arXiv subjects

Mehdi Ahmadi-Jahmani

Publications and source records attributed to Mehdi Ahmadi-Jahmani.

3 recordsLinked to original sources

arXiv2026

Trinity of Carrollian Gravity: Dynamically Equivalent Formulations of Magnetic Carrollian Gravity

In this paper, we extend the paradigm of the Geometrical Trinity of Gravity to the Carrollian geometry to construct a comprehensive framework of dynamically equivalent theories for Magnetic Carrollian gravity. Utilizing the inherent ambiguities and freedoms of affine connections on degenerate metrics, we systematically relax the metric-compatibility and zero-torsion constraints of the rigid magnetic sector. By imposing global flatness on these modified connections, we prove that the curvature of a Magnetic Carrollian universe can be dynamically traded for isolated kinetic energy densities of torsion and non-metricity. Unlike the Lorentzian Trinity which maps gravity to alternative gravitational frameworks, the Carrollian equivalences can also map spacetime geometry to non-gravitational theories. Specifically, we demonstrate that intrinsic torsion recovers Electric Carrollian gravity as the Teleparallel equivalent of Magnetic Carroll gravity; purely spatial torsion reproduces kinetic terms stracturally similar to the magnetic Hamiltonian of scalar-charge Fracton gauge theory; and temporal torsion sectors map independently to $U(1)$ Maxwell electric fields and Carroll-Weyl conformal dilaton theories. Finally, by formulating a Symmetric Teleparallel Carroll connection with minimal non-metricity, we show that the Magnetic Carrollian Lagrangian is dynamically equivalent to an ultralocal, isotropic Electric Carrollian gravity upon exploiting the present freedoms in connection. These results establish a geometric dictionary translating Carrollian gravitational dynamics into the language of tensor gauge theories, electromagnetism, and dilaton theory.

hep-th↗

arXiv2026

Carrollian Quantum Mechanics: Time-like, Space-like and Hybrid Sectors

We develop a comprehensive theoretical framework for Carrollian quantum mechanics by performing systematic ultra-relativistic contractions of the Klein--Gordon equation in the limit $c \to 0$. This limiting process uncovers three distinct sectors---time-like, space-like, and hybrid---each governed by a Carroll-invariant wave equation and accompanied by a consistent probabilistic interpretation. The time-like sector exhibits a novel temporal tunneling phenomenon, characterized by the relation $|\mathcal{T}|^2 = 1 + |\mathcal{R}|^2$, which reflects the indefinite character of the Klein--Gordon norm. In the space-like sector, the presence of spatial propagation necessitates a tachyonic dispersion relation, which forces the density to vanish for energy eigenstates, yielding zero-norm (null) states that gain physical relevance within Carrollian physics due to the underlying null geometric structure. The hybrid sector combines features of both sectors and admits two distinct formulations, which may be either tachyonic or non-tachyonic, and can be interpreted as an inhomogeneous Klein--Gordon equation. For all three sectors, we derive the corresponding continuity equations, probability densities, and currents, and investigate canonical quantum systems---including the particle in a box and tunneling phenomena---within the Carrollian regime.

hep-th↗

arXiv2026

Scaling Symmetry and Carrollian Gravity

We formulate matter-coupled scaling-Carroll gravity as a gauge theory and develop a conformal construction for generating local Carroll-invariant couplings. The construction relaxes Carrollian special conformal symmetry and leads to an enlarged gravity multiplet. After fixing the scaling symmetry, the theory is governed by the trace of the extrinsic curvature, the Carroll boost symmetry, a vector field descending from dilatation, and a symmetric tensor originating from the Carroll boost connection. The vector field acquires a Stückelberg-like transformation under Carroll boosts proportional to the trace of the extrinsic curvature. We show that appropriate gauge choices and field redefinitions give rise to Carrollian and Aristotelian descriptions, as well as a tensor-gauge description of the symmetric tensor field coupled to Aristotelian geometry. In the latter description, the Carroll boost parameter plays the role of a vector-valued gauge parameter.

hep-th↗