Giuseppe Nistico - Academia.edu (original) (raw)
Papers by Giuseppe Nistico
SciPost Physics Proceedings
Current quantum theories of an elementary free particle assume unitary space inversion and anti-u... more Current quantum theories of an elementary free particle assume unitary space inversion and anti-unitary time reversal operators. In so doing robust classes of possible theories are discarded. The present work shows that consistent theories can be derived through a strictly deductive development from the principle of relativistic invariance and position covariance, also with anti-unitary space inversion and unitary time reversal operators. In doing so the class of possible consistent theories is extended for positive but also zero mass particles. In particular, consistent theories for a Klein-Gordon particle are derived and the non-localizability theorem for a non zero helicity massless particle is extended.
Foundations of Physics, 2021
Journal of Physics: Conference Series, 2016
We point out a difficulty that arises in extending the group theoretical approach that deductivel... more We point out a difficulty that arises in extending the group theoretical approach that deductively establishes the quantum theory of a free particle to the case of an interacting particle. Then we develop an approach which overcomes this difficulty. The result is a theory of an interacting particle where the standard theory is characterized by specific covariance properties related to the interaction.
arXiv: Quantum Physics, 2018
The diffculties of relativistic particle theories formulated my means of canonical quantization, ... more The diffculties of relativistic particle theories formulated my means of canonical quantization, such as Klein-Gordon and Dirac theories, ultimately led theoretical physicists to turn on quantum field theory to model elementary particle physics. The aim of the present work is to pursue a method alternative to canonical quantization that avoids these dfficulties. In order to guarantee this result, the present approach is constrained to be developed deductively from physical principles. The physical principles assumed for a free particle consist of the symmetry properties of the particle with respect to the Poincar\'e group and of the transformation properties of the position observable, expressed by means of a suitably conceived notion of quantum transformation. In so doing, the effectiveness of group theoretical methods is exploited. Our work has pointed out the necessity of new classes of irreducible representations of the Poincar\'e group the theory can be based on. For sp...
Foundations of Physics, 2020
The difficulties of relativistic particle theories formulated by means of canonical quantization,... more 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 d...
Particles
Dirac’s theory is not the unique theory consistent with the physical principles specific of a fre... more Dirac’s theory is not the unique theory consistent with the physical principles specific of a free spin-one-half particle. In fact, we derive classes of theories of an elementary free particle from the principle of Poincaré’s invariance and from the principle of the covariance of the position. The theory of Dirac is just one of these theories, characterized by singular predictions, namely, the zitterbewegung. Yet, the class here derived contains families of consistent theories without singular predictions. For the time being, the experimental verifiability of these alternative theories is restricted to the predictions of free-particle theories for ideal experiments.
Journal of Mathematical Physics, 1984
The logic approach to axiomatic quantum mechanics via orthocomplemented partial ordered sets of y... more The logic approach to axiomatic quantum mechanics via orthocomplemented partial ordered sets of yes-no measurements, which constitute the observing part of a concretely realizable experiment on microworld, has been criticized from the empirical point of view by Mielnik, which on the contrary privileges the convex scheme linked to the preparing part. In this work we do assume that a description of quantum phenomenology must take into account both these two parts in which every elementary experiment can be decomposed. According to this predecision, we develop an axiomatic approach based on indistinguishability principles of a quantum information system. The very general concept of yes-no measurement or "question" is accepted, and then the set of all questions is classified according to the behavior with respect to a phenomenological orthogonality relation. In particular, we single out the set F offuzzy events or effects and the set E ~ F of exact events. The Mielnik critique is then refused since it regards the order structure of E using counterexamples which pertain to FIE. The notions of physical property and noperty are then introduced and an axiomatic foundation of quantum mechanics based on a pre-Hilbert space is discussed.
Journal of Mathematical Physics, 2000
An unsharp quantum observable can be considered a realization of a sharp observable if and only i... more An unsharp quantum observable can be considered a realization of a sharp observable if and only if it is commutative. In this paper we describe an explicit procedure for reconstructing such a sharp observable and for establishing the probabilistic correlations between the sharp reconstruction and the given unsharp observable.
