Mathematical Physics
[Submitted on 12 May 2014 (v1), last revised 17 Feb 2016 (this version, v2)]
Title:Quantized Mechanics of Affinely-Rigid Bodies
View PDFAbstract:In this paper we develope the main ideas of the quantized version of affinely-rigid (homogeneously deformable) motion. We base our consideration on the usual Schrödinger formulation of quantum mechanics in the configuration manifold which is given, in our case, by the affine group or equivalently by the semi-direct product of the linear group ${\rm GL}(n,\mathbb{R})$ and the space of translations $\mathbb{R}^{n}$, where $n$ equals the dimension of the "physical space". In particular, we discuss the problem of dynamical invariance of the kinetic energy under the action of the whole affine group, not only under the isometry subgroup. Technically, the treatment is based on the two-polar decomposition of the matrix of the internal configuration and on the Peter-Weyl theory of generalized Fourier series on Lie groups. One can hope that our results may be applied in quantum problems of nuclear dynamics or even in apparently exotic phenomena in vibrating neutron stars. And, of course, some more prosaic applications in macroscopic elasticity, structured continua, molecular dynamics, dynamics of inclusions, suspensions, and bubbles are also possible.
Submission history
From: Vasyl Kovalchuk [view email][v1] Mon, 12 May 2014 09:44:20 UTC (31 KB)
[v2] Wed, 17 Feb 2016 11:41:02 UTC (28 KB)
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