Recently I have been trying to understand condensed matter analogs to
particle physics and cosmological phenomenon. In particular the
emergence of SU(N) gauge, Lorentz, and general covariance symmetries
in the low energy sector. I first came upon these ideas in articles by
Volovik (gr-qc/0005091) and have since found that a great deal of
researchers are interested in the notion of emergent symmetries (e.g.
S.C. Zhang, Laughlin, H.B. Nielsen, M. Visser). I must say, however,
that while Volovik's work with superfluid helium is tantalizingly
appealing in the picture it portrays - Fermi points as topologically
stable objects that appear to generate the aforementioned symmetries -
I find his work far from clear. That is to say I am not sure how the
topology of the Green's function mapping from momentum space to (the
appropriate) matrix group yields particularly gauge symmetry of low
energy excitations.

Barring an elucidation of Volovik's work in particular, isthere a
general framework in which to describe the emergence of Lorentz and
gauge symmetry in condensed matter contexts?

Haile Owusu:

Recently I have been trying to understand condensed matter analogs to
particle physics and cosmological phenomenon. In particular the
emergence of SU(N) gauge, Lorentz, and general covariance symmetries
in the low energy sector.

You have it backwards. The symmetry doesn't "emerge" in the low
energy regime, it's broken. The SU(3) x SU(2) x U(1) is presumed
to be a single gauge group (i.e., highly symmetric) at high energy.
At low energy, the symmetry is _broken_ into the gauge groups
depicted in the standard model. Those groups are simply what's
"leftover".

I first came upon these ideas in articles by
Volovik (gr-qc/0005091) and have since found that a great deal of
researchers are interested in the notion of emergent symmetries (e.g.
S.C. Zhang, Laughlin, H.B. Nielsen, M. Visser). I must say, however,
that while Volovik's work with superfluid helium is tantalizingly
appealing in the picture it portrays

Emergent seems to be the wrong word. Generally, condensation into
a ground state means an existing symmetry has been broken as it the
case for 3He(B).

- Fermi points as topologically
stable objects that appear to generate the aforementioned symmetries -
I find his work far from clear. That is to say I am not sure how the
topology of the Green's function mapping from momentum space to (the
appropriate) matrix group yields particularly gauge symmetry of low
energy excitations.

Barring an elucidation of Volovik's work in particular, isthere a
general framework in which to describe the emergence of Lorentz and
gauge symmetry in condensed matter contexts?

As fara as lorentz invariance, not that I'm aware of. It's been
tried (e.g., see Entropy and the Physics of Information, (1989) ed.
W. Zurek) but that's about all I know. As far as gauge symmetry
goes, I'm not sure what you mean. What we observe is the result
of breaking a larger symmetry down into smaller symmetries. For
example. See: arxiv:/hep-th/9905369 for a fairly good discussion
of the condensed matter analogy to the standard model. In particular,
the example given for comaparison is a superconductor.

While I agree I have it backwards, that misdirection is intentional in
the sense that I DO understand symmetry breaking as it pertains to the
standard model as well as in condensed matter systems. This however is
NOT what I am investigating. Symmetry breaking obviously moves one
from a highly symmmetric state to a lower symmetry condensed state.
What I am interested in are systems who, in their high energy limit
LOSE symmetry. This appears common in condensed matter systems, e.g.
the quantum hall effect is said to exhibit low energy excitations that
propogate relativistically (speed of sound being the analogue of speed
of light) and interact through the exchange of gauge bosons (see
Laughlin's Nobel Lecture), none of which lies explicit in the many
body Hamiltonian. This I do not understand well at all, but am
intrigued by.

There is an interesting book by Froggatt and H.B. Nielsen - ORigin of
Symmetries - on precisely this subject, but the mechanisms for this
sort of symmetry generation lie patchwork in the literature. I am
curious if anyone knows where, if at all, such ideas might be more
elegantly consolidated.

Haile

(Bilge) wrote in message ...
Haile Owusu:

Recently I have been trying to understand condensed matter analogs to
particle physics and cosmological phenomenon. In particular the
emergence of SU(N) gauge, Lorentz, and general covariance symmetries
in the low energy sector.

You have it backwards. The symmetry doesn't "emerge" in the low
energy regime, it's broken. The SU(3) x SU(2) x U(1) is presumed
to be a single gauge group (i.e., highly symmetric) at high energy.
At low energy, the symmetry is _broken_ into the gauge groups
depicted in the standard model. Those groups are simply what's
"leftover".

Haile Owusu:

Followups set to sci.physics.cond-matter


While I agree I have it backwards, that misdirection is intentional in
the sense that I DO understand symmetry breaking as it pertains to the
standard model as well as in condensed matter systems. This however is
NOT what I am investigating. Symmetry breaking obviously moves one
from a highly symmmetric state to a lower symmetry condensed state.
What I am interested in are systems who, in their high energy limit
LOSE symmetry. This appears common in condensed matter systems,

If that's true, I certainly cannot think of any right off hand.

e.g.
the quantum hall effect is said to exhibit low energy excitations that
propogate relativistically (speed of sound being the analogue of speed
of light) and interact through the exchange of gauge bosons (see
Laughlin's Nobel Lecture), none of which lies explicit in the many
body Hamiltonian. This I do not understand well at all, but am
intrigued by.

I still do not see where you think the system _loses_ symmetry in
in the "high energy limit" (which I assume you to mean, the point
where the phase transition occurs). The appearance of goldstone
bosons as the system cools, is manifestly an indication that the
symmetry is broken as the system cools.


There is an interesting book by Froggatt and H.B. Nielsen - ORigin of
Symmetries - on precisely this subject, but the mechanisms for this
sort of symmetry generation lie patchwork in the literature. I am
curious if anyone knows where, if at all, such ideas might be more
elegantly consolidated.

Can't help you there. None of the descriptions of the quantum hall effect
I found describe it the way you do.

My intention, of course, is not combat incredulity so much as to be
able to understand the claims of researchers. The phenomenon I am
describing is NOT continuous symmetry breaking and NOT, therefore,
associated with any Goldstone bosons. Consider Laughlin's Nobel
Lecture p.281:

http://www.nobel.se/physics/laureate...n-lecture.html

Here quasiparticles are shown to interact via a gauge force, though I
do not see how this is a gauge force, nor how it emerges from the
Fractional Quantum Hall Effect system. For clarity, this is (a
concrete example of) the phenomenon I am trying to understand.