The difficulties of relativistic particle theories formulated by means of canonical quantization, such as those of Klein–Gordon and Dirac, ultimately led theoretical physicists to turn to quantum field theory to model elementary particle physics. In order to overcome these difficulties, the theories of the present approach are developed deductively from the physical principles that specify the system, without making use of canonical quantization. For a free particle these starting assumptions are invariance of the theory and covariance of position with respect (...) to Poincaré transformations. In pursuing the approach, the effectiveness of group theoretical methods is exploited. The coherent development of our program has shown that robust classes of representations of the Poincaré group, discarded by the known particle theories, can in fact be taken as bases for perfectly consistent theories. For massive spin zero particles, six inequivalent theories have been determined, two of which do not correspond to any of the current ones; all of these theories overcome the difficulties of Klein–Gordon one. The present lack of the explicit transformation properties of position with respect to boosts prevents the complete determination of non zero spin particle theories. In the past a particular form of these transformation properties was adopted by Jordan and Mukunda. We check its consistency within the present approach and find that for spin \ particles there is only one consistent theory, which is unitarily related to Dirac’s; yet, once again, it requires classes of irreducible representations previously discarded. (shrink)

We single out an alternative, strict interpretation of the Einstein-Podolsky-Rosen criterion of reality, and identify the implied extensions of quantum correlations. Then we prove that the theorem of Bell, and the non-locality theorems without inequalities, fail if the new extensions are adopted. Therefore, these theorems can be interpreted as arguments against the wide interpretation of the criterion of reality rather than as a violation of locality.

We discuss the problem of how a (commutative) generalized observable in a finite-dimensional Hilbert space (communtative effect-valued resolution of the identity) can be considered as an unsharp realization of some standard observable (projection-valued resolution of the identity). In particular, we give a concrete procedure for constructing such a standard observable. Some results about the “uniqueness” of the resulting observable are also examined.

The theoretical scheme proposed by Aerts for describing two separated entities as a whole within a question-state structure is considered. The quoted author claims that two relevant axioms characterizing quantum physics cannot hold for a quantum, nonclassical entity consisting of two quantum separate entities. We suggest that Aerts' theory is not adequate, from the empirical point of view, to describe this situation.

The notion of coexistence between questions is introduced in the framework of Piron's approach to quantum physics, using Aerts' notion of performable-together questions. Relationships between coexistence of questions and Piron's compatibility of propositions are investigated. In particular, properties generated by coexistent and primitive questions are compatible.

The mathematical description of the three distinct fundamental notions of “individual sample” of “preparing procedure,” and of “Piron's state” of a physical entity are precisely introduced in the framework of the Piron's “preparation-question structure” (without specific axioms C, P, A) based on Ludwig's “selection structure.” We compare our realization of the above notions with a similar use of the standard terminology of the “Geneva School” adopted by Pykacz and Santos in a recent paper.

In the framework of the histories approach to quantum mechanics developed by Griffiths and Omnès, we consider the question of the uniqueness of the probability assigned to the histories; the question was solved by Omnès only in special cases. We find conditions which ensure uniqueness of such probability in the general case.

A relation ≺ϕ between noncommuting 1-0 quantum observables (i.e., projections) is introduced, ϕ being the state vector of the system. This relation extends the empirical implication between commuting projections. An operational interpretation of the new relation is given, which can be expressed also in counterfactual terms. It is shown that a relation proposed some years ago by Hardegree, namely the Sasaki arrow ↪ϕ, can be interpreted in terms of the relation ≺ϕ; furthermore, this new relation turns out to be successful (...) also in cases in which the Sasaki arrow fails. (shrink)

Current theories of massless free particle assume unitary space inversion and anti-unitary time reversal operators. In so doing robust classes of possible theories are discarded. In the present work theories of massless systems are derived through a strictly deductive development from the principle of relativistic invariance, so that a kind of space inversion or time reversal operator is ruled out only if it causes inconsistencies. As results, new classes of consistent theories for massless isolated systems are explicitly determined. On the (...) other hand, the approach determines definite constraints implied by the invariance principle; they were ignored by some past investigations that, as a consequence, turn out to be not consistent with the invariance principle. Also the problem of the localizability for massless systems is reconsidered within the new theoretical framework, obtaining a generalization and a deeper detailing of previous results. (shrink)