Landau functional to be $$\psi(x,t,p)=\frac{1}{4}(\frac{1}{x}+6x+px^3-4tx^2)$$ Now we plot Landau ...
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How do we known that $\langle \bar{\psi}_i \psi_j\rangle=(250 MeV)^3\delta_{ij}$?

I have started to read the phenomenology of QCD in low energy regime. I understand that, from the QCD renormalization group equation, the QCD becomes nonperturbative theory when energy scale is below $...
StupiXPerson's user avatar
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$C$-violation in SM Lagrangian?

It's usually said that SM Lagrangian violates charge conjugation, and should be obvious from the fact that "only left handed fermions are charged under $SU(2)_{L}$ but left and right handed ...
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Why are there no diccussions of hypercharge conservation or Dirac hypercharge monopoles?

The Maxwell equations can be derived from an equation for a spin 1 field with $U(1)$ symmetry. From this field equation is possible to postulate Dirac monopoles by simply roting the real and complex ...
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