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  1. Stephen L. Adler & Jeeva Anandan (1996). Nonadiabatic Geometric Phase in Quaternionic Hilbert Space. Foundations of Physics 26 (12):1579-1589.
    We develop the theory of the nonadiabatic geometric phase, in both the Abelian and non-Abelian cases, in quaternionic Hilbert space.
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  2. V. V. Afonin & V. Y. Petrov (2010). Is the Luttinger Liquid a New State of Matter? Foundations of Physics 40 (2):190-204.
    We are demonstrating that the Luttinger model with short range interaction can be treated as a type of Fermi liquid. In line with the main dogma of Landau’s theory one can define a fermion excitation renormalized by interaction and show that in terms of these fermions any excited state of the system is described by free particles. The fermions are a mixture of renormalized right and left electrons. The electric charge and chirality of the Landau quasi-particle is discussed.
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  3. James Albertson (1959). Causality and Chance in Modern Physics. The Modern Schoolman 36 (2):134-135.
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  4. S. Twareque Ali, Claudio Carmeli, Teiko Heinosaari & Alessandro Toigo (2009). Commutative POVMs and Fuzzy Observables. Foundations of Physics 39 (6):593-612.
    In this paper we review some properties of fuzzy observables, mainly as realized by commutative positive operator valued measures. In this context we discuss two representation theorems for commutative positive operator valued measures in terms of projection valued measures and describe, in some detail, the general notion of fuzzification. We also make some related observations on joint measurements.
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  5. Vidal Alonso, Salvatore De Vincenzo & Luigi Mondino (1999). Tensorial Relativistic Quantum Mechanics in (1+1) Dimensions and Boundary Conditions. Foundations of Physics 29 (2):231-250.
    The tensorial relativistic quantum mechanics in (1+1) dimensions is considered. Its kinematical and dynamical features are reviewed as well as the problem of finding the Dirac spinor for given finite multivectors. For stationary states, the dynamical tensorial equations, equivalent to the Dirac equation, are solved for a free particle, for a particle inside a box, and for a particle in a step potential.
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  6. T. B. Anders, R. Von Mellenthin, B. Pfeil & H. Salecker (1993). Unitarity Bounds for 4-Fermion Contact Interactions. Foundations of Physics 23 (3):399-410.
    In this paper we consider the effect of unitarity bounds sb⩾s≡(E1+E2) cms 2 for the recently proposed types of nonderivative 4-fermion contact interactions. To this purpose we decompose the helicity amplitudes at c.m.s. into partial waves. The bounds are defined to hold for all reaction channels due to the same type of contact interaction. We find sb=τ4π/κ. Here κ is the coupling constant. The factor τ depends on the type of coupling and on the different cases to identify the fermions. (...)
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  7. D. Arsenović, N. Burić, D. M. Davidović & S. Prvanović (2014). Lagrangian Form of Schrödinger Equation. Foundations of Physics 44 (7):725-735.
    Lagrangian formulation of quantum mechanical Schrödinger equation is developed in general and illustrated in the eigenbasis of the Hamiltonian and in the coordinate representation. The Lagrangian formulation of physically plausible quantum system results in a well defined second order equation on a real vector space. The Klein–Gordon equation for a real field is shown to be the Lagrangian form of the corresponding Schrödinger equation.
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  8. R. Arshansky & L. P. Horwitz (1985). The Landau-Peierls Relation and a Causal Bound in Covariant Relativistic Quantum Theory. Foundations of Physics 15 (6):701-715.
    Thought experiments analogous to those discussed by Landau and Peierls are studied in the framework of a manifestly covariant relativistic quantum theory. It is shown that momentum and energy can be arbitrarily well defined, and that the drifts induced by measurement in the positions and times of occurrence of events remain within the (stable) spread of the wave packet in space-time. The structure of the Newton-Wigner position operator is studied in this framework, and it is shown that an analogous time (...)
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  9. Ray E. Artz (1981). Quantum Mechanics in Galilean Space-Time. Foundations of Physics 11 (11-12):839-862.
