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arXiv · 2012.08539

A Wavefunction Description for a Localized Quantum Particle in Curved Spacetimes

T. Rick Perche·Jonas Neuser
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Abstract

We reduce Dirac's spinor formalism for a spin 1/2 particle to a complex wavefunction description in curved spacetimes. We consider a localized fermionic particle in curved spacetimes and perform an expansion in terms of the acceleration and curvature around the center of mass of the system, generalizing the results of [Phys. Rev. D 22, 1922]. Under a non-relativistic approximation, one obtains a quantum description in a Hilbert space of complex wavefunctions defined in the rest space of the system. The wavefunction of the particle then evolves according to a modified Schr\"odinger equation associated with a symmetric Hamiltonian. When compared to the standard Schr\"odinger equation for a wavefunction, we obtain corrections in terms of the acceleration of the system's center of mass and curvature of spacetime along its trajectory. In summary, we provide a formalism for the use of a complex wavefunction to describe a localized quantum particle in curved spacetimes.

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BibTeXRIS

T. Rick Perche, Jonas Neuser. 2020-12-15. A Wavefunction Description for a Localized Quantum Particle in Curved Spacetimes. https://doi.org/10.1088/1361-6382/ac103d

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