Consistent gauge theory on Snyder–de Sitter space

Construct a consistent gauge theory on Snyder–de Sitter space, including a formulation that remains consistent when restricted to Snyder space alone.

Background

The paper constructs Poisson gauge transformations on the full Snyder–de Sitter phase space using the explicit Darboux representation derived earlier. Because the Poisson bracket of the spacetime coordinates depends on both coordinates and conjugate momenta, the gauge field must be defined on phase space rather than on spacetime alone. The authors identify the broader construction of a consistent gauge theory on Snyder–de Sitter space, or even on Snyder space alone, as unresolved.

References

A consistent formulation of gauge theory on Snyder–de Sitter, or even on Snyder space alone, remains an open problem.

— Canonical representation of the Snyder-de Sitter algebra with correct flat and commutative limits  (2608.21116 - Kupriyanov et al., 21 Aug 2026) in Section 5, Poisson gauge algebra for Snyder–de Sitter space, p. 5

An attempt to formulate a gauge theory on Snyder space without these additional degrees of freedom leads to nonassociativity [23], whose physical interpretation remains unclear.

— Canonical representation of the Snyder-de Sitter algebra with correct flat and commutative limits  (2608.21116 - Kupriyanov et al., 21 Aug 2026) in Section 5, Poisson gauge algebra for Snyder–de Sitter space, p. 5