ajb
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Status Updates posted by ajb
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Odd variables appear in quantum field theory when looking for semi-classical descriptions of fermions, like the electron and also are needed in gauge theories like Yang-Mills. Supersymmetric theories uses them, including superstring theory. They also can be very useful linear algebra and differential geometry as a neat description of alternating forms.
So, Ok maybe I could include ...
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Trying to understand if the classical BV-formalism of gauge theories can be generalised to situations where the odd bracket does not satisfy a derivation property. Watch this space : -)
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In physics differential geometry probably is advanced mathematics used "day to day". The reason for this is that physics, or for sure classical physics is usually smooth, i.e. you can take derivatives and does not depend on exactly how you decide to present it. Both these are fundamental ideas in differential geometry.
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Trying to understand differential calculi and the Cartan calculus on Manin's quantum superplane.
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I think I have a new class of sigma models, I know there internal symmetries and now I have no idea what to do with them! I have been trying to read up on quantum aspect of such models...not so easy for my models.
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The mechanics paper is now online. I will blog about this when the interview is online. http://iopscience.iop.org/1751-8121/48/20/205203/article
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The interview by JPhys A is now online. http://iopscience.iop.org/1751-8121/page/Interview-with-Janusz-Grabowski
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I now appear in the newsletter of the Institute of Mathematics of the Polish Academy of Science! They report that one of my co-authored papers was selected for 'Publishers' Pick' by the Journal of Physics A. Also I am mentioned in the article about the 'Jets and Fields' conference.
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Another paper accepted, this one is on generalising some aspects of Riemannian geometry to Lie algebroids and sigma models