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24
The cosmological constant and dark energy
 Reviews of Modern Physics
, 2003
"... Physics invites the idea that space contains energy whose gravitational effect approximates that of Einstein’s cosmological constant, Λ; nowadays the concept is termed dark energy or quintessence. Physics also suggests the dark energy could be dynamical, allowing the arguably appealing picture that ..."
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Cited by 40 (0 self)
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Physics invites the idea that space contains energy whose gravitational effect approximates that of Einstein’s cosmological constant, Λ; nowadays the concept is termed dark energy or quintessence. Physics also suggests the dark energy could be dynamical, allowing the arguably appealing picture that the dark energy density is evolving to its natural value, zero, and is small now because the
Hamiltonian systems with symmetry, coadjoint orbits and plasma physics
 IN PROC. IUTAMIS1MM SYMPOSIUM ON MODERN DEVELOPMENTS IN ANALYTICAL MECHANICS
, 1982
"... The symplectic and Poisson structures on reduced phase spaces are reviewed, including the symplectic structure on coadjoint orbits of a Lie group and the LiePoisson structure on the dual of a Lie algebra. These results are applied to plasma physics. We show in three steps how the MaxwellVlasov equ ..."
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Cited by 32 (21 self)
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The symplectic and Poisson structures on reduced phase spaces are reviewed, including the symplectic structure on coadjoint orbits of a Lie group and the LiePoisson structure on the dual of a Lie algebra. These results are applied to plasma physics. We show in three steps how the MaxwellVlasov equations for a collisionless plasma can be written in Hamiltonian form relative to a certain Poisson bracket. First, the PoissonVlasov equations are shown to be in Hamiltonian form relative to the LiePoisson bracket on the dual of the (finite dimensional) Lie algebra of infinitesimal canonical transformations. Then we write Maxwell’s equations in Hamiltonian form using the canonical symplectic structure on the phase space of the electromagnetic fields, regarded as a gauge theory. In the last step we couple these two systems via the reduction procedure for interacting systems. We also show that two other standard models in plasma physics, ideal MHD and twofluid electrodynamics, can be
Weinberg Formalism and New Looks at the Electromagnetic Theory
, 1996
"... In the first part of this paper we review several formalisms which give alternative ways for describing the light. They are: the formalism ‘baroque’ and the MajoranaOppenheimer form of electrodynamics, the Sachs ’ theory of Elementary Matter, the DiracFockPodol’sky model, its development by Staru ..."
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Cited by 11 (7 self)
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In the first part of this paper we review several formalisms which give alternative ways for describing the light. They are: the formalism ‘baroque’ and the MajoranaOppenheimer form of electrodynamics, the Sachs ’ theory of Elementary Matter, the DiracFockPodol’sky model, its development by Staruszkiewicz, the EvansVigier B (3) field, the theory with an invariant evolution parameter by Horwitz, the analysis of the actionatadistance concept, presented recently by Chubykalo and SmirnovRueda, and the analysis of the claimed ‘longitudinality ’ of the antisymmetric tensor field after quantization. The second part is devoted to the discussion of the Weinberg formalism and its recent development by Ahluwalia and myself. Connections between these models and possible significance of longitudinal modes are also discussed. I. HISTORICAL NOTES The Maxwell’s electromagnetic theory perfectly describes many observed phenomena. The accuracy in predictions of the quantum electrodynamics is without precedents [23]. They are widely accepted as the only tools to deal with electromagnetic phenomena. Other
NonBoolean Descriptions for MindMatter Problems
"... A framework for the mindmatter problem in a holistic universe which has no parts is outlined. The conceptual structure of modern quantum theory suggests to use complementary Boolean descriptions as elements for a more comprehensive nonBoolean description of a world without an apriorigiven mindmat ..."
