Abstract
The configuration space of a physical system is a differentiable manifold \(M\). The state of a system is given by a point \(x\) in \(M\) and a tangent vector \(v\) at \(x\), the velocity of the configuration. Call the tangent bundle \(TM\) of \(M\) the state space of the system (though the phrase “velocity phase space” is often used). A dynamical variable is a possibly time-dependent function on state space.
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References
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Nelson, E. (2014). Stochastic Mechanics of Particles and Fields. In: Atmanspacher, H., Haven, E., Kitto, K., Raine, D. (eds) Quantum Interaction. QI 2013. Lecture Notes in Computer Science(), vol 8369. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54943-4_1
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DOI: https://doi.org/10.1007/978-3-642-54943-4_1
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