scholarly journals A quantum route to the classical Lagrangian formalism

2021 ◽  
pp. 2150091
Author(s):  
F. M. Ciaglia ◽  
F. Di Cosmo ◽  
A. Ibort ◽  
G. Marmo ◽  
L. Schiavone ◽  
...  
Keyword(s):  
Quantum Mechanics ◽  
Smooth Manifold ◽  
Von Neumann Algebra ◽  
Fundamental Question ◽  
Lagrangian Formalism ◽  
Classical Dynamics ◽  
New Approach ◽  
Von Neumann ◽  
Dynamics Of Particles

Using the recently developed groupoidal description of Schwinger’s picture of Quantum Mechanics, a new approach to Dirac’s fundamental question on the role of the Lagrangian in Quantum Mechanics is provided. It is shown that a function [Formula: see text] on the groupoid of configurations (or kinematical groupoid) of a quantum system determines a state on the von Neumann algebra of the histories of the system. This function, which we call q-Lagrangian, can be described in terms of a new function [Formula: see text] on the Lie algebroid of the theory. When the kinematical groupoid is the pair groupoid of a smooth manifold M, the quadratic expansion of [Formula: see text] will reproduce the standard Lagrangians on TM used to describe the classical dynamics of particles.

scholarly journals Transfer principle in quantum set theory

2007 ◽  
Vol 72 (2) ◽  
pp. 625-648 ◽  
Author(s):  
Masanao Ozawa
Keyword(s):  
Quantum Mechanics ◽  
Quantum Logic ◽  
Set Theory ◽  
Von Neumann Algebra ◽  
Transfer Principle ◽  
Real Numbers ◽  
Von Neumann ◽  
Equality Relation ◽  
Adjoint Operators ◽  
Transfer Theorems

AbstractIn 1981, Takeuti introduced quantum set theory as the quantum counterpart of Boolean valued models of set theory by constructing a model of set theory based on quantum logic represented by the lattice of closed subspaces in a Hilbert space and showed that appropriate quantum counterparts of ZFC axioms hold in the model. Here, Takeuti's formulation is extended to construct a model of set theory based on the logic represented by the lattice of projections in an arbitrary von Neumann algebra. A transfer principle is established that enables us to transfer theorems of ZFC to their quantum counterparts holding in the model. The set of real numbers in the model is shown to be in one-to-one correspondence with the set of self-adjoint operators affiliated with the von Neumann algebra generated by the logic. Despite the difficulty pointed out by Takeuti that equality axioms do not generally hold in quantum set theory, it is shown that equality axioms hold for any real numbers in the model. It is also shown that any observational proposition in quantum mechanics can be represented by a corresponding statement for real numbers in the model with the truth value consistent with the standard formulation of quantum mechanics, and that the equality relation between two real numbers in the model is equivalent with the notion of perfect correlation between corresponding observables (self-adjoint operators) in quantum mechanics. The paper is concluded with some remarks on the relevance to quantum set theory of the choice of the implication connective in quantum logic.

Popper and the Quantum Theory

1995 ◽  
Vol 39 ◽  
pp. 163-176
Author(s):  
Michael Redhead
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Quantum Logic ◽  
Scientific Discovery ◽  
Von Neumann ◽  
Interpretation Of Probability ◽  
Propensity Interpretation

Popper wrote extensively on the quantum theory. In Logic der Forschung (LSD) he devoted a whole chapter to the topic, while the whole of Volume 3 of the Postscript to the Logic of Scientific Discovery is devoted to the quantum theory. This volume entitled Quantum Theory and the Schism in Physics (QTSP) incorporated a famous earlier essay, ‘Quantum Mechanics without “the Observer”’ (QM). In addition Popper's development of the propensity interpretation of probability was much influenced by his views on the role of probability in quantum theory, and he also wrote an insightful critique of the 1936 paper of Birkhoff and von Neumann on nondistributive quantum logic (BNIQM).

