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Abstract

Quantum and noncommutative corrections to the Newtonian law of inertia are considered in the general setting of Verlinde’s entropic force postulate. We demonstrate that the form for the modified Newtonian dynamics (MOND) emerges in a classical setting by seeking appropriate corrections in the entropy. We estimate the correction term by using concrete coherent states in the standard and generalized versions of Heisenberg’s uncertainty principle. Using Jackiw’s direct and analytic method, we compute the explicit wavefunctions for these states, producing minimal length as well as minimal products. Subsequently, we derive a further selection criterium restricting the free parameters in the model in providing a canonical formulation of the quantum corrected Newtonian law by setting up the Lagrangian and Hamiltonian for the system.

Publication Type:	Article
Additional Information:	Electronic version of an article published as Bagchi, B. and Fring, A. (2019). Quantum, noncommutative and MOND corrections to the entropic law of gravitation. International Journal of Modern Physics B, 33(05), doi: 10.1142/s0217979219500188 © 2019 World Scientific Publishing Company. https://www.worldscientific.com/doi/abs/10.1142/S0217979219500188
Publisher Keywords:	Entropic law of gravitation, modified Newtonian dynamics, noncommutative corrections
Subjects:	Q Science > QA Mathematics
Departments:	School of Science & Technology > Mathematics
SWORD Depositor:	Symplectic Administrator

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