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May27-05, 03:48 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>> It is a mystery why math theories describe electrons. But why\n> does math theories also apply so well to Wall Street?\n\nThe second quantization formalism of QFTs is a generic linearization\nalgorithm for nonlinear systems of PDEs and integro-differential\nequations. It contains no more intrinsic physics in it than, say, the\nRunge-Kutta numeric integration algorithm does. The N-point Green\nfunctions (propagators) computed via Feynman diagrams approximate\nnonlinear dynamics evolution of the classical interacting fields (e.g.\nMaxwell-Dirac coupled PDEs) with piecewise linear evolution between the\nN scattering events (the "interactions"). That is the mathematical\nbasis of their usefulness, in QFT and elsewhere. Check, for example,\npapers by K. Kowalski on arXiv:\n\nhttp://arxiv.org/find/grp_nlin/1/au:+kowalski_k/0/1/0/all/0/1\nhttp://arxiv.org/abs/hep-th/9212031\n\nwhere the linearization aspect (of 2nd quantization) is explicit and\n(unlike the typical QED/QFT textbooks) entirely non-mysterious. He uses\nFock space methods to solve variety of nonlinear diff. equations,\nrecurrences (difference equations), kinetic processes etc. The late\nAsim Barut has developed similar results in 1980s. The ICTP site has\naround 150 of his papers online at:\n\nhttp://library.ictp.it/pages/psearch/prep.php?PAGE=7&NEXT=/ARCHIVE/preprint/SDW?W%3DAUTHOR+PH+WORDS+%27barut%27+ORDER+BY+EVERY +ICNUM/Ascend%26M%3D1%26R%3DY\n\nOn the linearization aspect of Maxwell-Dirac (treated as classical\ninteracting fields without 2nd quantization of either EM or Dirac\nmatter field), check especially his paper "QUANTUM-ELECTRODYNAMICS\nBASED ON SELF-ENERGY" (sect. 4, from page 7) at:\n\nhttp://library.ictp.trieste.it/DOCS/P/87/248.pdf\n\nAdditional discussion on 2nd quantization is in his paper "COMBINING\nRELATIVITY AND QUANTUM MECHANICS: SCHRODINGER\'S INTERPRETATION OF PSI"\nat:\n\nhttp://library.ictp.trieste.it/DOCS/P/87/157.pdf\n\nwhich describes physical motivation for his approach. He and his PhD\nstudents had replicated QED radiative corrections up to order alpha^5\n(including Lamb shift and g-2 which require loop diagrams; note that\nBarut\'s self-fields are not the "semiclassical" tree level\napproximation of the QED -- the QED is a piecewise linearized\napproximation of the Barut\'s self-fields aka of the cooupled\nMaxwell-Dirac system). You may also check a recent discussion on this\ntopic in the PhysicsForum:\n\nhttp://www.physicsforums.com/showpost.php?p=540794&postcount=100\nhttp://www.physicsforums.com/showpost.php?p=541484&postcount=114\nhttp://www.physicsforums.com/showpost.php?p=541708&postcount=118\nhttp://www.physicsforums.com/showthread.php?t=71297&page=3&pp=40\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>> It is a mystery why math theories describe electrons. But why
> does math theories also apply so well to Wall Street?
The second quantization formalism of QFTs is a generic linearization
algorithm for nonlinear systems of PDEs and integro-differential
equations. It contains no more intrinsic physics in it than, say, the
Runge-Kutta numeric integration algorithm does. The N-point Green
functions (propagators) computed via Feynman diagrams approximate
nonlinear dynamics evolution of the classical interacting fields (e.g.
