arXiv subjects

Vincenzo Chilla

Publications and source records attributed to Vincenzo Chilla.

6 recordsLinked to original sources

arXiv2026

The classical boundaries of the EPR argument and quantum ontology

Von Neumann's Hilbert-space formalism of quantum mechanics constitutes a logico-physical theory of observed or measured reality. Imposing the logical constraint of Booleanity, essential for objectively shareable descriptions among observers, reveals the physical meaning of classicality inherently embedded within the formalism itself. Starting from this consideration, the present work reformulates the quantum-classical transition via Hilbert-space classical mechanics (HCM), grounding classicality not in the dynamical limit ($\hbar \to 0$), but in the logical constraint of Booleanity (i.e., the mutual commutativity of preparable states). Within this state-centric framework, applying the Einstein-Podolsky-Rosen (EPR) criterion alongside locality and measurement independence reduces standard quantum mechanics to the HCM model. Thus, the EPR argument reveals not quantum incompleteness, but the implicit classical boundaries of its own premises. To resolve this impasse, we articulate a nuanced quantum ontology grounded in a fundamental structural bipartition between the observational environment and the observed object, which accommodates three categorical distinctions: ontic, processional, and tropos-existential. Building on this, we propose a criterion of objective reality wherein descriptive objectivity is treated as merely a sufficient condition for physical reality. This addresses the historical Bohr-Einstein ambiguity, enabling the quantum formalism to ontologically unify objective measured phenomena and non-objective observed interference within a context-dependent framework.

quant-ph↗

arXiv2026

Duality and measurement: the Copenhagen reconciliation

Duality, not monism, constitutes the hermeneutic lens that characterizes the original Copenhagen interpretation of Quantum Mechanics. Therefore, evoking the principles of correspondence and complementarity, in this work we re-assert a dual-aspect reading of quantum theory, structured through a multi-perspective schema encompassing its ontological, analytical, epistemological, causal, and information dimensions. We then show how this schema dissolves the so-called 'measurement problem', along with the associated 'knowledge-information' and 'macro-micro' dichotomies, issues historically raised within later monistic or universalist philosophical settings that ultimately depart from the traditional Copenhagen spirit.

quant-ph↗

arXiv2007

Selection and identity rules for subductions of type A quantum Iwahori-Hecke algebras

This paper is concerned with the subduction problem of type A quantum Iwahori-Hecke algebras $\mathbb{C} \mathbf{H}(\mathfrak{S}_f,q^2)$ with a real deformation parameter $q$, i.e. the problem of decomposing irreducible representations of such algebras as direct sum of irreducible representations of the subalgebras $\mathbb{C}\mathbf{H}(\mathfrak{S}_{f_1}, q^2) \times \mathbb{C}\mathbf{H}(\mathfrak{S}_{f_2}, q^2)$, with $f_1 + f_2 = f$. After giving a suitable combinatorial description for the subduction issue, we provide a selection rule, based on the Richardson-Littlewood criterion, which allows to determine the vanishing coupling coefficients between standard basis vectors for such representations, and we also present an equivariance condition for the subduction coefficients. Such results extend those ones corresponding to the subduction problem in symmetric group algebras $\mathbb{C}\mathfrak{S}_f \downarrow \mathbb{C}\mathfrak{S}_{f_1} \times \mathbb{C} \mathfrak{S}_{f_2}$ which are obtained by $q$ approaching the value 1.

math-ph↗

arXiv2006

Combinatorics of transformations from standard to non-standard bases in Brauer algebras

Transformation coefficients between standard bases for irreducible representations of the Brauer centralizer algebra $\mathfrak{B}_f(x)$ and split bases adapted to the $\mathfrak{B}_{f_1} (x) \times \mathfrak{B}_{f_2} (x) \subset \mathfrak{B}_f (x)$ subalgebra ($f_1 +f_2 = f$) are considered. After providing the suitable combinatorial background, based on the definition of $i$-coupling relation on nodes of the subduction grid, we introduce a generalized version of the subduction graph which extends the one given in J. Phys. A: Math. Gen. $\mathbf{39}$ 7657-7668 for symmetric groups. Thus, we can describe the structure of the subduction system arising from the linear method and give an outline of the form of the solution space. An ordering relation on the grid is also given and then, as in the case of symmetric groups, the choices of the phases and of the free factors governing the multiplicity separations are discussed.

math-ph↗

arXiv2006

On the linear equation method for the subduction problem in symmetric groups

We focus on the tranformation matrices between the standard Young-Yamanouchi basis of an irreducible representation for the symmetric group S_n and the split basis adapted to the direct product subgroups S_{n_1} \times S_{n-n_1} . We introduce the concept of subduction graph and we show that it conveniently describes the combinatorial structure of the equation system arisen from the linear equation method. Thus we can outline an improved algorithm to solve the subduction problem in symmetric groups by a graph searching process. We conclude observing that the general matrix form for multiplicity separations, resulting from orthonormalization, can be expressed in terms of Sylvester matrices relative to a suitable inner product in the multiplicity space.

math-ph↗

arXiv2006

A reduced subduction graph and higher multiplicity in S_n transformation coefficients

Transformation coefficients between {\it standard} bases for irreducible representations of the symmetric group $S_n$ and {\it split} bases adapted to the $S_{n_1} \times S_{n_2} \subset S_n$ subgroup ($n_1 +n_2 = n$) are considered. We first provide a \emph{selection rule} and an \emph{identity rule} for the subduction coefficients which allow to decrease the number of unknowns and equations arising from the linear method by Pan and Chen. Then, using the {\it reduced subduction graph} approach, we may look at higher multiplicity instances. As a significant example, an orthonormalized solution for the first multiplicity-three case, which occurs in the decomposition of the irreducible representation $[4,3,2,1]$ of $S_{10}$ into $[3,2,1] \otimes [3,1]$ of $S_6 \times S_4$, is presented and discussed.

math-ph↗