Noncommutative geometry, topology, and the standard model vacuum

@article{citeulike:1320134, abstract = {As a ramification of a motivational discussion for previous joint work, in which equations of motion for the finite spectral action of the standard model were derived, we provide a new analysis of the results of the calculations therein, switching from the perspective of spectral triple to that of Fredholm module and thus from the analogy with Riemannian geometry to the premetrical structure of the noncommutative geometry. Using a suggested noncommutative version of Morse theory together with algebraic K theory to analyze the vacuum solutions, the first two summands of the algebra for the finite triple of the standard model arise up to Morita equivalence. We also demonstrate a new vacuum solution whose features are compatible with the physical mass matrix. \©2006 American Institute of Physics}, author = {Martins, Dawe R. A. }, citeulike-article-id = {1320134}, doi = {10.1063/1.2374880}, journal = {Journal of Mathematical Physics}, keywords = {noncommutative, quantum-vacuum, standard-model}, number = {11}, posted-at = {2007-05-23 00:29:04}, priority = {2}, publisher = {AIP}, title = {Noncommutative geometry, topology, and the standard model vacuum}, url = {http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal\&id=JMAPAQ000047000011113507000001\&idtype=cvips\&gifs=yes}, volume = {47}, year = {2006} }

TY - JOUR ID - citeulike:1320134 L3 - citeulike-article-id:1320134 TI - Noncommutative geometry, topology, and the standard model vacuum JF - Journal of Mathematical Physics VL - 47 IS - 11 PB - AIP N2 - As a ramification of a motivational discussion for previous joint work, in which equations of motion for the finite spectral action of the standard model were derived, we provide a new analysis of the results of the calculations therein, switching from the perspective of spectral triple to that of Fredholm module and thus from the analogy with Riemannian geometry to the premetrical structure of the noncommutative geometry. Using a suggested noncommutative version of Morse theory together with algebraic K theory to analyze the vacuum solutions, the first two summands of the algebra for the finite triple of the standard model arise up to Morita equivalence. We also demonstrate a new vacuum solution whose features are compatible with the physical mass matrix. ©2006 American Institute of Physics KW - noncommutative KW - quantum-vacuum KW - standard-model AU - Martins, Dawe PY - 2006/// UR - http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JMAPAQ000047000011113507000001&idtype=cvips&gifs=yes ER -