A wavefunction description for a localized quantum particle in curved spacetimes

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 Parker (1980 Phys. Rev. Lett. 44 1559), Parker (1980 Phys. Rev. D 22 1922-1934). 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 Schrodinger equation associated with a symmetric Hamiltonian. When compared to the standard Schrodinger 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.

Automated summary

We simplified Dirac's spinor formalism to describe a spin 1/2 particle in curved spacetimes using complex wavefunctions. By expanding around the center of mass in terms of acceleration and curvature, we generalized previous results and obtained a quantum description in a Hilbert space of complex wavefunctions. The evolution of the wavefunction is governed by a modified Schrodinger equation associated with a symmetric Hamiltonian, introducing corrections due to the acceleration and curvature of spacetime.