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<div class="moz-forward-container"><span
style="mso-ansi-language:EN-US" lang="EN-US">Dear colleagues,</span></div>
<div class="moz-forward-container"><span
style="mso-ansi-language:EN-US" lang="EN-US"><br>
</span></div>
<div class="moz-forward-container"><span
style="mso-ansi-language:EN-US" lang="EN-US">I have recently
started and trying to warm up "models-of-particles" (</span><span
style="mso-ansi-language:EN-US" lang="EN-US"><span
style="mso-ansi-language:EN-US" lang="EN-US">e.g. as solitons)
</span>Google email group with ~40 physicists and have just
found this looking related one. We have also a bit more general
QM foundations online seminar (
<a class="moz-txt-link-freetext" href="http://th.if.uj.edu.pl/~dudaj/QMFNoT">http://th.if.uj.edu.pl/~dudaj/QMFNoT</a></span> ) - talks are
welcomed, I can also add to the email group.</div>
<div class="moz-forward-container">Let me briefly introduce myself (
<a class="moz-txt-link-freetext" href="http://th.if.uj.edu.pl/~dudaj/">http://th.if.uj.edu.pl/~dudaj/</a> ). I have education in Physics
(PhD), computer science (PhD) and mathematics (MSc). I am
interested in physics foundations since ~2006 when I have started
<a moz-do-not-send="true"
href="https://en.wikipedia.org/wiki/Maximal_entropy_random_walk">MERW
</a>(alongside <a moz-do-not-send="true"
href="https://en.wikipedia.org/wiki/Asymmetric_numeral_systems">ANS</a>)
showing where disagreement between diffusion and QM comes from
(only approximating crucial maximal entropy principle), then in
2009 I have started working on particle models as topological
solitons, which turned out expansion of Faber's model of electron
(slides: <a class="moz-txt-link-freetext" href="https://www.dropbox.com/s/aj6tu93n04rcgra/soliton.pdf">https://www.dropbox.com/s/aj6tu93n04rcgra/soliton.pdf</a> ).<br>
</div>
<br>
<div class="moz-forward-container"><span
style="mso-ansi-language:EN-US" lang="EN-US"><br>
</span></div>
<div class="moz-forward-container"><span
style="mso-ansi-language:EN-US" lang="EN-US">Let me start with
this general view thered/question, also to get some glimpse
about your group:<br>
</span>
<p class="MsoNormal"><span style="mso-ansi-language:EN-US"
lang="EN-US">Most of us would like to use topological
mechanisms to stabilize field configurations into </span><span
style="mso-ansi-language:EN-US" lang="EN-US"><span
style="mso-ansi-language:EN-US" lang="EN-US">localized </span>models
of particle (?) </span></p>
<p class="MsoNormal"><span style="mso-ansi-language:EN-US"
lang="EN-US">There is a large variety on both topological and
particle sides here, so maybe let us try to discuss the most
promising correspondences e.g. to properties like electric
charge, spin, baryon number - to target in such models.</span></p>
<p class="MsoNormal"><span style="mso-ansi-language:EN-US"
lang="EN-US">Here are some very basic topological structures –
what should they correspond to?</span></p>
<p class="MsoNormal"><br>
<span style="mso-ansi-language:EN-US" lang="EN-US"><span
style="mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;
mso-ansi-language:EN-US" lang="EN-US"><span
style="mso-list:Ignore"><span style="font:7.0pt
"Times New Roman""> </span></span></span><span
style="mso-ansi-language:EN-US" lang="EN-US"><b>1) 2D
topological charge</b> in cross-section e.g. in
fluxons/Abrikosov vortex in superconductors. It agrees with
quantum rotation operator: rotating spin ‘s’ particle by phi
angle, the phase rotates by phi * s. Topological constraint
resembles Ampere's law here e.g. for fluxon carrying quant
of magnetic field, what might be related with spins
corresponding to magnetic dipole moments (?)</span></span></p>
<p class="MsoNormal"><span style="mso-ansi-language:EN-US"
