Rigged-Hilbert-Space construction of

We present a novel formulation of quantum mechanics in which thetraditional dichotomy between space and time is entirely dissolved,giving rise to a fully covariant and relational framework. Within thisconstruction, the quantum state is defined not as a time-indexed wavefunctionin three-dimensional space, but as a distribution in the fullfour-dimensional spectral manifold R4, corresponding to the simultaneouseigenvalues of the four-momentum operator Pμ. This approachnaturally accommodates positive, zero, and negative energy componentswithin a single spectral amplitude, permitting a unified interpretationof particle and antiparticle degrees of freedom as smoothinstantiations across the spectral domain.Wave-packet states are rigorously constructed as elements of arigged Hilbert space, enabling the controlled use of generalized eigenvectorsfor sharp four-momentum while maintaining smooth spacetimelocalization via Fourier duality. Probability densities and expectationvalues are defined fundamentally in spectral space, with covariant fourcurrentsin spacetime emerging as secondary, physically interpretableconstructs. Interactions are implemented as Hermitian operators actingin spectral space, producing smooth reshaping of wave packetsand naturally incorporating energy-sign interference without invokinga preferred temporal slicing.