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Generalized Dirac Equation for a particle in a gravitational field

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Abstract

The existence of a minimal observable length modifies the Heisenberg’s uncertainty principle at Plank scales and leads to some modifications of the Dirac equation. Here, we consider the generalized uncertainty principle (GUP) theory in order to deduce a generalized Dirac equation and solve its eigenvalue problem for a particle within a gravitational field created by a central mass. We use two different approximations to tackle the problem, based on the Schwarzschild and a modified Schwarzschild metrics.

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Acknowledgements

The work is partially supported by a MINECO/ FEDER Grant Number PID2020-113758GB-I00 and an AGAUR (Generalitat de Catalunya) Grant Number 2017SGR 1276 and Icrea Academia.

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Authors and Affiliations

  1. Applied Physics Section of Environmental Science Department, Universitat de Lleida, Av. Jaume II, 69, 25001, Lleida, Spain

    Daniel Chemisana & Jaime Madrid

  2. Departament de Matemàtica, Universitat de Lleida, Av. Jaume II, 69, 25001, Lleida, Catalonia, Spain

    Jaume Giné

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  1. Daniel Chemisana
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  2. Jaume Giné
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  3. Jaime Madrid
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Correspondence to Jaume Giné.

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Chemisana, D., Giné, J. & Madrid, J. Generalized Dirac Equation for a particle in a gravitational field. Gen Relativ Gravit 53, 65 (2021). https://doi.org/10.1007/s10714-021-02834-y

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