Consequences of Antisymmetry

Diana Haskins

Exclusion, antisymmetry, uncertainty—and Planck’s constant—are derived, not assumed.By enforcing degeneracy–structure consistency, quantum behavior emerges as a necessary consequence of admissible structure, with ħ appearing as the conversion factor that expresses structural limits in physical units.

Анатолий Григорьевич Муха

The Pauli exclusion principle is one of the fundamental laws of modern physics. It determines the structure of atoms, the stability of matter, the properties of fermionic systems, and macroscopic phenomena ranging from chemistry to astrophysics. In standard quantum mechanics (QM), this principle is formulated as an axiom of antisymmetry: the wave function of two fermions must change sign under the exchange of coordinates. However, the origin of this antisymmetry remains unexplained within QM itself. Within ZEBTS — the Law of Unity of Being of the Triune Substance — the Pauli principle acquires a geometric and topological foundation. In this ontology, fermions are not treated as elementary particles but as topological modes of the operator metric, arising from the spectral structure of quantum geometry. Antisymmetry and the prohibition of identical states emerge as consequences of: the non‑commutativity of the operator metric, the topological charge λ, the spectral non‑intersection of eigenvalues, holographic constraints on information density. Thus, ZEBTS derives the Pauli principle as a topological law of quantum geometry, rather than a postulate.

R. Shankar

David John Baker

Francisco Marcelo Fernández

Abstract It is well known that the allowed wavefunctions for an N -electron system should be antisymmetric with respect to the permutation of any pair of electron labels. On the other hand, the Hamiltonian for such a system is invariant under any permutation of electron labels and, consequently, its eigenfunctions are the basis for the irreducible representations of the symmetric group S N . Here, we investigate which symmetry species of the S N group are compatible with the antisymmetry principle. We illustrate the conclusions by means of simple N -particle one-dimensional models with harmonic interactions.