  The Standard Model (SM) ascribes the observed mass of elementary particles to
an effective interaction between basis states defined without mass terms and a
scalar potential associated with the Higgs boson. In the relativistic field
theory that underlies the SM, mass itself, understood as the Lorentz-invariant
squared 4-momentum of a particle or field, is fixed a priori, imposing a
constraint on possible momentum states. Stueckelberg introduced an alternative
approach, positing antiparticles as particles evolving backward in time, thus
relaxing the mass shell constraint for individual particles. Further work by
Piron and Horwitz established a covariant Hamiltonian mechanics on an
unconstrained 8D phase space, leading to a gauge field theory that mediates the
exchange of mass between particles, while the total mass of particles and
fields remains conserved. In a recently developed extension of general
relativity, consistent with this approach, the spacetime metric evolves in a
manner that permits the exchange of mass across spacetime through the
gravitational field. Mechanisms that restrict mass exchange between particles
have also been identified. Nevertheless, mass exchange remains possible under
certain circumstances and may have phenomenological implications in particle
physics and cosmology.
