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  1. Big Toy Models: Representing Physical Systems as Chu Spaces.Samson Abramsky - 2012 - Synthese 186 (3):697 - 718.
    We pursue a model-oriented rather than axiomatic approach to the foundations of Quantum Mechanics, with the idea that new models can often suggest new axioms. This approach has often been fruitful in Logic and Theoretical Computer Science. Rather than seeking to construct a simplified toy model, we aim for a 'big toy model', in which both quantum and classical systems can be faithfully represented—as well as, possibly, more exotic kinds of systems. To this end, we show how Chu spaces can (...)
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  2. The Quantum Probabilistic Approach to the Foundations of Quantum Theory: Urns and Chameleons.Luigi Accardi - 1999 - In Roberto Giuntini, Maria Luisa Dalla Chiara & Federico Laudisa (eds.), Language, Quantum, Music. pp. 95.
  3. Quantum Theory: Reconsideration of Foundations-3: Växjö, Sweden, 6-11 June 2005.Guillaume Adenier, A. I͡U Khrennikov & Theo M. Nieuwenhuizen (eds.) - 2006 - American Institute of Physics.
    This Växjö conference was devoted to the reconsideration of quantum foundations. Due to increasing research in quantum information theory, especially on quantum computing and cryptography, many questions regarding the foundations of quantum mechanics, which have long been considered to be exclusively of philosophical interest, nowadays play an important role in theoretical and experimental quantum physics.
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  4. A Theory of Concepts and Their Combinations II: A Hilbert Space Representation.Diederik Aerts & Liane Gabora - 2005 - Philosophical Explorations.
    The sets of contexts and properties of a concept are embedded in the complex Hilbert space of quantum mechanics. States are unit vectors or density operators, and contexts and properties are orthogonal projections. The way calculations are done in Hilbert space makes it possible to model how context influences the state of a concept. Moreover, a solution to the combination of concepts is proposed. Using the tensor product, a procedure for describing combined concepts is elaborated, providing a natural solution to (...)
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  5. Quantum Topo-Dynamics in Higher Dimensions.Y. Aharonov & M. Schwartz - 1986 - In Roger Penrose & C. J. Isham (eds.), Quantum Concepts in Space and Time. New York ;Oxford University Press. pp. 255.
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  6. Quantum Mechanics and Paradigm Shifts.Valia Allori - 2015 - Topoi 2015 (2):313-323.
    It has been argued that the transition from classical to quantum mechanics is an example of a Kuhnian scientific revolution, in which there is a shift from the simple, intuitive, straightforward classical paradigm, to the quantum, convoluted, counterintuitive, amazing new quantum paradigm. In this paper, after having clarified what these quantum paradigms are supposed to be, I analyze whether they constitute a radical departure from the classical paradigm. Contrary to what is commonly maintained, I argue that, in addition to radical (...)
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  7. Coordinate Transformations and the Theory of Measurement.Martin S. Altschul - 1978 - Foundations of Physics 8 (1-2):69-92.
    We discuss the criteria for deriving new information from coordinate transformations, focusing on the property of implementability, or measurability in practice. We contrast the role of coordinate transformations in classical and quantum physics, and demonstrate that many well-known applications fail to meet the criteria for new information. Finally, we discuss some mathematical properties of the coordinate transformations, and then relate these properties to a practical measurement scheme.
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  8. A Geometric Approach to Quantum Mechanics.J. Anandan - 1991 - Foundations of Physics 21 (11):1265-1284.
    It is argued that quantum mechanics is fundamentally a geometric theory. This is illustrated by means of the connection and symplectic structures associated with the projective Hilbert space, using which the geometric phase can be understood. A prescription is given for obtaining the geometric phase from the motion of a time dependent invariant along a closed curve in a parameter space, which may be finite dimensional even for nonadiabatic cyclic evolutions in an infinite dimensional Hilbert space. Using the natural metric (...)
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  9. On the Hypotheses Underlying Physical Geometry.J. Anandan - 1980 - Foundations of Physics 10 (7-8):601-629.