    The usual quantum mechanical treatment of a Schrödinger particle is translated into manifestly Galilean-invariant language, primarily through the use of Wigner-distribution methods. The hydrodynamical formulation of quantum mechanics is derived directly from the Wigner-distribution formulation, and the two formulations are compared. Wigner distributions are characterized directly, i.e., without reference to wave functions, and a heuristic interpretation of Wigner distributions and their evolution is developed.
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  10. David Atkinson, Dirac's Quantum Jump.
    This minicourse on quantum mechanics is intended for students who have already been rather well exposed to the subject at an elementary level. It is assumed that they have surmounted the first conceptual hurdles and also have struggled with the Schrödinger equation in one dimension.
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  11. R. Aurich & F. Steiner (2001). Orbit Sum Rules for the Quantum Wave Functions of the Strongly Chaotic Hadamard Billiard in Arbitrary Dimensions. Foundations of Physics 31 (4):569-592.
    Sum rules are derived for the quantum wave functions of the Hadamard billiard in arbitrary dimensions. This billiard is a strongly chaotic (Anosov) system which consists of a point particle moving freely on a D-dimensional compact manifold (orbifold) of constant negative curvature. The sum rules express a general (two-point)correlation function of the quantum mechanical wave functions in terms of a sum over the orbits of the corresponding classical system. By taking the trace of the orbit sum rule or pre-trace formula, (...)
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  12. William Band & James L. Park (1978). Generalized Two-Level Quantum Dynamics. II. Non-Hamiltonian State Evolution. Foundations of Physics 8 (1-2):45-58.
    A theorem is derived that enables a systematic enumeration of all the linear superoperators ℒ (associated with a two-level quantum system) that generate, via the law of motion ℒρ= $\dot \rho$ , mappings ρ(0) → ρ(t) restricted to the domain of statistical operators. Such dynamical evolutions include the usual Hamiltonian motion as a special case, but they also encompass more general motions, which are noncyclic and feature a destination state ρ(t → ∞) that is in some cases independent of ρ(0).
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  13. A. S. Barabash (2010). Experimental Test of the Pauli Exclusion Principle. Foundations of Physics 40 (7):703-718.
    A short review is given of three experimental works on tests of the Pauli Exclusion Principle (PEP) in which the author has been involved during the last 10 years. In the first work a search for anomalous carbon atoms was done and a limit on the existence of such atoms was determined, $^{12}\tilde{\mathrm{C}}$ /12C <2.5×10−12. In the second work PEP was tested with the NEMO-2 detector and the limits on the violation of PEP for p-shell nucleons in 12C were obtained. (...)
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  14. A. O. Barut (1995). Quantum Theory of Single Events Continued. Accelerating Wavelets and the Stern-Gerlach Experiment. Foundations of Physics 25 (2):377-381.
    Exact wavelet solutions of the wave equation for accelerating potentials are found and applied to single individual events in Stern-Gerlach experiment.
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  15. A. O. Barut (1990). Quantum Theory of Single Events: Localized De Broglie Wavelets, Schrödinger Waves, and Classical Trajectories. [REVIEW] Foundations of Physics 20 (10):1233-1240.
    For an arbitrary potential V with classical trajectoriesx=g(t), we construct localized oscillating three-dimensional wave lumps ψ(x, t,g) representing a single quantum particle. The crest of the envelope of the ripple follows the classical orbitg(t), slightly modified due to the potential V, and ψ(x, t,g) satisfies the Schrödinger equation. The field energy, momentum, and angular momentum calculated as integrals over all space are equal to the particle energy, momentum, and angular momentum. The relation to coherent states and to Schrödinger waves is (...)
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  16. James Baugh, David Ritz Finkelstein, Andrei Galiautdinov & Mohsen Shiri-Garakani (2003). Transquantum Dynamics. Foundations of Physics 33 (9):1267-1275.
    Segal proposed transquantum commutation relations with two transquantum constants ħ′, ħ″ besides Planck's quantum constant ħ and with a variable i. The Heisenberg quantum algebra is a contraction—in a more general sense than that of Inönü and Wigner—of the Segal transquantum algebra. The usual constant i arises as a vacuum order-parameter in the quantum limit ħ′,ħ″→0. One physical consequence is a discrete spectrum for canonical variables and space-time coordinates. Another is an interconversion of time and energy accompanying space-time meltdown (disorder), (...)
