Mathematical structures and the foundations of quantum theory

P. A. M. Dirac

David Halenta

This paper provides the formal and mathematical foundation for the Quantum Continuum Theory (QCT) introduced in the author’s earlier publication Observation as Projection of an Invariant Superposition. It establishes projection as a structural and mathematically necessary consequence of universal invariance rather than an interpretive device. Through theorems by Gleason and Naimark, the work demonstrates formal equivalence with standard quantum mechanics while offering a distinct ontological framework grounded in projectional geometry. The paper consolidates QCT into a coherent, self-consistent theory linking invariance, coherence, curvature, and entropy—bridging quantum foundations with information geometry and epistemic structure.

Tian Yu Cao

Quantum field theory (QFT) can be analyzed in terms of its mathematical structure, its conceptual scheme, or its basic ontology. The analysis can be done logically or historically. In this chapter, only the genesis of the conceptual foundations of QFT relevant to its basic ontology will be treated carefully; no detailed discussion of its mathematical structures or its epistemological underpinnings will be given. Some conceptual problems, such as those related to probability and measurement, will be discussed, but only because of their relevance to the basic ontology of QFT, rather than their intrinsic philosophical interest.

Valter Moretti

Valter Moretti