Matti Pitkanen
Oct11-04, 03:08 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet 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>Dear All,\n\nDan Smith mentioned in his positing octonions, quaternions and\nCP_2 in his comments. During last 25 years I have developed a\nunification that I call Topological Geometrodynamics based\non the assumption that space-times are representable as\n4-surfaces in H= M^4xCP_2. Octonions and quaternion appear\nin a number theoretic formulation of TGD too.\n\nTGD can be regarded either as a generalization of string\nmodel by replacing string world sheet with space-time\n4-surface or as a fusion of special and general\nrelativities to obtain a Poincare invariant theory of\ngravitation.\n\nIn contrast to Kaluza-Klein theories, classical gravitation\nand gauge fields are unified in terms of induction of\nM^4xCP_2 metric and spinor structure. Standard model\nquantum numbers are understood in terms of isometry and\nholonomy groups apart from family replication. Baryon and\nlepton numbers correspond to different chiralities for\nH-spinors induced to space-time surface and quark and\nlepton numbers are separately conserved.\n\nThe basic (not the only one) conformal invariance is\nnaturally associated with metrically 2-dimensional light\nlike causal determinants (call them X^3_l) which by the\ngeneral coordinate invariance can be selected as\nrepresentatives of 3-spaces. This conformal invariance\nimplies effective 2-dimensionality: the physics is coded\nby certain 2-dimensional sections X^2 of X^3_l so that a\nformalism reduces to a form very reminiscent of conformal\nfield theories. Family replication corresponds to the\ndifferent genera (sphere, torus, etc.) for X^2 and there\nis an argument explaining why only the 3 lowest genera are\nrealized.\n\nThere are four books about TGD and its applications at\nhttp://www.physics.helsinki.fi/~matpitka/ . The chapter\n"Overview about the Evolution of Quantum TGD" explains the\nevolution of the ideas can be found at\nhttp://www.physics.helsinki.fi/~matpitka/tgd.htlm#tgdevo .\n\nWith Best Regards,\nMatti Pitkanen\n\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>Dear All,
Dan Smith mentioned in his positing octonions, quaternions and
CP_2 in his comments. During last 25 years I have developed a
unification that I call Topological Geometrodynamics based
on the assumption that space-times are representable as
4-surfaces in H= M^{4xCP_2}. Octonions and quaternion appear
in a number theoretic formulation of TGD too.
TGD can be regarded either as a generalization of string
model by replacing string world sheet with space-time
4-surface or as a fusion of special and general
relativities to obtain a Poincare invariant theory of
gravitation.
In contrast to Kaluza-Klein theories, classical gravitation
and gauge fields are unified in terms of induction of
M^{4xCP_2} metric and spinor structure. Standard model
quantum numbers are understood in terms of isometry and
holonomy groups apart from family replication. Baryon and
lepton numbers correspond to different chiralities for
H-spinors induced to space-time surface and quark and
lepton numbers are separately conserved.
The basic (not the only one) conformal invariance is
naturally associated with metrically 2-dimensional light
like causal determinants (call them X^{3_l}) which by the
general coordinate invariance can be selected as
representatives of 3-spaces. This conformal invariance
implies effective 2-dimensionality: the physics is coded
by certain 2-dimensional sections X^2 of X^{3_l} so that a
formalism reduces to a form very reminiscent of conformal
field theories. Family replication corresponds to the
different genera (sphere, torus, etc.) for X^2 and there
is an argument explaining why only the 3 lowest genera are
realized.
There are four books about TGD and its applications at
http://www.physics.helsinki.fi/~matpitka/ . The chapter
"Overview about the Evolution of Quantum TGD" explains the
evolution of the ideas can be found at
http://www.physics.helsinki.fi/~matpitka/tgd.htlm#tgdevo .
With Best Regards,
Matti Pitkanen
Dan Smith mentioned in his positing octonions, quaternions and
CP_2 in his comments. During last 25 years I have developed a
unification that I call Topological Geometrodynamics based
on the assumption that space-times are representable as
4-surfaces in H= M^{4xCP_2}. Octonions and quaternion appear
in a number theoretic formulation of TGD too.
TGD can be regarded either as a generalization of string
model by replacing string world sheet with space-time
4-surface or as a fusion of special and general
relativities to obtain a Poincare invariant theory of
gravitation.
In contrast to Kaluza-Klein theories, classical gravitation
and gauge fields are unified in terms of induction of
M^{4xCP_2} metric and spinor structure. Standard model
quantum numbers are understood in terms of isometry and
holonomy groups apart from family replication. Baryon and
lepton numbers correspond to different chiralities for
H-spinors induced to space-time surface and quark and
lepton numbers are separately conserved.
The basic (not the only one) conformal invariance is
naturally associated with metrically 2-dimensional light
like causal determinants (call them X^{3_l}) which by the
general coordinate invariance can be selected as
representatives of 3-spaces. This conformal invariance
implies effective 2-dimensionality: the physics is coded
by certain 2-dimensional sections X^2 of X^{3_l} so that a
formalism reduces to a form very reminiscent of conformal
field theories. Family replication corresponds to the
different genera (sphere, torus, etc.) for X^2 and there
is an argument explaining why only the 3 lowest genera are
realized.
There are four books about TGD and its applications at
http://www.physics.helsinki.fi/~matpitka/ . The chapter
"Overview about the Evolution of Quantum TGD" explains the
evolution of the ideas can be found at
http://www.physics.helsinki.fi/~matpitka/tgd.htlm#tgdevo .
With Best Regards,
Matti Pitkanen