Quantum Gravity and String Theory

    

On Clifford-valued Actions, Generalized Dirac Equation and Quantization of Branes

Authors: Carlos Castro

We explore the construction of a generalized Dirac equation via the introduction of the notion of Clifford-valued actions, and which was inspired by the work of [1],[2] on the De Donder-Weyl theory formulation of field theory. Crucial in this construction is the evaluation of the $exponentials$ of $multivectors$ associated with Clifford (hypercomplex) analysis. Exact $matrix$ solutions (instead of spinors) of the generalized Dirac equation in $ D = 2,3$ spacetime dimensions were found. This formalism can be extended to curved spacetime backgrounds like it happens with the Schroedinger-Dirac equation. We conclude by proposing a wave-functional equation governing the quantum dynamics of branes living in $ C$-spaces (Clifford spaces), and which is based on the De Donder-Weyl Hamiltonian formulation of field theory.

Comments: 12 Pages.

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Submission history

[v1] 2023-04-24 11:23:04

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