The Pauli Exclusion Principle and the Problems of its Theoretical Substantiation 1
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THE PAULI EXCLUSION PRINCIPLE AND THE PROBLEMS OF ITS THEORETICAL SUBSTANTIATION1 I. G. Kaplan
UDC 539.194:535.37
The modern state of the Pauli Exclusion Principle (PEP) is discussed. PEP can be considered from two viewpoints. On the one hand, it asserts that particles with half-integer spin (fermions) are described by antisymmetric wave functions, and particles with integer spin (bosons) are described by symmetric wave functions. This is the so-called spin-statistics connection (SSC). As we will discuss, the physical reasons why SSC exists are still unknown. On the other hand, according to PEP, the permutation symmetry of the total wave functions can be only of two types: symmetric or antisymmetric, both belong to one-dimensional representations of the permutation group, all other types of permutation symmetry are forbidden; whereas the solution of the Schrödinger equation may have any permutation symmetry. It is demonstrated that the proof in some textbooks on quantum mechanics that only symmetric and antisymmetric states can exist is wrong. However, the scenarios, in which arbitrary permutation symmetry (degenerate permutation states) is permitted, lead to contradictions with the concepts of particle identity and their independence. Thus, the existence in our Nature of particles only in nondegenerate permutation states (symmetric and antisymmetric) is not accidental and so-called symmetrization postulate should not be considered as a postulate, since all other symmetry options for the total wave function may not be realized. From this an important conclusion follows: we may not expect that in the future some unknown elementary particles can be discovered that are not fermions or bosons. Keywords: Pauli exclusion principle, spin-statistics connection, indistinguishability principle, permutation symmetry, boson and fermion particles
1. DISCOVERY OF THE PAULI EXCLUSION PRINCIPLE FOR ELECTRONS AND ITS GENERALIZATION IN THE FRAME OF QUANTUM MECHANICS FOR ALL ELEMENTARY PARTICLES Wolfgang Pauli formulated his principle before the creation of the contemporary quantum mechanics. It is well known that the main conceptions of quantum mechanics were formulated in 1925 by Heisenberg, Born, and Jordan [1, 2] in the matrix formalism. In 1926 Schrödinger relying on the wave-particle dualism, suggested by de Broglie [3], introduced the wave function ψ describing micro-particles and formulated his famous wave equation [4, 5]. Pauli arrived at the formulation of his principle trying to explain regularities in the anomalous Zeeman effect in strong magnetic fields. In his first studies of the Zeeman effect, Pauli was interested in the explanation of the simplest case, the doublet structure of the alkali spectra. In December of 1924 Pauli submitted a paper on the Zeeman effect [6], in which he showed that Bohr’s theory of doublet structure, which was based on the non-vanishing angular moment of
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The paper is devoted to the memory of Victor Plotnikov.
Material Research Institute, National Autonomous University of Mexico, Mexic
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