Complex-Time Quantum–Thermal–Geometric Dynamics and Its Extension to Quantum Field Theory

We propose a unified theoretical framework, Complex-Time Quantum–Thermal–Geometric Dynamics (CTQTG), in which quantum mechanics, thermal physics, and emergent geometry are integrated into a single evolution governed by complex time. The fundamental evolution equation readsequation_ (, x) = - H (x) - _^ (g) (, x), equationwhere = + i t / is the complex time, is a geometric diffusion coupling, and _^ (g) is the Laplace-Beltrami operator on a curved complex-time manifold. We generalize this equation from quantum mechanics to quantum field theory, demonstrating that thermal effects arise naturally from imaginary-time periodicity, and that emergent geometry arises as a low-energy effective consequence of quantum fluctuations. This formalism provides a first-principles pathway to unify quantum mechanics, thermodynamics, and gravity within a single complex-time framework.