<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','to olbar=no,location=no,scrollbars=yes,resizable=yes, status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usene t ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Tangloids are usually made as two oriented fermions.\nThen, we can swap them and the result is the same as\nrotating one of their fermion parts by 2pi.\n\n4pi rotations lead to initial states for an object\nwith arbitrary space anchoring, not just only to the\nsecond (fermion) part of a tangloid.\n\nSimple picture of 3-fermion extended tangloid where\nA and B (together with their connection) form classical\ntangloid:\n\n.. * A\n.. / |\n.. C * |\n.. \\ |\n.. * B\n\nDoes the 2pi rotation <-> swap equivalence hold for\nsuch extended tangloids too? Of course, the extra\n(fermion) constraints have to be symmetrical.\n\nWhile the 4pi <-> 0pi equivalence comes from double\ncovering of SO(3) by simply connected SU(2), and\nthe simple swap can be illustrated, I do not know how\nto handle 2pi vs. swap action on extended tangloids.\n\nThe things like tangloids and around are described in:\nhttp://en.wikipedia.org/wiki/Tangloids\nhttp://www.umsl.edu/~fraundor/p231/spinexcl.html\nhttp://math.ucr.edu/home/baez/lie/lie.html\n\nThanks,\nMartin Saturka\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Tangloids are usually made as two oriented fermions.
Then, we can swap them and the result is the same as
rotating one of their fermion parts by 2pi.
4pi rotations lead to initial states for an object
with arbitrary space anchoring, not just only to the
second (fermion) part of a tangloid.
Simple picture of 3-fermion extended tangloid where
A and B (together with their connection) form classical
tangloid:
.. * A
.. / |
..
.. \ |
.. * B
Does the 2pi rotation <-> swap equivalence hold for
such extended tangloids too? Of course, the extra
(fermion) constraints have to be symmetrical.
While the 4pi <-> 0pi equivalence comes from double
covering of SO(3) by simply connected SU(2), and
the simple swap can be illustrated, I do not know how
to handle 2pi vs. swap action on extended tangloids.
The things like tangloids and around are described in:
http://en.wikipedia.org/wiki/Tangloids
http://www.umsl.edu/~fraundor/p231/spinexcl.html
http://math.ucr.edu/home/baez/lie/lie.html
Thanks,
Martin Saturka
