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arXiv:2606.09592

Conceptual and Geometric Foundations for a Teleparallel Approach to Quantum Gravity

Alexandre Landry

gr-qchep-thmath-phquant-phSubmitted Jun 8, 2026• Announced Jun 9, 2026
arXivHTMLPDF

Abstract

We revisit quantum field theory in curved spacetime (QFTCS) as a semi-classical framework for quantum matter on classical geometries, emphasizing its limitations, including vacuum ambiguity and background dependence. We briefly review major approaches to quantum gravity (QG), including Loop Quantum Gravity (LQG), string theory, and asymptotic safety, highlighting their conceptual challenges. Motivated by these issues, we outline a teleparallel framework based on coframe and spin-connection variables, where gravity is encoded in torsion rather than curvature. This framework naturally incorporates local Lorentz symmetry and fermionic couplings while displaying a gauge-like structure. We argue that the coframe/spin-connection pair provides an alternative and geometrically refined description of gravitational variables, which may serve as a useful starting point for future investigations of QG. The purpose of this work is not to provide a complete quantization of teleparallel gravity but to identify the geometric and conceptual ingredients that such a formulation would require.

Journal reference
Axioms 2026, 15(6), 427
DOI
10.3390/axioms15060427
Comments
13 pages, no figure; publication appeared in a special issue of Axioms Journal

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We revisit quantum field theory in curved spacetime (QFTCS) as a semi-classical framework for quantum matter on classical geometries, emphasizing its limitations, including vacuum ambiguity and background dependence. We briefly review major approaches to quantum gravity (QG), including Loop Quantum Gravity (LQG), string theory, and asymptotic safety, highlighting their conceptual challenges. Motivated by these issues, we outline a teleparallel framework based on coframe and spin-connection variables, where gravity is encoded in torsion rather than curvature. This framework naturally incorporates local Lorentz symmetry and fermionic couplings while displaying a gauge-like structure. We argue that the coframe/spin-connection pair provides an alternative and geometrically refined description of gravitational variables, which may serve as a useful starting point for future investigations of QG. The purpose of this work is not to provide a complete quantization of teleparallel gravity but to identify the geometric and conceptual ingredients that such a formulation would require.
Usual quantum mechanics requires a fixed background spacetime geometry and its associated causal structure. A generalization of the usual theory may therefore be needed at the Planck scale for quantum theories of gravity in which spacetime geometry is a quantum variable. The elements of generalized quantum theory are briefly reviewed and illustrated by generalizations of usual quantum theory that incorporate spacetime alternatives, gauge degrees of freedom, and histories that move forward and backward in time. A generalized quantum framework for cosmological spacetime geometry is sketched. This theory is in fully four-dimensional form and free from the need for a fixed causal structure. Usual quantum mechanics is recovered as an approximation to this more general framework that is appropriate in those situations where spacetime geometry behaves classically.
We uncover the quantum geometric structure of graviton Wigner functions and stress-energy tensors via quantum field theory in curved spacetime, revealing the phase-space geometry of spacetime and relativistic quantum-state manifolds. We show that the polarization mode expansion of the underlying graviton field operator is fully captured by quantum geometry, as encoded in the spinor-helicity formalism, thereby establishing the geometric framework from the outset. Applying this to a weak gravitational background, we demonstrate the roles of the quantum metric and connection in describing graviton transport beyond the chiral vortical effect. We also clarify the role of the quantum metric in normalizing the perfect-fluid graviton stress tensor within this approach. This work paves the path for explorations of multistate Hilbert-space geometry in high-energy and gravitational physics. In addition, this framework naturally encompasses lower-spin excitations, allowing for a unified quantum geometric treatment of bosonic and fermionic many-body systems in condensed matter and particle physics.
General relativity is a background-independent theory of a dynamical classical spacetime geometry. Quantum theory is formulated in a classical spacetime, as an intrinsically probabilistic, contextual theory of non-classical, interfering probabilities, with a fixed Born rule for computing those probabilities. We argue that the quantum nature of spacetime, which includes a non-commutative dual companion to the (observed) classical spacetime, is the reason behind an intrinsically probabilistic and contextual nature of quantum theory, with the fixed Born rule. In quantum gravity, we claim, quantum theory is gravitized into a background-independent structure with dynamical and contextual quantum probabilities. This proposal implies intrinsic triple and higher-order interference in the context of massive quantum probes, which sheds light on string theory and the observed vacuum energy as well as the masses of elementary particles.
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Usual quantum mechanics requires a fixed, background, spacetime geometry and its associated causal structure. A generalization of the usual theory may therefore be needed at the Planck scale for quantum theories of gravity in which spacetime geometry is a quantum variable. The elements of generalized quantum theory are briefly reviewed and illustrated by generalizations of usual quantum theory that incorporate spacetime alternatives, gauge degrees of freedom, and histories that move forward and backward in time. A generalized quantum framework for cosmological spacetime geometry is sketched. This theory is in fully four-dimensional form and free from the need for a fixed causal structure. Usual quantum mechanics is recovered as an approximation to this more general framework that is appropriate in those situations where spacetime geometry behaves classically. (Talk given at the Workshop on Physics at the Planck Scale, Puri, India, December12-21, 1994. This talk is a precis of the author's 1992 Les Houches Lectures: Spacetime Quantum Mechanics and the Quantum Mechanics of Spacetime, gr-qc/9304006).