All Questions
Tagged with symmetry-breaking gauge-invariance
42
questions
2
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answers
64
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Masses of $SU(2)$ gauge bosons
I'm currently learning quantum field theory and I'm wondering one thing.The way I understood it is that in the $SU(2)$ Yang-Mills theory, all gauge bosons have the same mass due to the spontaneous ...
- 41
0
votes
1
answer
63
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Is there an operator to measure pre-SSB boson states?
A common statement is that post-SSB electroweak gauge bosons are linear combinations of pre-SSB gauge bosons.
It is also usually stated that pre-SSB bosons can also be thought of as linear ...
- 127
2
votes
0
answers
62
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Predicting a nonzero mass for the photon
This is a concern I had after I had read the reply for a previous question I had: On the masslessness of the photon
So, I have been told that there are cases in which the gauge symmetry that preserves ...
- 3,982
2
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128
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What is the current theoretical and experimental understanding of the mass of the photon? [duplicate]
To what extend are we allowed to claim that the photon has some sort of mass, below some threshold. We certainly have no experimental evidence that the photon is completely massless, but, due to the ...
- 3,982
1
vote
1
answer
112
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Symmetries changing depending on spacetime?
Just as the Lorentz symmetry holds globally in Minkowski spacetime, could the opposite also occur? That is, are there any spacetimes where the Lorentz symmetry would be broken (locally, not just ...
- 2,466
2
votes
1
answer
123
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Spontaneous Symmetry Breaking and gauge symmetry
As mention in David Tong's Lecture note:
Gauge symmetry is, in many ways, an odd foundation on which to build our best theories of physics. It is not a property of Nature, but rather a property of ...
- 171
1
vote
1
answer
70
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Explicit computation in finding the minima of a gauge symmetry invariant potential
I'm reading some notes about the symmetry breaking and the standard model. From what I understand, typically one has a symmetry group of transformations (the gauge group) acting on vectors of fields, ...
- 23
3
votes
1
answer
254
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Structure Group vs Gauge Group in Gauge Spontaneous Symmetry Breaking
Recently I’ve been learning about spontaneous symmetry breaking (SSB) for gauge theories. I’ve stumbled across some really helpful resources, such as Hamilton’s Mathematical Gauge Theory – With ...
- 559
0
votes
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91
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In QCD, Why the order parameter of chiral symmetry takes the form $\langle0 \lvert \bar{\psi}\psi\rvert 0 \rangle$?
A simple question, why the order parameter of QCD chiral symmetry (chiral condensate) take this form:
(or let's say why choose $\bar{\psi}\psi$ to judge there is SSB(spontaneous symmetry breaking) or ...
4
votes
2
answers
873
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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
3
votes
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answers
134
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Why are these loop diagrams involving Goldstone bosons cancelling one another in the zero-momentum limit?
I have been working with one-loop corrections to certain processes. Let's say, corrections to the $Z\bar{f}f$ vertex. Of, course I need to consider the following diagrams:
Here $\phi^{\pm}$ is the ...
- 41
5
votes
0
answers
122
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Why are photons massless? [duplicate]
I am trying to understand, from the QFT perspective, why photons are massless. Let's consider the following Lagrangian for a massive U(1) gauge boson
$\mathcal{L}=-\frac{1}{4}F^{\mu\nu}F_{\mu\nu}+m^2A^...
- 130
5
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164
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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
3
votes
1
answer
165
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Hidden gauge symmetry in spontaneously broken phase?
Throughout this post I will be using Weinberg's notation. When a global symmetry group $G$ is spontaneously broken down to a subgroup $H$, it is often useful to reparametrize whatever fields that make ...
- 3,514
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197
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Current conservation in presence of SSB: weak currents
The Standard Model SSB breaks the $SU(2)_W \times U(1)_Y$ to $U(1)_{EM}$. The Noether currents associated to the unbroken group are $J_{a,\mu} = \bar{\psi} \gamma_\mu \frac{\tau_a}{2} P_L \psi $ and $...