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A framework for the mindmatter problem in a holistic universe which has no parts is outlined. The conceptual structure of modern quantum theory suggests to use complementary Boolean descriptions as elements for a more comprehensive nonBoolean description of a world without an apriorigiven mindmatter distinction. Such a description in terms of a locally Boolean but globally nonBoolean structure makes allowance for the fact that Boolean descriptions play a privileged role in science. If we accept the insight that there are no ultimate building blocks, the existence of holistic correlations between contextually chosen parts is a natural consequence. The main problem of a genuinely nonBoolean description is to find an appropriate partition of the universe of discourse. If we adopt the idea that all fundamental laws of physics are invariant under time translations, then we can consider a partition of the world into a tenseless and a tensed domain. In the sense of a regulative principle, the material domain is defined as the tenseless domain with its homogeneous time. The tensed domain contains the mental domain with a tensed time characterized by a privileged position, the Now. Since this partition refers to two complementary descriptions which are not given apriori,wehavetoexpectcorrelations between these two domains. In physics it corresponds to Newton’s separation of universal laws of nature and contingent initial conditions. Both descriptions have a nonBoolean structure and can be encompassed into a single nonBoolean description. Tensed and tenseless time can be synchronized by holistic correlations. 1.
Complementarity and uncertainty in MachZehnder interferometry and beyond
, 504
"... A coherent account of the connections and contrasts between the principles of complementarity and uncertainty is developed starting from a survey of the various formalizations of these principles. The conceptual analysis is illustrated by means of a set of experimental schemes based on MachZehnder ..."
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A coherent account of the connections and contrasts between the principles of complementarity and uncertainty is developed starting from a survey of the various formalizations of these principles. The conceptual analysis is illustrated by means of a set of experimental schemes based on MachZehnder interferometry. In particular, path detection via entanglement with a probe system and (quantitative) quantum erasure are exhibited to constitute instances of joint unsharp measurements of complementary pairs of physical quantities, path and interference observables. The analysis uses the representation of observables as positiveoperatorvalued measures (POVMs). The reconciliation of complementary experimental options in the sense of simultaneous unsharp preparations and measurements is expressed in terms of uncertainty relations of different kinds. The feature of complementarity, manifest in the present examples in the mutual exclusivity of path detection and interference observation, is recovered as a limit case from the appropriate uncertainty relation. It is noted that the complementarity and uncertainty principles are neither completely logically independent nor logical consequences of one another. Since entanglement is an instance of the uncertainty of quantum properties (of compound systems), it is moot to play out uncertainty and entanglement against each other as possible mechanisms enforcing complementarity.
Essay on the NonMaxwellian Theories of Electromagnetism, Hadronic
 Journal Supplement
, 1997
"... In the first part of this paper we review several formalisms which give alternative ways for describing the light. They are: the formalism ‘baroque’ and the MajoranaOppenheimer form of electrodynamics, the Sachs ’ theory of Elementary Matter, the DiracFockPodol’sky model, its development by Staru ..."
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Cited by 5 (0 self)
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In the first part of this paper we review several formalisms which give alternative ways for describing the light. They are: the formalism ‘baroque’ and the MajoranaOppenheimer form of electrodynamics, the Sachs ’ theory of Elementary Matter, the DiracFockPodol’sky model, its development by Staruszkiewicz, the EvansVigier B (3) field, the theory with an invariant evolution parameter of Horwitz, the analysis of the actionatadistance concept, presented recently by Chubykalo and SmirnovRueda, and the analysis of the claimed ‘longitudity ’ of the antisymmetric tensor field after quantization. The second part is devoted to the discussion of the Weinberg formalism and its recent development by Ahluwalia and myself. I. HISTORICAL NOTES The Maxwell’s electromagnetic theory perfectly describes many observed phenomena. The accuracy in predictions of the quantum electrodynamics is without precedents [22]. They are widely accepted as the only tools to deal with electromagnetic phenomena. Other modern field theories have been built on the basis of the similar principles to deal with
DIFFERENTIAL FORMS ON WASSERSTEIN SPACE AND INFINITEDIMENSIONAL HAMILTONIAN SYSTEMS
"... Abstract. Let M denote the space of probability measures on RD endowed with the Wasserstein metric. A differential calculus for a certain class of absolutely continuous curves in M was introduced in [4]. In this paper we develop a calculus for the corresponding class of differential forms on M. In p ..."
