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Results tagged with symmetry-breaking
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user 50583
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.
3
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How are scale of renormalization and scale of symmetry breaking related?
Contrary to what the language implies, spontaneous symmetry breaking in usual vacuum QFT is not something that "occurs at a scale". Rather, the symmetry breaking scale is the scale below one may not p …
- 129k
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Is Norton's dome valid (or does $\frac{d^2 \vec{p}}{dt^2} = \vec{0} \implies \frac{d^n \vec{...
Your example is not analogous to Norton's dome.
Norton's point is that Newtonian mechanics says that the trajectory of a particle obeys $\ddot{x}(t) = F(x(t),\dot{x}(t), t)$ at every point in time $t$ …
- 129k
4
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Do expectation values of quantum fields behave like classical fields?
The QFT version of Ehrenfest's theorem are the Schwinger-Dyson equations, stating that the classical equation of motion (in presence of a source $J$) $\frac{\delta S}{\delta \phi} + J = 0$ holds as an …
- 129k
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Spontaneous symmetry breaking (SSB) in adjoint representation
The adjoint representation is the same as the Lie algebra $\mathfrak{su}(n)$ itself, with the action given by the Lie bracket/commutator. Since you are apparently presenting $\Phi$ as a matrix, note t …
- 129k
7
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Center group and Symmetry breaking
I'll start with describing the best known instance of center symmetry breaking:
The center of the gauge group is significant in lattice gauge theories because the expectation value of the Polyakov lo …
- 129k
11
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Does the Coleman-Weinberg mechanism belong to the dynamical symmetry breaking or the anomaly?
First, dynamical symmetry breaking (which I take to be either synonymous with or a subset of spontaneous symmetry breaking) and anomalies are two completely different things. An anomaly is when a symm …
- 129k
2
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Could a second Big Bang produce different masses for elementary particles?
All the possible Higgs vacua on the lowest point of the Mexican hat have the same absolute value, they're just different in a "phase" related to the $\mathrm{SU}(2)$-theory being broken. With the curr …
- 129k
10
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Terminology of Higgs boson and Goldstone boson
The Higgs mass does not stem from eating Goldstone bosons, since the Higgs is not a gauge field. Since we are breaking an $\mathrm{SU}(2) \subset \mathrm{SU}(2)_L \times \mathrm{U}(1)_Y$ completely, w …
- 129k
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Why is a minimum field configuration called a vacuum state in SSB?
To call a classical extremum of the field a "vacuum state" is a common abuse of terminology. It is not the extremum itself that is a vacuum state, but to every classical extremum there is (to first or …
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Is the Higgs mechanism a gauge transformation or not? ( $U(1)$ context )
Let's introduce a bit more notation because I think you're confusing yourself with the $\to$ notation:
Let $\theta : \mathbb{R}^4\to\mathbb{R}$ be any function. Then the gauge transformed fields are
…
- 129k
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Relation between gauge symmetry and mass difference
JakobH's comment as an answer:
The electroweak gauge group $\mathrm{SU}(2)_L \times \mathrm{U}(1)_Y$ is broken into the electromagnetic $\mathrm{U}(1)_\text{em}$ by the Higgs field acquiring a non-ze …
- 129k
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What is classical Lagrangian? The Bare one or renormalized one? Are counterterms quantum cor...
The classical Lagrangian is the bare Lagrangian.
(and 3.) It's not the counterterms that have a physical effect, it's renormalization itself. Renormalization in the modern Wilsonian understanding mea …
- 129k
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Why is a nonzero VEV for a spinor field said to break Lorentz invariance?
The $v$ you write is itself a spinor, not a scalar. A non-zero spinor is obviously not invariant under Lorentz transformations, so a non-zero spinorial VEV breaks Lorentz invariance of the 1-point fun …
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Peccei-Quinn-symmetry and effective Lagrangian for the Axion field
You don't need the first and second terms for invariance as such. But you should recognize that these are simply the kinetic and interaction terms for the axion field. Are you proposing to include a …
- 129k
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Why is a superposition of vacuum states possible in QCD, but not in electroweak theory?
The difference between the two cases is the nature of the vacua.
In the case of spontaneous symmetry breaking, you find that the tunneling amplitude between them is proportional to the volume, so t …
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