ÿþ<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd"> <HTML> <HEAD> <META HTTP-EQUIV="Content-Type" CONTENT="text/html;charset=utf-8"> <TITLE>Klaus Scharnhorst - Publications - Paper [31]</TITLE> <BASE HREF="http://www.nat.vu.nl/~scharnh/paper31.htm"> </HEAD> <BODY BGCOLOR="#FFFFFF"> <CENTER> <B>Klaus Scharnhorst - Publications</B> </CENTER> <HR> <P> J.-W. van Holten, K. Scharnhorst: <I>Nonlinear Bogolyubov-Valatin transformations and quaternions</I>. Journal of Physics A: Mathematical and General <B>38</B>(2005)10245-10252 [quant-ph/0411170, NIKHEF preprint NIKHEF 04-024] (DOI: 10.1088/0305-4470/38/47/012). [<A HREF="http://www.slac.stanford.edu/spires/find/hep/www?key=6057594">SPIRES record</A>] <P> <B>Abstract</B>: In introducing second quantization for fermions, Jordan and Wigner (1927/1928) observed that the algebra of a single pair of fermion creation and annihilation operators in quantum mechanics is closely related to the algebra of quaternions <B>H</B>. For the first time, here we exploit this fact to study nonlinear Bogolyubov-Valatin transformations (canonical transformations for fermions) for a single fermionic mode. By means of these transformations, a class of fermionic Hamiltonians in an external field is related to the standard Fermi oscillator <P> <UL> <LI>Electronic copy of the article: <A HREF="http://dx.doi.org/10.1088/0305-4470/38/47/012"> Journal of Physics A: Mathematical and General</A> <LI>Electronic copy of the preprint: <A HREF="http://arXiv.org/abs/quant-ph/0411170"> quant-ph/0411170</A> <LI><A HREF="cite31.htm">Citations</A> <P> <LI>Misprints, errata, addenda: <UL> <LI> </UL> </UL> <HR> <A HREF="pub.htm">Up</A>, or back to: <A HREF="homepage.htm">home page of Klaus Scharnhorst</A> / <A HREF="http://www.nat.vu.nl/en/research/theoretical-physics/index.asp">Theoretical Physics</A> / <A HREF="http://www.nat.vu.nl/en/index.asp">Department of Physics and Astronomy</A> <HR> <ADDRESS> &#169; K. Scharnhorst <IMG SRC="melvutype.gif" ALT="melvu" ALIGN=MIDDLE>. Document last modified: April 27, 2011 </ADDRESS> <HR> <ADDRESS> Document address: http://www.nat.vu.nl/~scharnh/paper31.htm </ADDRESS> </BODY> </HTML>