All Questions
Tagged with symmetry-breaking gauge-invariance
18
questions
46
votes
3
answers
9k
views
What role does "spontaneous symmetry breaking" play in the "Higgs Mechanism"?
In talking about Higgs mechanism, the first part is always some introduction to the concept of spontaneous symmetry breaking (SSB), some people saying that Higgs mechanism is the results of SSB of ...
- 6,095
27
votes
2
answers
3k
views
Are there massless bosons at scales above electroweak scale?
Spontaneous electroweak symmetry breaking (i.e. $SU(2)\times U(1)\to U(1)_{em}$ ) is at scale about 100 Gev. So, for Higgs mechanism, gauge bosons $Z$ & $W$ have masses about 100 GeV. But before ...
- 373
14
votes
2
answers
4k
views
Understanding Elitzur's theorem from Polyakov's simple argument?
I was reading through the first chapter of Polyakov's book "Gauge-fields and Strings" and couldn't understand a hand-wavy argument he makes to explain why in systems with discrete gauge-symmetry only ...
- 1,418
16
votes
1
answer
2k
views
Is there a spontaneous $U(1)$ symmetry breaking in atomic BECs?
In the theory of Bose-Einstein condensation, one way to define the order parameter is by using the concept of spontaneous symmetry breaking. One says that, below the critical temperature, the ...
- 161
7
votes
1
answer
479
views
Massive Gauge Bosons without Higgs fields
In a possible theory like our Standard model but without a Higgs i.e.:
$$ \mathcal{L}=i\bar{\Psi}_f\gamma_\mu D^\mu\Psi_f-\text{Tr}[G^b_{\mu\nu}G^{b\,\mu\nu}] $$
where $b,f$ run over the typical ...
- 823
6
votes
3
answers
809
views
Review: If true, what makes the vacuum of a local ${\rm U(1)}$ gauge theory unique?
Long back, I posted a question with title Is the vacuum of a local ${\rm U(1)}$ gauge theory unique?, which, as the title suggests asked whether the vacuum of a "spontaneously broken" the ...
- 26.7k
2
votes
0
answers
215
views
Where is the gauge symmetry in an ideal Bose gas?
It seems in the literature that there is a certain notion of a “macroscopic wavefunction” associated with a Bose-Einstein system (see this PSE answer) which exhibits a global $U(1)$-phase symmetry. ...
- 2,568
20
votes
1
answer
1k
views
Conformal Field Theory in 1+1d Spontaneously Breaking Conformal Symmetry
Take any 1+1 dimensional conformal field theory on the plane. The Hamiltonian is invariant under the infinite-dimensional Virasoro algebra (with some central charge $c$), generated by $L_i$ ($i\in \...
- 9,031
8
votes
1
answer
924
views
Electric charge conservation in a superconductor
In a superconductor, $U(1)$ gauge symmetry is spontaneously broken. But $U(1)$ gauge symmetry is responsible for conservation of electric charge. Then it appears to me that the electric charge ...
- 26.7k
8
votes
1
answer
533
views
Counting degrees of freedom in the Higgs mechanism for different gauges
I am wondering how to count the degrees of freedom (dof) for a massive gauge field in different gauges. I've been reading some other answers, but haven't found a solution yet.
I am looking at the ...
- 2,648
7
votes
1
answer
828
views
Vacuum expectation value (VEV) of a Gauge theory - Spontaneous Symmetry Breaking (SSB) - Higgs Mechanism
I am dealing with a sort of scalar QED with a term of SSB
\begin{equation}
\mathcal{L}=\left|D_{\mu} \phi\right|^{2}-\frac{1}{4}\left(F_{\mu \nu}\right)^{2}-V\left(\phi^{*} \phi\right)
\end{equation}
...
- 900
5
votes
0
answers
164
views
Intuition/Motivation behind necessity of Spontaneous Symmetry Breaking to generate massive gauge bosons
In field theory textbooks, it is shown that while any gauge invariant Lagrangian must involve massless gauge fields, to obtain massive gauge bosons, we must postulate the existence of a Higgs scalar ...
- 1,588
4
votes
2
answers
874
views
Local $SU(2)$ symmetry breaking and unitary gauge
In a $SU(2)$ gauge field theory with scalar field $\phi$ in the fundamental representation of the $SU(2)$ group with lagrangian $$\mathcal{L} = -\frac{1}{2}TrF_{\mu\nu}F^{\mu\nu} + (D_{\mu}\phi)^\...
- 43
4
votes
0
answers
470
views
Mermin Wagner theorem in superconductors, massive Goldstone mode
For a continuous symmetry breaking one receives a massless Goldstone mode which leads to divergent phase fluctuations in 2 and 1 dimension, thus we end up with a disordered state.
However in ...
- 111
3
votes
0
answers
184
views
Is the vacuum of a local ${\rm U(1)}$ gauge theory unique? [duplicate]
Consider a spontaneously broken scalar field theory with a global ${\rm U(1)}$ symmetry described by the Lagrangian $$\mathscr{L}=(\partial_\mu\phi^*)(\partial^\mu\phi)-\mathcal{V}(\phi),\\ \mathcal{V}...
- 26.7k