Akademik Veri Yönetim Sistemi
European Physical Journal C, cilt.86, sa.1, 2026 (SCI-Expanded, Scopus)
We develop and apply the Batalin–Fradkin–Vilkovisky (BFV) formalism for the covariant quantization of generic off-diagonal solutions of the Einstein equations in general relativity (GR). In the classical regime, such nonholonomic configurations are formulated entirely within GR and are characterized by nonlinear symmetries of generating functions, running cosmological constants, integration functions, and effective matter sources. These constructions are further extended to quantum gravity (QG) models involving effective local Lorentz symmetry violations and anisotropic scaling, as realized in Hořva–Lifshitz (HL)-type theories. The classical geometric framework is formulated on Lorentz manifolds endowed with nonholonomic 2+2 and 3+1 splitting structures and subsequently generalized to quantum configurations determined by HL-type generating functions. The 2+2 dyadic splitting, incorporating connection distortions, provides a systematic method for constructing exact and parametric classical and quantum solutions described by generating functions and effective sources depending on all spacetime coordinates, physical constants, and anisotropic scaling or deformation parameters. The complementary 3+1 splitting allows for a consistent implementation of the BFV quantization procedure. We demonstrate the renormalizability of off-diagonal quantum HL-type deformations of GR. The resulting classical and quantum nonholonomic BFV models represent viable candidates for asymptotically free theories of gravity and may provide a mechanism for resolving unitarity issues in QG. In appropriate classical limits, the framework reproduces physically relevant off-diagonal GR solutions with or without locally anisotropic scaling, offering potential applications to nonlinear classical and quantum phenomena in accelerating cosmology and dark energy and dark matter physics.