Constraint-Induced Effective Mass in Massless Field Propagation

Constrained propagation of massless fields is ubiquitous in physical systems, arising fromboundaries, material structure, or other restrictions on admissible modes. This papershows that such constraints generically induce mass-like terms in the effective dispersionrelation, without modifying the underlying field equations or introducing new degrees offreedom. Working at an abstract level, constraints are represented as linear operatorsacting on the field’s mode space. Restriction of the admissible mode manifold produces aspectral gap whose magnitude is set by the smallest non-zero eigenvalue of an associatedpositive semidefinite operator. This gap may be identified with an effective massparameter, yielding a Proca-like dispersion relation in the long-wavelength limit. Theresulting Mass Induction Principle identifies rank reduction of the accessible mode spaceas the structural mechanism responsible for effective mass generation in constrainedmassless fields. Familiar systems such as plasmas, superconductors, and periodic mediarealise this structure as special cases, without introducing new dynamics. The analysis isdeliberately dispersion-level and non-phenomenological: it does not assert a field-theoreticmass term, does not address vacuum propagation, and does not make claims about boundson intrinsic particle masses.