Turkish Journal of Physics
Abstract
The recent trend of incorporating fractional derivatives into Lagrangians prompts a critical assessment of their physical viability. This work analyzes such theories through the lenses of classical mechanics and quantum field theory (QFT), revealing profound foundational issues. While the nonlocal nature of fractional operators circumvents Ostrogradsky's theorem, it introduces more severe problems. Classically, these include a complicated variational principle and the violation of energy conservation due to broken time-translation symmetry. In QFT, the pathologies are fatal: the propagator violates the K\"all\'en--Lehmann spectral representation, leading to acausal propagation, ghost states, complex poles, and a loss of unitarity. We conclude that Lagrangians with fractional derivatives in the kinetic term are fundamentally incompatible with the core principles of a physical, unitary quantum field theory.
Author ORCID Identifier
NICOLA FABIANO: 0000-0003-1645-2071
DOI
10.55730/1300-0101.2949
Keywords
Fractional derivatives, Lagrangian formalism, Ostrogradsky theorem, quantum field theory
First Page
410
Last Page
422
Publisher
The Scientific and Technological Research Council of Türkiye (TÜBİTAK)
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Recommended Citation
FABIANO, N (2026). Are Lagrangians involving fractional derivatives physically viable?. Turkish Journal of Physics 50 (5): 410-422. https://doi.org/10.55730/1300-0101.2949