    The relationship between physics and geometry is examined in classical and quantum physics based on the view that the symmetry group of physics and the automorphism group of the geometry are the same. Examination of quantum phenomena reveals that the space-time manifold is not appropriate for quantum theory. A different conception of geometry for quantum theory on the group manifold, which may be an arbitrary Lie group, is proposed. This provides a unified description of gravity and gauge fields as well (...)
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  10. Beyond and Behind Hilbert Spaces: Interpreting Quantum Theories Via Mathematical Advances. [REVIEW]Aristidis Arageorgis - 2014 - Metascience 23 (1):71-77.
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  11. A Model for the Schrödinger Zitterbewegung and the Plane Monochromatic Wave.J. C. Aron - 1981 - Foundations of Physics 11 (11-12):863-872.
    The stochastic approach worked out in earlier papers is applied to the Dirac fluid. It gives a model of the Schrödinger zitterbewegung, from which, by the spinor-vector correspondence, a model of the plane monochromatic wave in the rest frame is derived. The relation of the scheme with quantization is found to have the same character as in the previous papers. The link of spin with relativity is explained.
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  12. Brussels-Austin Nonequilibrium Statistical Mechanics: Large Poincar´E Systems and Rigged Hilbert Space.Harald Atmanspacher - manuscript
    The fundamental problem on which Ilya Prigogine and the Brussels- Austin Group have focused can be stated briefly as follows. Our observations indicate that there is an arrow of time in our experience of the world (e.g., decay of unstable radioactive atoms like Uranium, or the mixing of cream in coffee). Most of the fundamental equations of physics are time reversible, however, presenting an apparent conflict between our theoretical descriptions and experimental observations. Many have thought that the observed arrow of (...)
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  13. Book Review:Perspectives in Quantum Theory: Essays in Honor of Alfred Lande Wolfgang Yourgrau, Alwyn Van Der Merwe. [REVIEW]Michael N. Audi - 1973 - Philosophy of Science 40 (2):323-.
  14. Group-Theoretic Treatment of the Axioms of Quantum Mechanics.James Ax - 1976 - Foundations of Physics 6 (4):371-399.
    This axiomatization is based on the observation that ifG is the group of automorphisms of the states (induced, e.g., by suitable evolutions), then we can define a spherical function by mapping each element ofG to the matrix of its transition probabilities. Starting from five physically conservative axioms, we utilize the correspondence between spherical functions and representations to apply the structure theory for compact Lie groups and their orbits in representation spaces to arrive at the standard complex Hilbert space structure of (...)
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  15. Gauge- and Galilei-Invariant Geometric Phases.Guido Bacciagaluppi - unknown
    Neither geometric phases nor differences in geometric phases are generally invariant under time-dependent unitary transformations (unlike differences in total phases), in particular under local gauge transformations and Galilei transformations. (This was pointed out originally by Aharonov and Anandan, and in the case of Galilei transformations has recently been shown explicitly by Sjoeqvist, Brown and Carlsen.) In this paper, I introduce a phase, related to the standard geometric phase, for which phase differences are both gauge- and Galilei-invariant, and, indeed, invariant under (...)
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  16. Pentagrams and Paradoxes.Piotr Badzia̧g, Ingemar Bengtsson, Adán Cabello, Helena Granström & Jan-Åke Larsson - 2011 - Foundations of Physics 41 (3):414-423.
    Klyachko and coworkers consider an orthogonality graph in the form of a pentagram, and in this way derive a Kochen-Specker inequality for spin 1 systems. In some low-dimensional situations Hilbert spaces are naturally organised, by a magical choice of basis, into SO(N) orbits. Combining these ideas some very elegant results emerge. We give a careful discussion of the pentagram operator, and then show how the pentagram underlies a number of other quantum “paradoxes”, such as that of Hardy.
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  17. Division Algebras and Quantum Theory.John C. Baez - 2012 - Foundations of Physics 42 (7):819-855.
    Quantum theory may be formulated using Hilbert spaces over any of the three associative normed division algebras: the real numbers, the complex numbers and the quaternions. Indeed, these three choices appear naturally in a number of axiomatic approaches. However, there are internal problems with real or quaternionic quantum theory. Here we argue that these problems can be resolved if we treat real, complex and quaternionic quantum theory as part of a unified structure. Dyson called this structure the ‘three-fold way’. It (...)
