2025/06/09 by Hateley, James
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2506.08165
We introduce a two-dimensional temporal framework in which time is represented by a compact manifold T2 = (t1, t2), with t1 encoding classical causal structure and t2 representing quantum coherence. This construction unifies unitary evolution, decoherence, measurement collapse, and gravitational dynamics within a consistent geometric and algebraic formalism. Compactification of the coherence time t2 yields a minimal temporal resolution Δt2 ∼ √(α'), leading to a discretized spectrum of temporal modes and regularized ultraviolet behavior in quantum field theory and string-theoretic gravity. We formulate an extended Schrödinger equation and generalized Lindblad dynamics on T2, and demonstrate the compatibility of this structure with local gauge symmetry through a complexified BRST quantization procedure. Using para-Hermitian geometry and generalized complex structures, we derive a covariant formulation of temporal T-duality that accommodates both Lorentzian and Euclidean signatures. The T2 framework provides new insights into modular thermodynamics, black hole entropy, and the emergence of classical time from quantum coherence, offering a compact and quantized model of temporal geometry rooted in string theory and quantum gravity.