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  17. Almut Beige, Gerhard C. Hegerfeldt & Dirk G. Sondermann (1997). Atomic Quantum Zeno Effect for Ensembles and Single Systems. Foundations of Physics 27 (12):1671-1688.
    The so-called quantum Zeno effect is essentially a consequence of the projection postulate for ideal measurements. To test the effect, Itanoet al. have performed an experiment on an ensemble of atoms where rapidly repeated level measurements were realized by means of short laser pulses. Using dynamical considerations, we give an explanation why the projection postulate can be applied in good approximation to such measurements. Corrections to ideal measurements are determined explicitly. This is used to discuss how far the experiment of (...)
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  18. M. G. Benedict & W. Schleich (1993). On the Correspondence of Semiclassical and Quantum Phases in Cyclic Evolutions. Foundations of Physics 23 (3):389-397.
    Based on the exactly solvable case of a harmonic oscillator, we show that the direct correspondence between the Bohr-Sommerfeld phase of semiclassical quantum mechanics and the topological phase of Aharonov and Anandan is restricted to the case of a coherent state. For other Gaussian wave packets the geometric quantum phase strongly depends on the amount of squeezing.
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  19. R. Bernabei, P. Belli, F. Cappella, R. Cerulli, C. J. Dai, A. D'Angelo, H. L. He, A. Incicchitti, H. H. Kuang, X. H. Ma, F. Montecchia, F. Nozzoli, D. Prosperi, X. D. Sheng & Z. P. Ye (2010). Non-Paulian Nuclear Processes in Highly Radiopure NaI(Tl): Status and Perspectives. [REVIEW] Foundations of Physics 40 (7):807-813.
    Searches for non-paulian nuclear processes, i.e. processes normally forbidden by the Pauli–Exclusion–Principle (PEP) with highly radiopure NaI(Tl) scintillators allow the test of this fundamental principle with high sensitivity. Status and perspectives are addressed.
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  20. Robin Blume-Kohout, Carlton M. Caves & Ivan H. Deutsch (2002). Climbing Mount Scalable: Physical Resource Requirements for a Scalable Quantum Computer. [REVIEW] Foundations of Physics 32 (11):1641-1670.
    The primary resource for quantum computation is Hilbert-space dimension. Whereas Hilbert space itself is an abstract construction, the number of dimensions available to a system is a physical quantity that requires physical resources. Avoiding a demand for an exponential amount of these resources places a fundamental constraint on the systems that are suitable for scalable quantum computation. To be scalable, the effective number of degrees of freedom in the computer must grow nearly linearly with the number of qubits in an (...)
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  21. Martin Bohata & Jan Hamhalter (2010). Bell's Correlations and Spin Systems. Foundations of Physics 40 (8):1065-1075.
    The structure of maximal violators of Bell’s inequalities for Jordan algebras is investigated. It is proved that the spin factor V 2 is responsible for maximal values of Bell’s correlations in a faithful state. In this situation maximally correlated subsystems must overlap in a nonassociative subalgebra. For operator commuting subalgebras it is shown that maximal violators have the structure of the spin systems and that the global state (faithful on local subalgebras) acts as the trace on local subalgebras.
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  22. A. Bohm, M. Loewe, P. Patuleanu & C. Püntmann (1997). Jordan Blocks and Exponentially Decaying Higher-Order Gamow States. Foundations of Physics 27 (5):613-624.
    In the framework of the rigged Hilbert space, unstable quantum systems associated with first-order poles of the analytically continued S-matrix can be described by Gamow vectors which are generalized vectors with exponential decay and a Breit-Wigner energy distribution. This mathematical formalism can be generalized to quasistationary systems associated with higher-order poles of the S-matrix, which leads to a set of Gamow vectors of higher order with a non-exponential time evolution. One can define a state operator from the set of higher-order (...)
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  23. M. A. Braun & K. Urbanowski (1992). On the Description of Multiple Measurements of an Unstable State. Foundations of Physics 22 (4):617-630.