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  18. Beyond Measure: Modern Physics, Philosophy, and the Meaning of Quantum Theory.J. E. Baggott - 2003 - Oxford University Press.
    Quantum theory is one the most important and successful theories of modern physical science. It has been estimated that its principles form the basis for about 30 per cent of the world's manufacturing economy. This is all the more remarkable because quantum theory is a theory that nobody understands. The meaning of Quantum Theory introduces science students to the theory's fundamental conceptual and philosophical problems, and the basis of its non-understandability. It does this with the barest minimum of jargon and (...)
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  19. Can One Detect the State of an Individual System?L. E. Ballentine - 1992 - Foundations of Physics 22 (3):333-342.
    Some interpretations of quantum mechanics regard a mixed quantum state as a ensemble, each individual member of which has a definite but unknown state vector. Other interpretations ascribe a state vector only to anensemble of similarly prepared systems, but not to anindividual. Previous attempts to detect the hypothetical individual state vectors have failed, essentially because the state operator enters the relevant equations linearly. An example from nonlinear dynamics, in which a density matrix enters nonlinearly, is examined because it might appear (...)
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  20. The Feynman Path Integrals and Everett's Universal Wave Function.D. Bar - 1998 - Foundations of Physics 28 (8):1383-1391.
    We study here the properties of some quantum mechanical wave functions, which, in contrast to the regular quantum mechanical wave functions, can be predetermined with certainty (probability 1) by performing dense measurements (or continuous observations). These specific “certain” states are the junction points through which pass all the diverse paths that can proceed between each two such neighboring “sure” points. When we compare the properties of these points to the properties of the well-known universal wave functions of Everett we find (...)
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  21. Local Tomography and the Jordan Structure of Quantum Theory.Howard Barnum & Alexander Wilce - 2014 - Foundations of Physics 44 (2):192-212.
    Using a result of H. Hanche-Olsen, we show that (subject to fairly natural constraints on what constitutes a system, and on what constitutes a composite system), orthodox finite-dimensional complex quantum mechanics with superselection rules is the only non-signaling probabilistic theory in which (i) individual systems are Jordan algebras (equivalently, their cones of unnormalized states are homogeneous and self-dual), (ii) composites are locally tomographic (meaning that states are determined by the joint probabilities they assign to measurement outcomes on the component systems) (...)
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  22. The Strange World of Quantum Mechanics Daniel F. Styer. [REVIEW]Jeffrey A. Barrett - 2001 - British Journal for the Philosophy of Science 52 (2):393-396.
  23. The VIP Experimental Limit on the Pauli Exclusion Principle Violation by Electrons.S. Bartalucci, S. Bertolucci, M. Bragadireanu, M. Cargnelli, C. Curceanu, S. Di Matteo, J.-P. Egger, C. Guaraldo, M. Iliescu, T. Ishiwatari, M. Laubenstein, J. Marton, E. Milotti, D. Pietreanu, T. Ponta, A. Romero Vidal, D. L. Sirghi, F. Sirghi, L. Sperandio, O. Vazquez Doce, E. Widmann & J. Zmeskal - 2010 - Foundations of Physics 40 (7):765-775.
    In this paper we describe an experimental test of the validity of the Pauli Exclusion Principle (for electrons) which is based on a straightforward idea put forward a few years ago by Ramberg and Snow (Phys. Lett. B 238:438, 1990). We perform a very accurate search of X-rays from the Pauli-forbidden atomic transitions of electrons in the already filled 1S shells of copper atoms. Although the experiment has a very simple structure, it poses deep conceptual and interpretational problems. Here we (...)
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  24. On the Gyromagnetic Ratio in the Kaluza-Klein Theories and the Schuster-Blackett Law.A. O. Barut & Thomas Gornitz - 1985 - Foundations of Physics 15 (4):433-437.
    Pauli's five-dimensional Dirac equation in projective space, which results in an anomalous magnetic moment term in four dimensions, is related to the Schuster-Blackett law of the magnetic field of rotating bodies and to the recent results on the gyromagnetic ratio in Kaluza-Klein theories.