lang="EN-US"><span style="mso-ansi-language:EN-US"
lang="EN-US"><span
style="mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;
mso-ansi-language:EN-US" lang="EN-US"><span
style="mso-list:Ignore"><span style="font:7.0pt
"Times New Roman""> </span></span></span><span
style="mso-ansi-language:EN-US" lang="EN-US"><b>2) </b></span></span></span><span
style="mso-ansi-language:EN-US" lang="EN-US"><span
style="mso-ansi-language:EN-US" lang="EN-US">Such vortices
can form <b>knot</b><b>-like structures</b>: which can be
relatively stable local minima, but are not global – they
could decay especially in </span><span
style="mso-ansi-language:EN-US" lang="EN-US"><span
style="mso-ansi-language:EN-US" lang="EN-US">high
temperature</span>.</span></span></p>
<p class="MsoNormal"><span style="mso-ansi-language:EN-US"
lang="EN-US"><span style="mso-ansi-language:EN-US"
lang="EN-US"><span style="mso-ansi-language:EN-US"
lang="EN-US"><span
style="mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;
mso-ansi-language:EN-US" lang="EN-US"><span
style="mso-list:Ignore"><span style="font:7.0pt
"Times New Roman""> </span></span></span><span
style="mso-ansi-language:EN-US" lang="EN-US"><b>3) </b></span></span></span></span><span
style="mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;
mso-ansi-language:EN-US" lang="EN-US"><span
style="mso-list:Ignore"><span style="font:7.0pt "Times
New Roman""></span></span></span><span
style="mso-ansi-language:EN-US" lang="EN-US"><b>3D topological
charge</b> e.g. hedgehog-like localized configuration.
Gauss-Bonnet theorem acts as Gauss law with built-in charge
quantization here: integrating field’s curvature over closed
surface, we get 3D topological charge inside, which has to be
integer.</span></p>
<span
style="mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;
mso-ansi-language:EN-US" lang="EN-US"><span
style="mso-list:Ignore"><span style="font:7.0pt "Times
New Roman""></span></span></span><span
style="mso-ansi-language:EN-US" lang="EN-US"></span><span
style="mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin;
mso-ansi-language:EN-US" lang="EN-US"><span
style="mso-list:Ignore"><span style="font:7.0pt "Times
New Roman""></span></span></span><span
style="mso-ansi-language:EN-US" lang="EN-US"><img
src="cid:part3.C394FD8D.2C4BEFA7@gmail.com" alt="" class=""> <br>
</span>
<p class="MsoNormal"><span style="mso-no-proof:yes"><br>
</span><span style="mso-ansi-language: EN-US" lang="EN-US"></span></p>
<p class="MsoNormal"><span style="mso-ansi-language:EN-US"
lang="EN-US">Baryon number doesn’t seem to have Gauss law (?)
and usually is believed that it can be violated in extreme
temperatures – during baryogenesis just after Big Bang, or for
Hawking radiation inside Black Hole.</span></p>
<p class="MsoNormal"><span style="mso-ansi-language:EN-US"
lang="EN-US">So personally I would assign: 2D charge ->
spin, 3D charge -> electric charge, baryon number as
example of knotting.</span></p>
<p class="MsoNormal"><span style="mso-ansi-language:EN-US"
lang="EN-US">But e.g. Skyrmion models disagree: assigning 3D
charge -> baryon number, and usually neglecting electric
charge and spin.<br>
</span></p>
<p class="MsoNormal"><span style="mso-ansi-language:EN-US"
lang="EN-US">So which assignment is the most promising? Why?</span></p>
<p class="MsoNormal"><span style="mso-ansi-language:EN-US"
lang="EN-US">Best,</span></p>
<p class="MsoNormal"><span style="mso-ansi-language:EN-US"
lang="EN-US">Jarek Duda<br>
</span></p>
<p class="MsoNormal"><span style="mso-ansi-language:EN-US"
lang="EN-US">ps. Related: is photon number conserved e.g. as
topological? If not, why single photon does not dissipate? (I
would bet on angular momentum)</span></p>
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