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Results tagged with symmetry-breaking
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user 2190
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.
4
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If a symmetry operator S in a QFT annihilates the vacuum, why does S preserve the space of 1...
This is a heuristic explanation of Witten's statement, without going into the subtleties of axiomatic quantum field theory issues, such as vacuum polarization or renormalization.
A particle is charac …
- 31.2k
7
votes
Accepted
Why do the conserved charges in the case of SSB of a global symmetry not exist?
This is called the Fabri-Picasso theorem. Their argument requires both the vacuum and the charge $Q$ to be translationally invariant: $P |0\rangle = 0$, and $[P, Q] = 0$.
The argument goes as follow …
- 31.2k
10
votes
Accepted
What is dynamical symmetry breaking, exactly?
As correctly stated in the following answer by flippiefanus , dynamical symmetry breaking is identical to spontaneous symmetry breaking except that in the case of dynamical symmetry breaking a composi …
- 31.2k
14
votes
Accepted
Spontaneous symmetry breaking in classical mechanics, quantum mechanics and quantum field th...
The third question Q3 is basically the subject of a very recent work by N.P. Landsman.
In quantum theory, spontaneous symmetry breaking requires the system to be infinite dimensional. When the numbe …
- 31.2k
3
votes
Accepted
Is the superfluid state a coherent state?
The ground state of a superfluid can be indeed (very precisely) approximated by a coherent state. More accurately by a squeezed coherent state. Please see Zhang equation (72):
$$|\{z_k \beta_k\}\rang …
- 31.2k
10
votes
What is spontaneous symmetry breaking in quantum systems?
I think that one way to visualize spontaneous symmetry breaking in quantum systems is as follows:
The theory's Hilbert space is infinite dimensional. Given a Hamiltonian, one method to seek approxima …
- 31.2k
15
votes
Accepted
Spontaneous breaking of Lorentz invariance in gauge theories
The possibility of spontaneous Lorentz symmetry violation due to the infrared problem of the Dirac-Maxwell equation was conjectured a long time ago by Frohlich, Morchio and Strocchi, in references [1, …
- 31.2k
11
votes
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What is a quark condensate?
The quark condensate is the vacuum expectation $\langle 0|\bar{\psi}\psi|0\rangle$ responsible for the breakdown of the chiral symmetry in QCD.
Its importance in QCD is by being one of the main contri …
- 31.2k
12
votes
Accepted
Why does a Heisenberg magnet break the O(3) symmetry instead of SU(2)?
The Heisenberg model:
$$H = \sum_{i \ne j} \mathbf{S}_i\cdot \mathbf{S}_j$$
has an $O(3)$ symmetry group rather than $SU(2)$ even though it is expressed in terms of spin $\frac{1}{2}$ operators
$$\m …
- 31.2k
10
votes
Accepted
If spontaneous symmetry breaking only occurs in infinite systems, why do we observe similar ...
This question exactly is addressed and rigorously treated by N.P. Landsman. The explanation is that in the large $N$ limit the symmetric ground state becomes exponentially sensitive to asymmetric pert …
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