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  25. Classical Interpretation of a Deformed Quantum Oscillator.J. Batouli & M. El Baz - 2014 - Foundations of Physics 44 (2):105-113.
    Following the same procedure that allowed Shcrödinger to construct the (canonical) coherent states in the first place, we investigate on a possible classical interpretation of the deformed harmonic oscillator. We find that, these oscillator, also called q-oscillators, can be interpreted as quantum versions of classical forced oscillators with a modified q-dependant frequency.
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  26. Postulates for Time Evolution in Quantum Mechanics.B. Baumgartner - 1994 - Foundations of Physics 24 (6):855-872.
    A detailed list of postulates is formulated in an algebraic setting. These postulates are sufficient to entail the standard time evolution governed by the Schrödinger or Dirac equation. They are also necessary in a strong sense: Dropping any one of the postulates allows for other types of time evolution, as is demonstrated with examples. Some philosophical remarks hint on possible further investigations.
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  27. Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy.J. S. Bell - 2004 - Cambridge University Press.
    This book comprises all of John Bell's published and unpublished papers in the field of quantum mechanics, including two papers that appeared after the first edition was published. It also contains a preface written for the first edition, and an introduction by Alain Aspect that puts into context Bell's great contribution to the quantum philosophy debate. One of the leading expositors and interpreters of modern quantum theory, John Bell played a major role in the development of our current understanding of (...)
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  28. Quantum Mechanics Andp-Adic Numbers.E. G. Beltrametti & G. Cassinelli - 1972 - Foundations of Physics 2 (1):1-7.
    We study the possibility of representing the proposition lattice associated with a quantum system by a linear vector space with coefficients from ap-adic field. We find inconsistencies if the lattice is assumed, as usual, to be irreducible, complete, orthocomplemented, atomic, and weakly modular.
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  29. Empirical State Determination of Entangled Two-Level Systems and Its Relation to Information Theory.Y. Ben-Aryeh, A. Mann & B. C. Sanders - 1999 - Foundations of Physics 29 (12):1963-1975.
    Theoretical methods for empirical state determination of entangled two-level systems are analyzed in relation to information theory. We show that hidden variable theories would lead to a Shannon index of correlation between the entangled subsystems which is larger than that predicted by quantum mechanics. Canonical representations which have maximal correlations are treated by the use of Schmidt and Hilbert-Schmidt decomposition of the entangled states, including especially the Bohm singlet state and the GHZ entangled states. We show that quantum mechanics does (...)
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  30. Quantum Phenomena in a Classical Model.Vieri Benci - 1999 - Foundations of Physics 29 (1):1-28.
    This work is part of a program which has the aim to investigate which phenomena can be explained by nonlinear effects in classical mechanics and which ones require the new axioms of quantum mechanics. In this paper, we construct a nonlinear field equation which admits soliton solutions. These solitons exibit a dynamics which is similar to that of quantum particles.
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  31. Constructibility in Quantum Mechanics.David BenDaniel - unknown
    CONSTRUCTIBILITY IN QUANTUM MECHANICS D.J. BENDANIEL Cornell University Ithaca NY, 14853, USA We pursue an approach in which space-time proves to be relational and its differential properties fulfill the strict requirements of Einstein-Weyl causality. Space-time emerges here from a set theoretical foundation for a constructible mathematics. In this theory the Schrödinger equation can be obtained by adjoining a physical postulate of action symmetry in generalized wave phenomena. This result now allows quantum mechanics to be considered conceptually cumulative with prior physics. (...)
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  32. Spin-Statistics Connection for Relativistic Quantum Mechanics.A. F. Bennett - 2015 - Foundations of Physics 45 (4):370-381.
    The spin-statistics connection has been proved for nonrelativistic quantum mechanics . The proof is extended here to the relativistic regime using the parametrized Dirac equation. A causality condition is not required.
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  33. Superposition in Quantum and Classical Mechanics.M. K. Bennett & D. J. Foulis - 1990 - Foundations of Physics 20 (6):733-744.
    Using the mathematical notion of an entity to represent states in quantum and classical mechanics, we show that, in a strict sense, proper superpositions are possible in classical mechanics.
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  34. A Quantum Mechanical Version of the Paper by E. Schrödinger “Über Die Umkehrung der Naturgesetze”.Otto Bergmann - 1988 - Foundations of Physics 18 (3):373-378.