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Cited by 3 (1 self)
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Abstract. Let M denote the space of probability measures on RD endowed with the Wasserstein metric. A differential calculus for a certain class of absolutely continuous curves in M was introduced in [4]. In this paper we develop a calculus for the corresponding class of differential forms on M. In particular we prove an analogue of Green’s theorem for 1forms and show that the corresponding first cohomology group, in the sense of de Rham, vanishes. For D = 2d we then define a symplectic distribution on M in terms of this calculus, thus obtaining a rigorous framework for the notion of Hamiltonian systems as introduced in [3]. Throughout the paper we emphasize the geometric viewpoint and the role played by certain diffeomorphism groups of RD. 1.
CYCLOTOMIC QUANTUM CLOCK
, 2003
"... In the wake of our recent work on cyclotomic effects in quantum phaselocking [M. Planat & H. C. Rosu, Phys. Lett. A 315, 1 (2003)], we briefly discuss here a cyclotomic extension of the Salecker & Wigner quantum clock. We also hint on a possible cyclotomic structure of time at the Planck scales. 1 ..."
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In the wake of our recent work on cyclotomic effects in quantum phaselocking [M. Planat & H. C. Rosu, Phys. Lett. A 315, 1 (2003)], we briefly discuss here a cyclotomic extension of the Salecker & Wigner quantum clock. We also hint on a possible cyclotomic structure of time at the Planck scales. 1
Extended quantum mechanics
 Acta Physica Slovaca
, 2000
"... The work can be considered as an essay on mathematical and conceptual structure of nonrelativistic quantum mechanics (QM) which is related here to some other (more general, but also to more special – “approximative”) theories. QM is here primarily equivalently reformulated in the form of a Poisson s ..."
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The work can be considered as an essay on mathematical and conceptual structure of nonrelativistic quantum mechanics (QM) which is related here to some other (more general, but also to more special – “approximative”) theories. QM is here primarily equivalently reformulated in the form of a Poisson system on the phase space consisting of density matrices, where the “observables”, as well as “symmetry generators ” are represented by a specific type of real valued (densely defined) functions, namely the usual quantum expectations of corresponding selfadjoint operators. It is shown in this work that inclusion of additional (“nonlinear”) symmetry generators (i.e. “Hamiltonians”) into this reformulation of (linear) QM leads to a considerable extension of the theory: two kinds of quantum “mixed states ” should be distinguished, and operator – valued functions of density matrices should be used in the rôle of “nonlinear observables”. A general framework for physical theories is obtained in this way: By different choices of the sets of “nonlinear observables ” we obtain, as special cases, e.g. classical mechanics on homogeneous spaces of kinematical symmetry groups, standard (linear) QM, or nonlinear extensions of QM; also various “quasiclassical approximations ” to QM are
Complementarity and the algebraic structure of nite quantum systems
 J. of Physics: Conference Series
"... Abstract. Complementarity is a very old concept in quantum mechanics, however the rigorous de nition is not so old. Complementarity of orthogonal bases can be formulated in terms of maximal Abelian algebras and this may lead to avoid commutativity of the subalgebras. In some sense this means that qu ..."
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Cited by 1 (1 self)
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Abstract. Complementarity is a very old concept in quantum mechanics, however the rigorous de nition is not so old. Complementarity of orthogonal bases can be formulated in terms of maximal Abelian algebras and this may lead to avoid commutativity of the subalgebras. In some sense this means that quantum information is treated instead of classical (measurement) information. The subject is to extend to the quantum case some features from the classical case. This includes construction of complementary subalgebras. The Bell basis has also some relation. Several open questions are discussed. 1.