Quantization of Contact Manifolds and Thermodynamics

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dc.creatorRajeev, S. G.
dc.date2007-03-20
dc.date2007-03-27
dc.date.accessioned2026-07-07T11:23:48Z
dc.date.available2026-07-07T11:23:48Z
dc.descriptionThe physical variables of classical thermodynamics occur in conjugate pairs such as pressure/volume, entropy/temperature, chemical potential/particle number. Nevertheless, and unlike in classical mechanics, there are an odd number of such thermodynamic co-ordinates. We review the formulation of thermodynamics and geometrical optics in terms of contact geometry. The Lagrange bracket provides a generalization of canonical commutation relations. Then we explore the quantization of this algebra by analogy to the quantization of mechanics. The quantum contact algebra is associative, but the constant functions are not represented by multiples of the identity: a reflection of the classical fact that Lagrange brackets satisfy the Jacobi identity but not the Leibnitz identity for derivations. We verify that this `quantization' describes correctly the passage from geometrical to wave optics as well. As an example, we work out the quantum contact geometry of odd-dimensional spheres.
dc.descriptionAdditional references; typos fixed; a clarifying remark added
dc.identifierhttps://arxiv.org/abs/math-ph/0703061
dc.identifierhttp://arxiv.org/abs/math-ph/0703061
dc.identifierAnnalsPhys.323:768-782,2008
dc.identifierdoi:10.1016/j.aop.2007.05.001
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/195015
dc.subjectMathematical Physics
dc.subjectStatistical Mechanics
dc.subjectHigh Energy Physics - Theory
dc.subjectSymplectic Geometry
dc.subjectQuantum Physics
dc.titleQuantization of Contact Manifolds and Thermodynamics
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