Finite–Resolution Physics and the Emergence of Internal Symmetry: Boundary Architecture, Stabilizer Symmetry, and Scale–Dependent Gauge Structure

Translator

 

 

 

 

In conventional particle physics, internal symmetries are postu-
lated as fundamental kinematical inputs, while boundaries and inter-
faces merely select solutions within a fixed symmetry framework. In
this work we show that this logical order can be reversed.
Within Finite–Resolution Physics (FRP), physical descriptions are
constrained by finite resolution, global consistency, and statistical typ-
icality. We demonstrate that these constraints force boundary com-
patibility conditions whose dual structure uniquely determines the
internal symmetry content of the theory. Internal symmetry there-
fore emerges as a stabilizer of boundary coherence, rather than as an
independent postulate.
Technically, the finite–resolution constraints define a linear sub-
space of admissible boundary data. Its dual annihilator acts simulta-
neously across all representation sectors, giving rise to a Simultane-
ously Interlocked Lagrange Multiplier (SILM). For general background
on dual annihilators and constraint duality in linear settings, see [5, 6].
The stabilizer of the SILM induces an internal symmetry group
whose structure depends on the resolution scale, naturally producing
symmetry plateaux separated by transition regimes.
This boundary–first perspective explains why internal symmetries
are robust within certain resolution ranges, yet change across oth-
ers, without invoking symmetry breaking or additional dynamical as-
1
sumptions. A simple toy model illustrates how a Standard–Model–like
symmetry structure can arise as a stable finite–resolution plateau.
The results suggest that gauge symmetry is not a fundamental
input of microscopic physics, but a structural consequence of finite
resolution and boundary coherence.