    The nondecay probability of an unstable particle at a definite moment of time is investigated provided this particle existed at all earlier observation moments separated with the time interval Δ. Using the usual postulates for quantum measurements it is proved that this probability is described by the exponential function of Δ>0, and it tends to 1 as Δ → 0. An approximate formula is found for the effective decay width Γ(Δ) appearing in the case of multiple measurements. It is shown (...)
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  24. Ernst Breitenberger (1985). Uncertainty Measures and Uncertainty Relations for Angle Observables. Foundations of Physics 15 (3):353-364.
    Uncertainty measures must not depend on the choice of origin of the measurement scale; it is therefore argued that quantum-mechanical uncertainty relations, too, should remain invariant under changes of origin. These points have often been neglected in dealing with angle observables. Known measures of location and uncertainty for angles are surveyed. The angle variance angv {ø} is defined and discussed. It is particularly suited to the needs of quantum theory, because of its affinity to the Hilbert space metric, and its (...)
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  25. Philippe Briet, François Germinet & Georgi Raikov (eds.) (2009). Spectral and Scattering Theory for Quantum Magnetic Systems, July 7-11, 2008, Cirm, Luminy, Marseilles, France. American Mathematical Society.
    Volume 500, 2009 On the Infrared Problem for the Dressed Non-Relativistic Electron in a Magnetic Field Laurent Amour, ...
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  26. A. Brocklehurst & M. Suárez (2000). Review. Quantum State Diffusion. I Percival. British Journal for the Philosophy of Science 51 (3):527-530.
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  27. Paul Busch (1987). Some Realizable Joint Measurements of Complementary Observables. Foundations of Physics 17 (9):905-937.
    Noncommuting quantum observables, if considered asunsharp observables, are simultaneously measurable. This fact is exemplified for complementary observables in two-dimensional state spaces. Two proposals of experimentally feasible joint measurements are presented for pairs of photon or neutron polarization observables and for path and interference observables in a photon split-beam experiment. A recent experiment proposed and performed by Mittelstaedt, Prieur, and Schieder in Cologne is interpreted as a partial version of the latter example.
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  28. Paul Busch & Pekka Lahti, Observable (Compendium Entry).
    This is an entry to the Compendium of Quantum Physics, edited by F Weinert, K Hentschel and D Greenberg, to be published by Springer-Verlag.
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  29. C. Chandler, L. Cohen, C. Lee, M. Scully & K. Wódkiewicz (1992). Quasi-Probability Distribution for Spin-1/2 Particles. Foundations of Physics 22 (7):867-878.
    Quantum distribution functions for spin-1/2 systems are derived for various characteristic functions corresponding to different operator orderings.
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  30. Rob Clifton, Introductory Notes on the Mathematics Needed for Quantum Theory.
    These are notes designed to bring the beginning student of the philosophy of quantum mechanics 'up to scratch' on the mathematical background needed to understand elementary finite-dimensional quantum theory. There are just three chapters: Ch. 1 'Vector Spaces'; Ch. 2 'Inner Product Spaces'; and Ch. 3 'Operators on Finite-Dimensional Complex Inner Product Spaces'. The notes are entirely self-contained and presuppose knowledge of only high school level algebra.
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  31. F. Coester & W. Polyzou (1994). Vacuum Structures in Hamiltonian Light-Front Dynamics. Foundations of Physics 24 (3):387-400.
    Hamiltonian light-front dynamics of quantum fields may provide a useful approach to systematic nonperturbative approximations to quantum field theories. We investigate inequivalent Hilbert-space representations of the light-front field algebra in which the stability group of the light front is implemented by unitary transformations. The Hilbert space representation of states is generated by the operator algebra from the vacuum state. There is a large class of vacuum states besides the Fock vacuum which meet all the invariance requirements. The light-front Hamiltonian must (...)
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  32. Leon Cohen (1992). Multipart Wave Functions. Foundations of Physics 22 (5):691-711.
    Some wave functions separate into two or more distinct regions in phase space. Each region is characterized by a trajectory and a spread about that trajectory. The trajectory is the quantum mechanical current. We show that these regions correspond to parts of the wave function and that these parts are generally nonorthogonal.