Journal of Mathematical Physics, 1994
ABSTRACT
Journal of Mathematical Analysis and Applications, 1987
Baer*-semigroups are regarded as the main abstract structures for an algebraic analysis of comple... more Baer*-semigroups are regarded as the main abstract structures for an algebraic analysis of complex fuzzy events in generalized probability theory. This assumption is verified in the case of classical probability theory in the framework of measure and integration theory. The corresponding fuzzy language is extended to the noncommutative probability theory based on operators in Hilbert space. Starting from a quantum information system a quantum probability space is constructed, which is naturally embedded in a classical information system. In this last both exact than fuzzy quantum events are represented as classical fuzzy events. Lastly, the classical fuzzy events which correspond to exact quantum events are characterized by some minimality properties,
International Journal of Theoretical Physics, 2013
ABSTRACT
International Journal of Theoretical Physics, 1993
We give a model of the basic Jauch-Piron (JP) approach to quantum physics, i.e., of "preparation-... more We give a model of the basic Jauch-Piron (JP) approach to quantum physics, i.e., of "preparation-question structure" (with four basic axioms and without axioms C, P, A), in terms of Ludwig's "selection structure"; in the latter structure the primitive notion of "individual sample" of a physical entity is formally described (without making reference to any probability concept). Once we interpret Piron's concept of "question" in Ludwig's context of a selection structure, we find that there is no difficulty in formalizing notions such as "performable together questions"; moreover, results such as "a-~=a '' or "(aAfl)-= a~VYfl ~'' can be formally proved. We develop the theory along the lines of the JP approach; the set of JP propositions is derived and it turns out to be a complete lattice, as happens in Piron's theory, but with a different physical interpretation of the lattice operations. Finally, we study some connections between the standard Ludwig foundation and our approach.
International Journal of Theoretical Physics, 1992
We give a criterion to compare the physical content of different mathematical structures derived ... more We give a criterion to compare the physical content of different mathematical structures derived from a preparation-question structure. Then this criterion is used in order to compare the physical content of the (Jauch-Piron's) property lattice with the physical content of the poset of testable properties. We prove that for complete preparation-question structures these two structures carry the same physical content; moreover the set of testable properties has the algebraic structure of the Brouwer-Zadeh lattice. For more general preparation-question structures the physical content of the poset of testable property can be larger than that of the property lattice. Physically relevant examples of the possible cases are given.
International Journal of Theoretical Physics, 1991
Some of the most frequent misconceptions about axiomatic quantum physics are discussed with the a... more Some of the most frequent misconceptions about axiomatic quantum physics are discussed with the aim of clarifying their true significance, taking Piron's approach as conceptual framework. In particular, we deal with the following topics: the wrong identification of Piron's questions and Mackey's questions, and some curious alleged empirical consequences; the role of propositions as suitable equivalence classes of questions, their partial order structure, and the paradoxical consequences of the erroneous assignment to questions of some lattice properties involving propositions; the logical and the empirical purport of some "negative" theorems; the standard Hilbert space model of the theory and the consequent "metaphysical disasters" related to some identifications, which are peculiar of this model. A controversy between Foulis-Piron-Randall and Hadjisavvas-Thieffine-Mugur-Sch/ichter is analyzed on the basis of the proposed Hilbert space model (in which Piron's questions are realized by Hilbertian "effects," i.e., linear bounded operators F such that 9 which clarify the different point of views. As an example, we treat the unsharp localization operators in L2(N).
International Journal of Quantum Information, 2012
We design a double-slit experimental set-up, realizable at least in principle, for ascertaining t... more We design a double-slit experimental set-up, realizable at least in principle, for ascertaining three noncommuting quantum observables according to a method alternative to that of the "mean king" problem. Then, we exploit this experimental scheme to identify a physical situation where the known notions of quantum interferometry do not directly apply. A generalization of such notions is proposed that turns out to satisfy the authentic meaning of the interferometric quantum complementarity.
Fuzzy Sets and Systems, 1989
ABSTRACT
Foundations of Physics Letters, 1997
ABSTRACT
Foundations of Physics, 1997
We discuss the problem of how a (commutative) generalized observable in a finitedimensional Hilbe... more We discuss the problem of how a (commutative) generalized observable in a finitedimensional Hilbert space (commutative 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.
Foundations of Physics, 1990
The theoretieaI scheme proposed by Aerts for describing two separated entities as a whole within ... more The theoretieaI 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.
Foundations of Physics, 2011
We single out an alternative, strict interpretation of the Einstein-Podolsky-Rosen criterion of r... more 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.
