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1 vote

Can a $\mathbb{Z}_2 \times \mathbb{Z}_2$ symmetry generated by $\prod_{i} \sigma^x_i$ and $\prod_{i} \sigma^z_i$ be broken in a spin-$1/2$ chain?

If you do not want to impose translation symmetry, there are trivial (but valid) examples. If the number of sites is a multiple of 4, $$ H = -\sum_{i \text{ even}} (\sigma^x_i\sigma^x_{i+2} + \sigma^...
Nandagopal Manoj's user avatar
1 vote

What implements finite conformal transformations in two dimensions?

The statement that $L^\dagger_n = L_{-n}$, or its counterpart in higher dimensional notation which looks like \begin{equation} D^\dagger = D, \quad P_\mu^\dagger = K_\mu, \quad M_{\mu\nu}^\dagger = M_{...
Connor Behan's user avatar
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3 votes

Custodial symmetry of the standard model symmetry group $SU(2)_L \times SU(2)_R$

I have included 5 links, including a "primary" one, which should help clear up the trail map for you; I think you've gone off it, but I can't be sure, as weird misconceptions have crept in. ...
Cosmas Zachos's user avatar
3 votes

Why don't we include diagrams with fermion and gauge boson external lines while calculating the effective potential of Standard model?

As a Lorentz-invariant Lagrangian does not necessarily imply a Lorentz invariant ground state of the theory, Lorentz invariance might, in principle, be spontaneously broken just as well as an ...
Hyperon's user avatar
  • 6,148
1 vote

Can we prove in general that gauge fields associated with broken generators form representations of the unbroken group?

I fail to imagine the contrapositive. Assuming there are no matter fields to be integrated out in an effective theory (in a rearrangement spoiling renormalizability), in a pure gauge theory of G, all ...
Cosmas Zachos's user avatar
0 votes

Review: If true, what makes the vacuum of a local ${\rm U(1)}$ gauge theory unique?

I want to present a "counter"example to Ruben's answer --- a state that preserves local gauge symmetry but breaks the global symmetry. The issue is rooted in the thermodynamic limit. For ...
Yuan Yao's user avatar

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