    The principal results of Schrödinger's paper are reviewed and a possible extension of his formalism for diffusion processes to general quantum mechanical processes is given. The formalism is not in accord with the general theory of transformation of quantum mechanics and violates the basic assumption of the unpredictable change of a system due to a measurement. Nevertheless, the formalism leads to a density operator which is constructed according to accepted quantum mechanical rules.
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  35. A Constructive Formulation of Gleason's Theorem.Helen Billinge - 1997 - Journal of Philosophical Logic 26 (6):661-670.
    In this paper I wish to show that we can give a statement of a restricted form of Gleason's Theorem that is classically equivalent to the standard formulation, but that avoids the counterexample that Hellman gives in "Gleason's Theorem is not Constructively Provable".
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  36. Clifford Algebras in Symplectic Geometry and Quantum Mechanics.Ernst Binz, Maurice A. De Gosson & Basil J. Hiley - 2013 - Foundations of Physics 43 (4):424-439.
    The necessary appearance of Clifford algebras in the quantum description of fermions has prompted us to re-examine the fundamental role played by the quaternion Clifford algebra, C 0,2 . This algebra is essentially the geometric algebra describing the rotational properties of space. Hidden within this algebra are symplectic structures with Heisenberg algebras at their core. This algebra also enables us to define a Poisson algebra of all homogeneous quadratic polynomials on a two-dimensional sub-space, $\mathbb{F}^{a}$ of the Euclidean three-space. This enables (...)
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  37. Brussels-Austin Nonequilibrium Statistical Mechanics in the Later Years: Large Poincaré Systems and Rigged Hilbert Space.Robert Bishop - manuscript
    This second part of a two-part essay discusses recent developments in the Brussels-Austin Group after the mid 1980s. The fundamental concerns are the same as in their similarity transformation approach (see Part I), but the contemporary approach utilizes rigged Hilbert space (whereas the older approach used Hilbert space). While the emphasis on nonequilibrium statistical mechanics remains the same, the use of similarity transformations shifts to the background. In its place arose an interest in the physical features of large Poincaré systems, (...)
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  38. Quantum Time Arrows, Semigroups and Time-Reversal in Scattering.Robert C. Bishop - 2005 - International Journal of Theoretical Physics:723-733.
    Two approaches toward the arrow of time for scattering processes have been proposed in rigged Hilbert space quantum mechanics. One, due to Arno Bohm, involves preparations and registrations in laboratory operations and results in two semigroups oriented in the forward direction of time. The other, employed by the Brussels-Austin group, is more general, involving excitations and de-excitations of systems, and apparently results in two semigroups oriented in opposite directions of time. It turns out that these two time arrows can be (...)
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  39. Arrow of Time in Rigged Hilbert Space Quantum Mechanics.Robert C. Bishop - 2004 - International Journal of Theoretical Physics 43 (7):1675–1687.
    Arno Bohm and Ilya Prigogine's Brussels-Austin Group have been working on the quantum mechanical arrow of time and irreversibility in rigged Hilbert space quantum mechanics. A crucial notion in Bohm's approach is the so-called preparation/registration arrow. An analysis of this arrow and its role in Bohm's theory of scattering is given. Similarly, the Brussels-Austin Group uses an excitation/de-excitation arrow for ordering events, which is also analyzed. The relationship between the two approaches is discussed focusing on their semi-group operators and time (...)
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  40. A Note on the so-Called Yes-No Experiments and the Foundations of Quantum Mechanics.Øistein Bjørnestad - 1974 - Synthese 29 (1-4):243 - 253.
  41. The Time Reversal Operator for Semigroup Evolutions.Arno Bohm & Sujeewa Wickramasekara - 1997 - Foundations of Physics 27 (7):969-993.
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  42. On a Quantum Algebraic Approach to a Generalized Phase Space.D. Bohm & B. J. Hiley - 1981 - Foundations of Physics 11 (3-4):179-203.
