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Physical Review A

Internal symmetry of quantum systems and vertices of composite particles

Z. Chyliński

Published Aug 1, 1985• 2 citations
Publisher

Abstract

The hypothesis of an internal symmetry of quantum systems, presented in previous papers and recapitulated here, implies a modified geometrical interpretation of the nonrelativistic internal wave functions of loosely bound systems. This reinterpretation modifies the vertices of loosely bound composite particles and can be tested in elastic, inelastic, and dissociation processes. Three effects which follow from this hypothesis are analyzed.

DOI
10.1103/physreva.32.764

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The hypothesis of an internal symmetry of quantum systems, presented in previous papers and recapitulated here, implies a modified geometrical interpretation of the nonrelativistic internal wave functions of loosely bound systems. This reinterpretation modifies the vertices of loosely bound composite particles and can be tested in elastic, inelastic, and dissociation processes. Three effects which follow from this hypothesis are analyzed.
Abstract Physical systems often have some kind of obvious symmetry, such as the rotational symmetry of the central force field about a nucleus. Mathemati cally this means that the system is invariant under the action of a symmetry group G. (The main ideas of group theory are reviewed in Appendix Al.) Such a physical symmetry must also be present in quantum theory in a way that is compatible with the other important structures, namely the vector spaces and inner products. The simplest way in which this can happen is for G to act on the inner product space 1i by unitary transformations, since these respect both the linear structure and the inner product.
Particles are considered temporarily identical if the interchange of these particles does not cause any observable physical effects within a time interval Δt. An indistinguishability hypothesis is proposed for such particles, suggesting that two particles (or systems) with nearly the same degree of internal freedom will actually interchange under certain circumstances, thereby affecting the subsequent dynamics. This indistinguishability implies that, theoretically, it is possible to capture an elementary particle with extraordinarily large internal freedom by trading it for an isolated composite system of ordinary matter particles with almost the same total internal freedom as the large-freedom particle. Following this, the ordinary particles will instantly disperse into the environment, while the large-freedom particle will initially be captured and then gradually delocalized into the environment, an observable phenomenon. If this hypothesis is proven true in the future, it might provide a novel strategy for detecting dark matter particles.
We introduce a tensorial operator framework, referred to as the Tao–Bend formalism, for describing the emergence, stabilization, and large-scale behavior of interacting wave-based physical systems. The framework combines a con- vergence operator (Tao) with a nonlinear resistance and saturation mechanism (Bend), acting on ensembles of coherent and weakly bound wave modes. Rather than postulating new fundamental particles or modifying established interac- tion vertices, the approach operates at the level of effective dynamics, incorpo- rating field-dependent response, statistical averaging, and non-linear stabiliza- tion.We demonstrate that the proposed operators admit internally consistent be- havior across multiple physical contexts, including vacuum-mediated interactions, symmetry-breaking phenomena, and precision observables, when interpreted as an effective description. Numerical investigations show that, under increasing path multiplicity and interaction strength, the framework naturally suppresses quantum interference and yields an emergent classical limit characterized by a reduced effective action scale. The results suggest that the Tao–Bend formal- ism provides a unified mathematical structure for studying wave convergence, stability, and the quantum-to-classical transition within a single operator-based setting. While the framework does not replace established quantum field the- ories, it offers a complementary perspective for exploring emergent behavior in complex interacting systems. Disclaimer: No conflicts with standard model , the theory is trying to represent a hypothesis for extension to standard model