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  33. Leon Cohen & Chongmoon Lee (1987). Conditional Expectation Values in Quantum Mechanics. Foundations of Physics 17 (6):561-574.
    The general question of defining the expectation value of an operator for a fixed value of another noncommuting observable is considered and explicit expressions are derived. Due to the noncommutivity of operators a unique definition is not possible, and we consider different possible expressions. Special cases which have previously been considered in the literature are shown to be derivable from the methods presented.
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  34. P. Coleman (1996). Quantum Field Theory in Condensed Matter Physics. Foundations of Physics 26:1733-1735.
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  35. Nicola Cufaro-Petroni, Philippe Gueret & Jean-Pierre Vigier (1988). Second-Order Wave Equation for Spin-1/2 Fields: 8-Spinors and Canonical Formulation. Foundations of Physics 18 (11):1057-1075.
    The algebraic structure of the 8-spinor formalism is discussed, and the general form of the 8-component wave equation, equivalent to the second-order 4-component one, is presented. This allows a canonical formulation that will be the first stage of the future Clebsch parametrization, i.e., a relativistic generalization of the Bohm-Schiller-Tiomno pioneering work on the Pauli equation.
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  36. V. A. De Lorenci & N. F. Svaiter (1999). A Rotating Quantum Vacuum. Foundations of Physics 29 (8):1233-1264.
    We investigate how a uniformly rotating frame is defined as the rest frame of an observer rotating with constant angular velocity Ω around the z axis of an inertial frame. Assuming this frame to be a Lorentz one, we second quantize a free massless scalar field in the rotating frame and obtain that creation-annihilation operators of the field are not the same as those of an inertial frame. This leads to a new vacuum state—a rotating vacuum. After this, introducing an (...)
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  37. K. Dechoum & Humberto de Menezes França (1995). Non-Heisenberg States of the Harmonic Oscillator. Foundations of Physics 25 (11):1599-1620.
    The effects of the vacuum electromagnetic fluctuations and the radiation reaction fields on the time development of a simple microscopic system are identified using a new mathematical method. This is done by studying a charged mechanical oscillator (frequency Ω 0)within the realm of stochastic electrodynamics, where the vacuum plays the role of an energy reservoir. According to our approach, which may be regarded as a simple mathematical exercise, we show how the oscillator Liouville equation is transformed into a Schrödinger-like stochastic (...)
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  38. P. A. M. Dirac (1930). The Principles of Quantum Mechanics. Oxford, the Clarendon Press.
    THE PRINCIPLE OF SUPERPOSITION. The need for a quantum theory Classical mechanics has been developed continuously from the time of Newton and applied to an ...
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  39. Lisa M. Dolling (2009). Meeting the Universe Halfway: Quantum Physics and the Entanglement of Matter and Meaning. By Karen Barad. Hypatia 24 (1):212-218.
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  40. J. M. Domingos & M. H. Caldeira (1984). Self-Adjointness of Momentum Operators in Generalized Coordinates. Foundations of Physics 14 (2):147-154.
    The aim of this paper is to contribute to the clarification of concepts usually found in books on quantum mechanics, aided by knowledge from the field of the theory of operators in Hilbert space. Frequently the basic distinction between bounded and unbounded operators is not established in books on quantum mechanics. It is repeatedly overlooked that the condition for an unbounded operator to be symmetric (Hermitian) is not sufficient to make it self-adjoint. To make things worse, nearly all operators in (...)
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  41. Arthur Stanley Eddington (1943). The Combination of Relativity Theory and Quantum Theory. Institute for Advanced Studies.
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  42. James D. Edmonds Jr (1975). Second Quantized Quaternion Quantum Theory. Foundations of Physics 5 (4):643-648.
    The basic structure of a second quantized relativistic quantum theory is outlined. The vector space is over the ring of complex quaternions instead of the usual field of complex numbers. This is motivated by the simple quaternion structure of the Dirac equation.
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  43. Gérard G. Emch (2002). Mathematical Topics Between Classical and Quantum Mechanics. Studies in History and Philosophy of Science Part B 33 (1):148-150.