Maxwell-Dirac coupled PDEs) with piecewise linear evolution between the
N scattering events (the "interactions"). That is the mathematical
basis of their usefulness, in QFT and elsewhere. Check, for example,
papers by K. Kowalski on arXiv:
http://arxiv.org/find/grp_nlin/1/au:+kowalski_k/0/1/0/all/0/1
http://arxiv.org/abs/http://www.arxiv.org/abs/hep-th/9212031
where the linearization aspect (of 2nd quantization) is explicit and
(unlike the typical QED/QFT textbooks) entirely non-mysterious. He uses
Fock space methods to solve variety of nonlinear diff. equations,
recurrences (difference equations), kinetic processes etc. The late
Asim Barut has developed similar results in 1980s. The ICTP site has
around 150 of his papers online at:
http://library.ictp.it/pages/psearch/prep.php?PAGE=7&NEXT=/ARCHIVE/preprint/SDW?W%3DAUTHOR+PH+WORDS+%27barut%27+ORDER+BY+EVERY +ICNUM/Ascend%26M%3D1%26R%3DY
On the linearization aspect of Maxwell-Dirac (treated as classical
interacting fields without 2nd quantization of either EM or Dirac
matter field), check especially his paper "QUANTUM-ELECTRODYNAMICS
BASED ON SELF-ENERGY" (sect. 4, from page 7) at:
http://library.ictp.trieste.it/DOCS/P/87/248.pdf
Additional discussion on 2nd quantization is in his paper "COMBINING
RELATIVITY AND QUANTUM MECHANICS: SCHRODINGER'S INTERPRETATION OF \PSI"
at:
http://library.ictp.trieste.it/DOCS/P/87/157.pdf
which describes physical motivation for his approach. He and his PhD
students had replicated QED radiative corrections up to order \alpha^5
(including Lamb shift and g-2 which require loop diagrams; note that
Barut's self-fields are not the "semiclassical" tree level
approximation of the QED -- the QED is a piecewise linearized
approximation of the Barut's self-fields aka of the cooupled
Maxwell-Dirac system). You may also check a recent discussion on this
topic in the PhysicsForum:
http://www.physicsforums.com/showpost.php?p=540794&postcount=100
http://www.physicsforums.com/showpost.php?p=541484&postcount=114
http://www.physicsforums.com/showpost.php?p=541708&postcount=118
http://www.physicsforums.com/showthread.php?t=71297&page=3&pp=40
> does math theories also apply so well to Wall Street?
The second quantization formalism of QFTs is a generic linearization
algorithm for nonlinear systems of PDEs and integro-differential
equations. It contains no more intrinsic physics in it than, say, the
Runge-Kutta numeric integration algorithm does. The N-point Green
functions (propagators) computed via Feynman diagrams approximate
nonlinear dynamics evolution of the classical interacting fields (e.g.
Maxwell-Dirac coupled PDEs) with piecewise linear evolution between the
N scattering events (the "interactions"). That is the mathematical
basis of their usefulness, in QFT and elsewhere. Check, for example,
papers by K. Kowalski on arXiv:
http://arxiv.org/find/grp_nlin/1/au:+kowalski_k/0/1/0/all/0/1
http://arxiv.org/abs/http://www.arxiv.org/abs/hep-th/9212031
where the linearization aspect (of 2nd quantization) is explicit and
(unlike the typical QED/QFT textbooks) entirely non-mysterious. He uses
Fock space methods to solve variety of nonlinear diff. equations,
recurrences (difference equations), kinetic processes etc. The late
Asim Barut has developed similar results in 1980s. The ICTP site has
around 150 of his papers online at:
http://library.ictp.it/pages/psearch/prep.php?PAGE=7&NEXT=/ARCHIVE/preprint/SDW?W%3DAUTHOR+PH+WORDS+%27barut%27+ORDER+BY+EVERY +ICNUM/Ascend%26M%3D1%26R%3DY
On the linearization aspect of Maxwell-Dirac (treated as classical
interacting fields without 2nd quantization of either EM or Dirac
matter field), check especially his paper "QUANTUM-ELECTRODYNAMICS
BASED ON SELF-ENERGY" (sect. 4, from page 7) at:
http://library.ictp.trieste.it/DOCS/P/87/248.pdf
Additional discussion on 2nd quantization is in his paper "COMBINING
RELATIVITY AND QUANTUM MECHANICS: SCHRODINGER'S INTERPRETATION OF \PSI"
at:
http://library.ictp.trieste.it/DOCS/P/87/157.pdf
which describes physical motivation for his approach. He and his PhD
students had replicated QED radiative corrections up to order \alpha^5
(including Lamb shift and g-2 which require loop diagrams; note that
Barut's self-fields are not the "semiclassical" tree level
approximation of the QED -- the QED is a piecewise linearized
approximation of the Barut's self-fields aka of the cooupled
Maxwell-Dirac system). You may also check a recent discussion on this
topic in the PhysicsForum:
http://www.physicsforums.com/showpost.php?p=540794&postcount=100
http://www.physicsforums.com/showpost.php?p=541484&postcount=114
http://www.physicsforums.com/showpost.php?p=541708&postcount=118
http://www.physicsforums.com/showthread.php?t=71297&page=3&pp=40