| _version_ | 1866902306037956608 |
|---|---|
| author | Francisco Ancelmo, Pinheiro Ferreira |
| author_facet | Francisco Ancelmo, Pinheiro Ferreira |
| contents | <p>This work presents a novel formulation of quantum field theory (QFT) in which spacetime geometry emerges relationally from the field's own dynamics, without the need to quantize the metric or introduce a fundamental length scale such as the Planck length. The construction is based on a deformed Hopf algebra that encodes energy- and momentum-dependent commutation relations, leading to an effective metric tied to the Compton scale of the field.</p> <p>We derive a fully regularized scalar field theory, along with its quantization, propagators, and vacuum energy — all finite without ad hoc cutoffs. We then generalize to spinor fields and propose a new class of dynamical equations for geometry, from which Einstein’s equations emerge in the classical limit. Our approach resolves longstanding problems such as ultraviolet divergence, the incompatibility between quantum superposition and a fixed background metric, and the problem of time in quantum gravity.</p> <p>The resulting framework offers new insights into high-energy particle propagation, relational time, and the coexistence of superposed geometries, with potential observational consequences in astrophysics and foundational implications for quantum gravity.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_15465637 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Relational Quantum Fields and the Emergence of Geometry Without Planck Scale Francisco Ancelmo, Pinheiro Ferreira Relacional quantum geometry Emergent spacetime Compton-scale physics Deformed Hopf algebra UV-finite quantum field theory Momentum-dependent metric Quantum gravity without Planck scale Einstein Equations from QFT Noncommutative field theory <p>This work presents a novel formulation of quantum field theory (QFT) in which spacetime geometry emerges relationally from the field's own dynamics, without the need to quantize the metric or introduce a fundamental length scale such as the Planck length. The construction is based on a deformed Hopf algebra that encodes energy- and momentum-dependent commutation relations, leading to an effective metric tied to the Compton scale of the field.</p> <p>We derive a fully regularized scalar field theory, along with its quantization, propagators, and vacuum energy — all finite without ad hoc cutoffs. We then generalize to spinor fields and propose a new class of dynamical equations for geometry, from which Einstein’s equations emerge in the classical limit. Our approach resolves longstanding problems such as ultraviolet divergence, the incompatibility between quantum superposition and a fixed background metric, and the problem of time in quantum gravity.</p> <p>The resulting framework offers new insights into high-energy particle propagation, relational time, and the coexistence of superposed geometries, with potential observational consequences in astrophysics and foundational implications for quantum gravity.</p> |
| title | Relational Quantum Fields and the Emergence of Geometry Without Planck Scale |
| topic | Relacional quantum geometry Emergent spacetime Compton-scale physics Deformed Hopf algebra UV-finite quantum field theory Momentum-dependent metric Quantum gravity without Planck scale Einstein Equations from QFT Noncommutative field theory |
| url | https://doi.org/10.5281/zenodo.15465637 |