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  44. John R. Fanchi (2011). Manifestly Covariant Quantum Theory with Invariant Evolution Parameter in Relativistic Dynamics. Foundations of Physics 41 (1):4-32.
    Manifestly covariant quantum theory with invariant evolution parameter is a parametrized relativistic dynamical theory. The study of parameterized relativistic dynamics (PRD) helps us understand the consequences of changing key assumptions of quantum field theory (QFT). QFT has been very successful at explaining physical observations and is the basis of the conventional paradigm, which includes the Standard Model of electroweak and strong interactions. Despite its record of success, some phenomena are anomalies that may require a modification of the Standard Model. The (...)
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  45. Valerio Faraoni & Donovan M. Faraoni (2002). Elimination of the Potential From the Schrödinger and Klein–Gordon Equations by Means of Conformal Transformations. Foundations of Physics 32 (5):773-788.
    The potential term in the Schrödinger equation can be eliminated by means of a conformal transformation, reducing it to an equation for a free particle in a conformally related fictitious configuration space. A conformal transformation can also be applied to the Klein–Gordon equation, which is reduced to an equation for a free massless field in an appropriate (conformally related) spacetime. These procedures arise from the observation that the Jacobi form of the least action principle and the Hamilton–Jacobi equation of classical (...)
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  46. L. Ferrari (1989). The Covariance Problem and the Hamiltonian Formalism in Quantum Mechanics. Foundations of Physics 19 (5):579-605.
    The traditional approach to the covariance problem in quantum mechanics is inverted and the space-time transformations are assumed as the basicunknowns, according to the prescription that the correspondence principle and the commutation rules must becovariant. It is shown that the only solutions are either Galilean or Lorentzian (including the possibility of an imaginary light-velocity c2<0). The Dirac formalism for the wave-equation and the condition c2>0 are obtained simoultaneously as theunique solution, provided that the Hamiltonian is Hermitean (in the usual sense), (...)
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  47. L. Ferrari (1987). The Continuity Equation and the Hamiltonian Formalism in Quantum Mechanics. Foundations of Physics 17 (4):329-343.
    The relationship between the continuity equation and the HamiltonianH of a quantum system is investigated from a nonstandard point of view. In contrast to the usual approaches, the expression of the current densityJ ψ is givenab initio by means of a transport-velocity operatorV T, whose existence follows from a “weak” formulation of the correspondence principle. Once given a Hilbert-space metricM, it is shown that the equation of motion and the continuity equation actually represent a system in theunknown operatorsH andV T, (...)
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  48. M. Flato, L. K. Hadjiivanov & I. T. Todorov (1993). Quantum Deformations of Singletons and of Free Zero-Mass Fields. Foundations of Physics 23 (4):571-586.
    We consider quantum deformations of the real symplectic (or anti-De Sitter) algebra sp(4), ℝ ≅ spin(3, 2) and of its singleton and (4-dimensional) zero-mass representations. For q a root of −1, these representations admit finite-dimensional unitary subrepresentations. It is pointed out that Uq (sp(4, ℝ)), unlike Uq (su(2, 2)), contains Uq (sl 2 ) as a quantum subalgebra.
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  49. Moshé Flato, Zhi-Cheng Lu & Daniel Sternheimer (1993). From Where Do Quantum Groups Come? Foundations of Physics 23 (4):587-598.
    The phase space realizations of quantum groups are discussed using *-products. We show that on phase space, quantum groups appear necessarily as two-parameter deformation structures, one parameter (v) being concerned with the quantization in phase space, the other (η) expressing the quantum groups as “deformation” of their Lie counterparts. Introducing a strong invariance condition, we show the uniqueness of the η-deformation. This suggests that the strong invariance condition is a possible origin of the quantum groups.
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  50. Gordon N. Fleming & Harry Bennett (1989). Hyperplane Dependence in Relativistic Quantum Mechanics. Foundations of Physics 19 (3):231-267.
    Through the explicit introduction of hyperplane dependence as a form of relativistic dynamical evolution, we construct a manifestly covariant description of a single positive energy particle interacting with any one of a large class of “moving” external potentials. In1+1 dimensions, the simplified mathematics allows us to display a number of general properties of solutions to the equations of motion for evolution on hyperplanes.
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