scholarly journals ON KOOPMAN–VON NEUMANN WAVES

2002 ◽  
Vol 17 (09) ◽  
pp. 1301-1325 ◽  
Author(s):  
D. MAURO
Keyword(s):  
Hilbert Space ◽  
Quantum Mechanics ◽  
Classical Mechanics ◽  
Wave Functions ◽  
Quantum Case ◽  
Von Neumann ◽  
Interference Experiment ◽  
Classical Wave

In this paper we study the classical Hilbert space introduced by Koopman and von Neumann in their operatorial formulation of classical mechanics. In particular we show that the states of this Hilbert space do not spread, differently from what happens in quantum mechanics. The role of the phases associated to these classical "wave functions" is analyzed in detail. In this framework we also perform the analog of the two-slit interference experiment and compare it with the quantum case.

scholarly journals Causality in Schwinger’s Picture of Quantum Mechanics

Entropy ◽  
2022 ◽  
Vol 24 (1) ◽  
pp. 75
Author(s):  
Florio M. Ciaglia ◽  
Fabio Di Di Cosmo ◽  
Alberto Ibort ◽  
Giuseppe Marmo ◽  
Luca Schiavone ◽  
...  
Keyword(s):  
Quantum Mechanics ◽  
Quantum System ◽  
Von Neumann Algebra ◽  
Operator Algebras ◽  
Quantum Mechanical ◽  
Von Neumann ◽  
Triangular Operator ◽  
Quantum Mechanical Systems ◽  
Causal Structures ◽  
Incidence Theorem

This paper begins the study of the relation between causality and quantum mechanics, taking advantage of the groupoidal description of quantum mechanical systems inspired by Schwinger’s picture of quantum mechanics. After identifying causal structures on groupoids with a particular class of subcategories, called causal categories accordingly, it will be shown that causal structures can be recovered from a particular class of non-selfadjoint class of algebras, known as triangular operator algebras, contained in the von Neumann algebra of the groupoid of the quantum system. As a consequence of this, Sorkin’s incidence theorem will be proved and some illustrative examples will be discussed.

Prologue: “The Most Primitive Question”

System ◽  
2016 ◽  
Author(s):  
Clifford Siskin
Keyword(s):  
Social Sciences ◽  
Quantum Mechanics ◽  
Fundamental Question ◽  
Social Sciences And Humanities ◽  
The Social ◽  
The World

The Prologues argues that the question “What is a system?” is a fundamental question across the disciplines, from quantum mechanics to the social sciences and humanities. To answer the question we need to see system not as an “idea” needing a definition but as a genre—a form that works physically in the world to mediate our efforts to know it. We can then identify features of that genre, such as scalability, that explain why system came to play such a central role in efforts to know the world for so long. We can also count systems and account for their becoming something to blame, as in “blaming the system,” and for the role they play in constituting infrastructure. The Prologue then begins this tale of how system has mediated knowledge by turning back to Galileo’s discovery of Jupiter’s lunar system, the entry of “system” into English, and a discussion of the role of The Re:Enlightenment Project’s touchstones—past and present, mediating technologies, connectivities—in shaping this book.

METAMORPHOSES OF THE POSTMODERN DISCOURSEAND CURRENT CHALLENGES NEOMODERNISM

2019 ◽  
Author(s):  
Yu.V. IRKHIN
Keyword(s):  
World Politics ◽  
New Approach ◽  
Postmodern Theory ◽  
The World ◽  
Conservative Values

The article analyzes the problems, achievements and contradictions in the genesis of the contemporary postmodern discourse. The author has carried out complex research, systematized and showed the main features and differences of postmodernism and metamodernism, as well as the role of neoliberal values in their development. The author has considered a new approach to the study of society and politics: neomodernist discourse with the dominant conservative values, opposing postmodern theory, methodology and practice he has identified the features of neomodernism: historicism, patriotism and healthy nationalism, populism, transactionalismn and realism in the world politics.