SciPost Physics Proceedings
Current quantum theories of an elementary free particle assume unitary space inversion and anti-u... more Current quantum theories of an elementary free particle assume unitary space inversion and anti-unitary time reversal operators. In so doing robust classes of possible theories are discarded. The present work shows that consistent theories can be derived through a strictly deductive development from the principle of relativistic invariance and position covariance, also with anti-unitary space inversion and unitary time reversal operators. In doing so the class of possible consistent theories is extended for positive but also zero mass particles. In particular, consistent theories for a Klein-Gordon particle are derived and the non-localizability theorem for a non zero helicity massless particle is extended.
Foundations of Physics, 2021
Journal of Physics: Conference Series, 2016
We point out a difficulty that arises in extending the group theoretical approach that deductivel... more We point out a difficulty that arises in extending the group theoretical approach that deductively establishes the quantum theory of a free particle to the case of an interacting particle. Then we develop an approach which overcomes this difficulty. The result is a theory of an interacting particle where the standard theory is characterized by specific covariance properties related to the interaction.
arXiv: Quantum Physics, 2018
The diffculties of relativistic particle theories formulated my means of canonical quantization, ... more The diffculties of relativistic particle theories formulated my means of canonical quantization, such as Klein-Gordon and Dirac theories, ultimately led theoretical physicists to turn on quantum field theory to model elementary particle physics. The aim of the present work is to pursue a method alternative to canonical quantization that avoids these dfficulties. In order to guarantee this result, the present approach is constrained to be developed deductively from physical principles. The physical principles assumed for a free particle consist of the symmetry properties of the particle with respect to the Poincar\'e group and of the transformation properties of the position observable, expressed by means of a suitably conceived notion of quantum transformation. In so doing, the effectiveness of group theoretical methods is exploited. Our work has pointed out the necessity of new classes of irreducible representations of the Poincar\'e group the theory can be based on. For sp...
Foundations of Physics, 2020
The difficulties of relativistic particle theories formulated by means of canonical quantization,... more 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 d...
Particles
Dirac’s theory is not the unique theory consistent with the physical principles specific of a fre... more Dirac’s theory is not the unique theory consistent with the physical principles specific of a free spin-one-half particle. In fact, we derive classes of theories of an elementary free particle from the principle of Poincaré’s invariance and from the principle of the covariance of the position. The theory of Dirac is just one of these theories, characterized by singular predictions, namely, the zitterbewegung. Yet, the class here derived contains families of consistent theories without singular predictions. For the time being, the experimental verifiability of these alternative theories is restricted to the predictions of free-particle theories for ideal experiments.
Journal of Mathematical Physics, 1984
The logic approach to axiomatic quantum mechanics via orthocomplemented partial ordered sets of y... more The logic approach to axiomatic quantum mechanics via orthocomplemented partial ordered sets of yes-no measurements, which constitute the observing part of a concretely realizable experiment on microworld, has been criticized from the empirical point of view by Mielnik, which on the contrary privileges the convex scheme linked to the preparing part. In this work we do assume that a description of quantum phenomenology must take into account both these two parts in which every elementary experiment can be decomposed. According to this predecision, we develop an axiomatic approach based on indistinguishability principles of a quantum information system. The very general concept of yes-no measurement or "question" is accepted, and then the set of all questions is classified according to the behavior with respect to a phenomenological orthogonality relation. In particular, we single out the set F offuzzy events or effects and the set E ~ F of exact events. The Mielnik critique is then refused since it regards the order structure of E using counterexamples which pertain to FIE. The notions of physical property and noperty are then introduced and an axiomatic foundation of quantum mechanics based on a pre-Hilbert space is discussed.
Journal of Mathematical Physics, 2000
An unsharp quantum observable can be considered a realization of a sharp observable if and only i... more An unsharp quantum observable can be considered a realization of a sharp observable if and only if it is commutative. In this paper we describe an explicit procedure for reconstructing such a sharp observable and for establishing the probabilistic correlations between the sharp reconstruction and the given unsharp observable.