    We approach the relationship between classical and quantum theories in a new way, which allows both to be expressed in the same mathematical language, in terms of a matrix algebra in a phase space. This makes clear not only the similarities of the two theories, but also certain essential differences, and lays a foundation for understanding their relationship. We use the Wigner-Moyal transformation as a change of representation in phase space, and we avoid the problem of “negative probabilities” by regarding (...)
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  43. Mathematical Quantum Theory I: Random Ultrafilters as Hidden Variables.William Boos - 1996 - Synthese 107 (1):83 - 143.
    The basic purpose of this essay, the first of an intended pair, is to interpret standard von Neumann quantum theory in a framework of iterated measure algebraic truth for mathematical (and thus mathematical-physical) assertions — a framework, that is, in which the truth-values for such assertions are elements of iterated boolean measure-algebras (cf. Sections 2.2.9, 5.2.1–5.2.6 and 5.3 below).The essay itself employs constructions of Takeuti's boolean-valued analysis (whose origins lay in work of Scott, Solovay, Krauss and others) to provide a (...)
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  44. Compact Quantum Systems and the Pauli Data Problem.A. J. Bracken & R. J. B. Fawcett - 1993 - Foundations of Physics 23 (2):277-289.
    Compact quantum systems have underlying compact kinematical Lie algebras, in contrast to familiar noncompact quantum systems built on the Weyl-Heisenberg algebra. Pauli asked in the latter case: to what extent does knowledge of the probability distributions in coordinate and momentum space determine the state vector? The analogous question for compact quantum systems is raised, and some preliminary results are obtained.
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  45. Spin Path Integrals and Generations.Carl Brannen - 2010 - Foundations of Physics 40 (11):1681-1699.
    The spin of a free electron is stable but its position is not. Recent quantum information research by G. Svetlichny, J. Tolar, and G. Chadzitaskos have shown that the Feynman position path integral can be mathematically defined as a product of incompatible states; that is, as a product of mutually unbiased bases (MUBs). Since the more common use of MUBs is in finite dimensional Hilbert spaces, this raises the question “what happens when spin path integrals are computed over products of (...)
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  46. Operational Quantum Physics.J. A. Brooke - 1996 - Foundations of Physics 26:1563-1566.
  47. Aspects of Objectivity in Quantum Mechanics.Harvey Brown - 1999 - In Jeremy Butterfield & Constantine Pagonis (eds.), From Physics to Philosophy. Cambridge University Press. pp. 45--70.
    The purpose of the paper is to explore different aspects of the covariance of non-relativistic quantum mechanics. First, doubts are expressed concerning the claim that gauge fields can be 'generated' by way of imposition of gauge covariance of the single-particle wave equation. Then a brief review is given of Galilean covariance in the general case of external fields, and the connection between Galilean boosts and gauge transformations. Under time-dependent translations the geometric phase associated with Schrödinger evolution is non-invariant, and the (...)
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  48. Simple Applications of Noether's First Theorem in Quantum Mechanics and Electromagnetism.Harvey R. Brown & Peter Holland - unknown
    Internal global symmetries exist for the free non-relativistic Schrodinger particle, whose associated Noether charges---the space integrals of the wavefunction and the wavefunction multiplied by the spatial coordinate---are exhibited. Analogous symmetries in classical electromagnetism are also demonstrated.
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  49. Time in Quantum Physics: From an External Parameter to an Intrinsic Observable. [REVIEW]Romeo Brunetti, Klaus Fredenhagen & Marc Hoge - 2010 - Foundations of Physics 40 (9-10):1368-1378.
    In the Schrödinger equation, time plays a special role as an external parameter. We show that in an enlarged system where the time variable denotes an additional degree of freedom, solutions of the Schrödinger equation give rise to weights on the enlarged algebra of observables. States in the associated GNS representation correspond to states on the original algebra composed with a completely positive unit preserving map. Application of this map to the functions of the time operator on the large system (...)
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  50. Interference, Noncommutativity, and Determinateness in Quantum Mechanics.Jeffrey Bub - 1995 - Topoi 14 (1):39-43.
    I consider to what extent the phenomenon of interference precludes the possibility of attributing simultaneously determinate values to noncommuting observables, and I show that, while all observables can in principle be taken as simultaneously determinate, it suffices to take a suitable privileged observable as determinate to solve the measurement problem.
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