Proposal: Imaginary Mass Extensions in Relativistic Field Theories

This upload (v1.0) presents an proposal for introducing a complex mass parameter M=m+iμM = m + i\muM=m+iμ into both general relativity and quantum field theory. Key features of this version include: Complexified Einstein–Hilbert action: Analytic continuation of the metric tensor gμνg_{\mu\nu}gμν to a complex metric GμνG_{\mu\nu}Gμν, with a clear definition of −det⁡G\sqrt{-\det G}−detG and resulting field equations for cases such as complex Schwarzschild and de Sitter solutions. PT-symmetric quantum framework: Modification of the Dirac and Schrödinger operators to include complex mass poles, together with contour-deformation and pseudo-Hermitian techniques to preserve causality and unitarity. Preliminary observational bounds: Using gravitational lensing and galaxy rotation-curve data to set an initial upper limit on the imaginary mass component μ\muμ, of order ∣μ∣≲10−22 eV/c2|\mu|\lesssim10^{-22}\,\mathrm{eV}/c^2∣μ∣≲10−22eV/c2. Physical implications: Exploration of dark-matter-like gravitational effects without new particle species, entanglement-induced geometry via the ER=EPR conjecture, and potential corrections to early-universe inflationary dynamics. Expanded literature review: Inclusion of foundational works on tachyon condensation, PT-symmetric quantum mechanics, ER=EPR bridges, and complex spacetime/geometric models. Files included: PDF of the proposal LaTeX source (.tex) Ancillary figures (PNG) illustrating key mathematical plots and zoomed analyses.