Monitoring the marine environment for small round structured viruses (SRSVS): a new approach to combating the transmission of these viruses by molluscan shellfish

1998 ◽  
Vol 38 (12) ◽  
pp. 51-56 ◽  
Author(s):  
K. Henshilwood ◽  
J. Green ◽  
D. N. Lees
Keyword(s):  
Enteric Virus ◽  
Winter Period ◽  
Rt Pcr ◽  
Cloning And Sequencing ◽  
New Approach ◽  
Human Enteric Virus ◽  
Different Strains ◽  
The Uk ◽  
Public Health Protection

This study investigates human enteric virus contamination of a shellfish harvesting area. Samples were analysed over a 14-month period for Small Round Structured Viruses (SRSVs) using a previously developed nested RT-PCR. A clear seasonal difference was observed with the largest numbers of positive samples obtained during the winter period (October to March). This data concurs with the known winter association of gastroenteric illness due to oyster consumption in the UK and also with the majority of the outbreaks associated with shellfish harvested from this area during the study period. RT-PCR positive amplicons were further characterised by cloning and sequencing. Sequence analysis of the positive samples identified eleven SRSV strains, of both Genogroup I and Genogroup II, occurring throughout the study period. Many shellfish samples contained a mixture of strains with a few samples containing up to three different strains with both Genogroups represented. The observed common occurrence of strain mixtures may have implications for the role of shellfish as a vector for dissemination of SRSV strains. These results show that nested RT-PCR can identify SRSV contamination in shellfish harvesting areas. Virus monitoring of shellfish harvesting areas by specialist laboratories using RT-PCR is a possible approach to combating the transmission of SRSVs by molluscan shellfish and could potentially offer significantly enhanced levels of public health protection.

Lattice Thermal Conductivity Modelling of a Diatomic Nanoscale Material

2020 ◽  
Vol 10 (5) ◽  
pp. 602-609
Author(s):  
Adil H. Awad
Keyword(s):  
Thermal Conductivity ◽  
Lattice Thermal Conductivity ◽  
Phonon Scattering ◽  
Correction Term ◽  
Nanoscale Material ◽  
New Approach ◽  
Two Samples ◽  
Conductivity Modelling ◽  
Callaway Model

Introduction: A new approach for expressing the lattice thermal conductivity of diatomic nanoscale materials is developed. Methods: The lattice thermal conductivity of two samples of GaAs nanobeam at 4-100K is calculated on the basis of monatomic dispersion relation. Phonons are scattered by nanobeam boundaries, point defects and other phonons via normal and Umklapp processes. Methods: A comparative study of the results of the present analysis and those obtained using Callaway formula is performed. We clearly demonstrate the importance of the utilised scattering mechanisms in lattice thermal conductivity by addressing the separate role of the phonon scattering relaxation rate. The formulas derived from the correction term are also presented, and their difference from Callaway model is evident. Furthermore their percentage contribution is sufficiently small to be neglected in calculating lattice thermal conductivity. Conclusion: Our model is successfully used to correlate the predicted lattice thermal conductivity with that of the experimental observation.

Randomness and Complexity

2018 ◽  
Author(s):  
Steven E. Vigdor
Keyword(s):  
Quantum Mechanics ◽  
Natural Selection ◽  
Rna World ◽  
Biological Evolution ◽  
Variable Theory ◽  
Cosmological Natural Selection ◽  
Einstein Podolsky Rosen ◽  
World Hypothesis ◽  
Rna World Hypothesis

Chapter 7 describes the fundamental role of randomness in quantum mechanics, in generating the first biomolecules, and in biological evolution. Experiments testing the Einstein–Podolsky–Rosen paradox have demonstrated, via Bell’s inequalities, that no local hidden variable theory can provide a viable alternative to quantum mechanics, with its fundamental randomness built in. Randomness presumably plays an equally important role in the chemical assembly of a wide array of polymer molecules to be sampled for their ability to store genetic information and self-replicate, fueling the sort of abiogenesis assumed in the RNA world hypothesis of life’s beginnings. Evidence for random mutations in biological evolution, microevolution of both bacteria and antibodies and macroevolution of the species, is briefly reviewed. The importance of natural selection in guiding the adaptation of species to changing environments is emphasized. A speculative role of cosmological natural selection for black-hole fecundity in the evolution of universes is discussed.

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