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How to quantize forces (?): An academic essay on how the strings could enter classical mechanics
- 1.0341389 - ÚJF 2010 RIV NL eng J - Journal Article
Kochan, Denis
How to quantize forces (?): An academic essay on how the strings could enter classical mechanics.
Journal of Geometry and Physics. Roč. 60, č. 2 (2010), s. 219-229. ISSN 0393-0440. E-ISSN 1879-1662
R&D Projects: GA MŠMT LC06002
Institutional research plan: CEZ:AV0Z10480505
Keywords : Line element contact bundle * Classical mechanics * Dissipative systems
Subject RIV: BE - Theoretical Physics
Impact factor: 0.652, year: 2010
Geometrical formulation of classical mechanics with forces that are not necessarily potential-generated is presented. It is shown that a natural geometrical "playground" for a mechanical system of point particles lacking Lagrangian and/or Hamiltonian description is an odd-dimensional line element contact bundle. Time evolution is governed by certain canonical two-form Omega (an analog of dp Lambda dq - dH Lambda dt), which is constructed purely from forces and the metric tensor entering the kinetic energy of the system. Attempt to "dissipative quantization" in terms of the two-form Omega is proposed. The Feynman path integral over histories of the system is rearranged to a "world-sheet" functional integral. The "umbilical string" surfaces entering the theory connect the classical trajectory of the system and the given Feynman history.
Permanent Link: http://hdl.handle.net/11104/0184395
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