Journal of Mathematical Physics, 1994
ABSTRACT
Journal of Mathematical Analysis and Applications, 1987
Baer*-semigroups are regarded as the main abstract structures for an algebraic analysis of comple... more Baer*-semigroups are regarded as the main abstract structures for an algebraic analysis of complex fuzzy events in generalized probability theory. This assumption is verified in the case of classical probability theory in the framework of measure and integration theory. The corresponding fuzzy language is extended to the noncommutative probability theory based on operators in Hilbert space. Starting from a quantum information system a quantum probability space is constructed, which is naturally embedded in a classical information system. In this last both exact than fuzzy quantum events are represented as classical fuzzy events. Lastly, the classical fuzzy events which correspond to exact quantum events are characterized by some minimality properties,
International Journal of Theoretical Physics, 2013
ABSTRACT
International Journal of Theoretical Physics, 1993
We give a model of the basic Jauch-Piron (JP) approach to quantum physics, i.e., of "preparation-... more We give a model of the basic Jauch-Piron (JP) approach to quantum physics, i.e., of "preparation-question structure" (with four basic axioms and without axioms C, P, A), in terms of Ludwig's "selection structure"; in the latter structure the primitive notion of "individual sample" of a physical entity is formally described (without making reference to any probability concept). Once we interpret Piron's concept of "question" in Ludwig's context of a selection structure, we find that there is no difficulty in formalizing notions such as "performable together questions"; moreover, results such as "a-~=a '' or "(aAfl)-= a~VYfl ~'' can be formally proved. We develop the theory along the lines of the JP approach; the set of JP propositions is derived and it turns out to be a complete lattice, as happens in Piron's theory, but with a different physical interpretation of the lattice operations. Finally, we study some connections between the standard Ludwig foundation and our approach.
International Journal of Theoretical Physics, 1992
We give a criterion to compare the physical content of different mathematical structures derived ... more We give a criterion to compare the physical content of different mathematical structures derived from a preparation-question structure. Then this criterion is used in order to compare the physical content of the (Jauch-Piron's) property lattice with the physical content of the poset of testable properties. We prove that for complete preparation-question structures these two structures carry the same physical content; moreover the set of testable properties has the algebraic structure of the Brouwer-Zadeh lattice. For more general preparation-question structures the physical content of the poset of testable property can be larger than that of the property lattice. Physically relevant examples of the possible cases are given.
International Journal of Theoretical Physics, 1991
Some of the most frequent misconceptions about axiomatic quantum physics are discussed with the a... more Some of the most frequent misconceptions about axiomatic quantum physics are discussed with the aim of clarifying their true significance, taking Piron's approach as conceptual framework. In particular, we deal with the following topics: the wrong identification of Piron's questions and Mackey's questions, and some curious alleged empirical consequences; the role of propositions as suitable equivalence classes of questions, their partial order structure, and the paradoxical consequences of the erroneous assignment to questions of some lattice properties involving propositions; the logical and the empirical purport of some "negative" theorems; the standard Hilbert space model of the theory and the consequent "metaphysical disasters" related to some identifications, which are peculiar of this model. A controversy between Foulis-Piron-Randall and Hadjisavvas-Thieffine-Mugur-Sch/ichter is analyzed on the basis of the proposed Hilbert space model (in which Piron's questions are realized by Hilbertian "effects," i.e., linear bounded operators F such that 9 which clarify the different point of views. As an example, we treat the unsharp localization operators in L2(N).
International Journal of Quantum Information, 2012
We design a double-slit experimental set-up, realizable at least in principle, for ascertaining t... more We design a double-slit experimental set-up, realizable at least in principle, for ascertaining three noncommuting quantum observables according to a method alternative to that of the "mean king" problem. Then, we exploit this experimental scheme to identify a physical situation where the known notions of quantum interferometry do not directly apply. A generalization of such notions is proposed that turns out to satisfy the authentic meaning of the interferometric quantum complementarity.
Fuzzy Sets and Systems, 1989
ABSTRACT
Foundations of Physics Letters, 1997
ABSTRACT
Foundations of Physics, 1997
We discuss the problem of how a (commutative) generalized observable in a finitedimensional Hilbe... more We discuss the problem of how a (commutative) generalized observable in a finitedimensional Hilbert space (commutative 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.
Foundations of Physics, 1990
The theoretieaI scheme proposed by Aerts for describing two separated entities as a whole within ... more The theoretieaI 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.
Foundations of Physics, 2011
We single out an alternative, strict interpretation of the Einstein-Podolsky-Rosen criterion of r... more 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.