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Relancio Martínez, José Javier Santamaría Sanz, Lucía 2025-01-23T07:33:48Z 2025-01-23T07:33:48Z 2024-10 2470-0010 http://hdl.handle.net/10259/10003 10.1103/PhysRevD.110.086004 2470-0029 In this work, we explore the quantum theories of the free massive scalar, the massive fermionic, and the electromagnetic fields in a doubly special relativity scenario. This construction is based on a geometrical interpretation of the kinematics of this kind of theory. In order to describe the modified actions, we find that a higher (indeed infinite) derivative field theory is needed, from which the deformed kinematics can be read. From our construction, we are able to restrict the possible models of doubly special relativity to those that preserve linear Lorentz invariance. We quantize the theories and also obtain a deformed version of the Maxwell equations. We analyze the electromagnetic vector potential for both an electric pointlike source and magnetic dipole. We observe that the electric and magnetic fields do not diverge at the origin for some models described with an anti–de Sitter momentum space, but they do for a de Sitter space in both problems. This research is supported by the Spanish Ministry of Science and Innovation MICIN, as well as by the Regional Government of Castilla y León (Junta de Castilla y León, Spain), with funding from European Union NextGenerationEU through the Quantum Communications in Castilla y León (QCAYLE) project (PRTRC17.I1). J. J. R. is funded by the Agencia Estatal de Investigación (Spain) through Grant No. PID2019– 106802GB-I00/AEI/10.13039/501100011033. application/pdf eng American Physical Society Physical Review D. 2024, V. 110, n. 8 https://doi.org/10.1103/PhysRevD.110.086004 Atribución 4.0 Internacional http://creativecommons.org/licenses/by/4.0/ info:eu-repo/semantics/openAccess Matemáticas Física Mathematics Physics Doubly special relativity as a nonlocal quantum field theory info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Physical Review D 110 8