Mathematics – Mathematical Physics
Scientific paper
Aug 2006
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006tmpg.conf..469s&link_type=abstract
Topics in Mathematical Physics, General Relativity and Cosmology in Honor of Jerzy Plebański. Proceedings of 2002 International
Mathematics
Mathematical Physics
Scientific paper
The mathematical theory of deformations has proved to be a powerful tool in modeling physical reality. We start with a short historical and philosophical review of the context and concentrate this rapid presentation on a few interrelated directions where deformation theory is essential in bringing a new framework - which has then to be developed using adapted tools, some of which come from the deformation aspect. Minkowskian space-time can be deformed into Anti de Sitter, where massless particles become composite (also dynamically): this opens new perspectives in particle physics, at least at the electroweak level, including prediction of new mesons. Nonlinear group representations and covariant field equations, coming from interactions, can be viewed as some deformation of their linear (free) part: recognizing this fact can provide a good framework for treating problems in this area, in particular global solutions. Last but not least, (algebras associated with) classical mechanics (and field theory) on a Poisson phase space can be deformed to (algebras associated with) quantum mechanics (and quantum field theory). That is now a frontier domain in mathematics and theoretical physics called deformation quantization, with multiple ramifications, avatars and connections in both mathematics and physics. These include representation theory, quantum groups (when considering Hopf algebras instead of associative or Lie algebras), noncommutative geometry and manifolds, algebraic geometry, number theory, and of course what is regrouped under the name of M-theory. We shall here look at these from the unifying point of view of deformation theory and refer to a limited number of papers as a starting point for further study.
No associations
LandOfFree
Deformation Theory and Physics Model Building does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Deformation Theory and Physics Model Building, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Deformation Theory and Physics Model Building will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-1106024