23 research outputs found

    Quantum and Classical Phase Space: Separability and Entanglement

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    The formalism of classical and quantum mechanics on phase space leads to symplectic and Heisenberg group representations, respectively. The Wigner functions give a representation of the quantum system using classical variables. The correspondence between the classical and the quantum criterion of separability for the system is obtained in terms of these functions. Entanglement is generic and separability is special. Some applications are discussed in commonly occuring examples and possibly in exotic systems.Comment: 8 pages, no figure

    Supersymmetric Yang Mills Fields and Black Holes ; In Ten Dimensional Unified Field Theory

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    The Ten dimensional Unified field theory has a 4 dimensional Riemannian spacetime and six dimensional Calabi Yau space structure. The supersymmetric Yang Mills fields and black holes are solutions in these theories. The formation of primordial black holes in early universe, the collapse to singularity of stellar black holes, the Hawking evaporation of microscopic black holes in LHC are topics of observational and theoretical interest. The observation of gamma ray bursts and creation of spectrum of particles and radiation of dark and normal matter occur due to primordial and microscopic black holes. The approach to singularity in black hole interior solutions, require the Bogoliubov transforms of SUSY YM fields in black hole geometries; both during formation and in evaporation. The Hawking effect of radiating black holes is applicable for all the fields. Invariants can be defined to give the conditions for these processes.Comment: 8 pages, no figures, [email protected] Physics deptt, St Xavier's college, Mumbai, India visitor, Institute of mathematical sciences, Chennai, Indi

    Particle and Field Symmetries and Noncommutative Geometry

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    The development of Noncommutative Geometry is creating a reworking and new possibilities in physics. This paper identifies some of the commutation and derivation structures that arise in particle and field interactions and fundamental symmetries. The requirements of coexisting structures, and their consistency, produce a mathematical framework that underlies a fundamental physics theory. Among other developments in Quantum theory of particles and fields are the symmetries of gauge fields and the Fermi-Bose symmetry of particles. These involve a gauge covariant derivation and the action functionals; and commutation algebras and Bogoliubov transforms. The non commutative Theta form introduces an additional and fundamental structure. This paper obtains the interrelations of various structures, and the conditions for the symmetries of Fermionic/Bosonic particles interacting with Yang Mills gauge fields. Many example physical systems are being solved, and the mathematical formalism is being created to understand the fundamental basis of physics.Comment: 9 pages, no figures, [email protected]

    Non commutative quantum spacetime with topological vortex states, and dark matter in the universe

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    Non commutative geometry is creating new possibilities for physics. Quantum spacetime geometry and post inflationary models of the universe with matter creation have an enormous range of scales of time, distance and energy in between. There is a variety of physics possible till the nucleosynthesis epoch is reached. The use of topology and non commutative geometry in cosmology is a recent approach. This paper considers the possibility of topological solutions of a vortex kind given by non commutative structures. These are interpreted as dark matter, with the grand unified Yang-Mills field theory energy scale used to describe its properties. The relation of the model with other existing theories is discussed.Comment: 7 pages, no figures. [email protected]

    Fundamental Field Theory in Ten Dimensions and The Early Universe

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    A unified field theory in ten dimensions, of all interactions, can describe high energy processes occuring in the early universe. In such a theory transitions that give properties of the universe can occur due to the presence of algebraic and geometric structures. A correspondence between theory and observations of the universe is made, to obtain a new interpretation and properties. This paper consists of a field theory and cosmological model of dark and normal energy and matter, cosmological constant, acceleration and inflation in the early universe.Comment: 11 pages,no figures,[email protected]

    Unified Gauge Field Theory and Topological Transitions

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    The search for a Unified description of all interactions has created many developments of mathematics and physics. The role of geometric effects in the Quantum Theory of particles and fields and spacetime has been an active topic of research. This paper attempts to obtain the conditions for a Unified Gauge Field Theory, including gravity. In the Yang Mills type of theories with compactifications from a 10 or 11 dimensional space to a spacetime of 4 dimensions, the Kaluza Klein and the Holonomy approach has been used. In the compactifications of Calabi Yau spaces and sub manifolds, the Euler number Topological Index is used to label the allowed states and the transitions. With a SU(2) or SL(2,C) connection for gravity and the U(1)*SU(2)*SU(3) or SU(5) gauge connection for the other interactions, a Unified gauge field theory is expressed in the 10 or 11 dimension space. Partition functions for the sum over all possible configurations of sub spaces labeled by the Euler number index and the Action for gauge and matter fields are constructed. Topological Euler number changing transitions that can occur in the gauge fields and the compactified spaces, and their significance are discussed. The possible limits and effects of the physical validity of such a theory are discussed.Comment: 14 pages, no figures, [email protected], (Physics department, St Xavier's college, Mumbai and visitor, Institute of Mathematical Sciences, Chennai, India

    Bose Fermi Supersymmetry with Bogoliubov transforms in Cosmology

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    Field theory including Supersymmetry and Bose Fermi Symmetry is an active subject of particle physics and cosmology. Recent and expected observational evidence gives indicators for the creation and destruction of normal and supersymmetric dark matter in the universe. This paper uses Bogoliubov transforms in supersymmetric and Bose Fermi form for obtaining the vaccuum expectation values at any two times in cosmological and black hole geometries. The isotropic Robertson Walker and slightly anisotropic Bianchi I geometry mode functions have a differential equation form analogous to the supersymmetric Hamiltonian. The condition for mixed and distinct representations for bosonic and fermionic fields of normal and supersymmetric partner particles are found.Comment: 11 pages, no figures. Visitor, Institute of Mathematical Sciences, Chennai; [email protected]

    Quantisation on general spaces

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    Quantisation on spaces with properties of curvature, multiple connectedness and non orientablility is obtained. The geodesic length spectrum for the Laplacian operator is extended to solve the Schroedinger operator. Homotopy fundamental group representations are used to obtain a direct sum of Hilbert spaces, with a Holonomy method for the non simply connected manifolds.The covering spaces of isometric and hence isospectral manifolds are used to obtain the representation of states on orientable and non orientable spaces. Problems of deformations of the operators and the domains are discussed.Possible applications of the geometric and topological effects in physics are mentioned.Comment: 7 pages. No figure

    Stability of Thermohaline circulation with respect to fresh water release

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    The relatively warm climate found in the North- Western Europe is due to the gulf stream that circulates warm saline water from southern latitudes to Europe. In North Atlantic ocean the stream gives out a large amount of heat, cools down and sinks to the bottom to complete the Thermohaline circulation. There is considerable debate on the stability of the stream to inputs of fresh water from the melting ice in Greenland and Arctic. The circulation, being switched off, will have massive impact on the climate of Europe. Intergovernmental panel on climate change (IPCC) has warned of this danger in its recent report. Our aim is to model the Thermohaline circulation at the point where it sinks in the North-Atlantic. We create a two dimensional discrete map modeling the salinity gradient and vertical velocity of the stream. We look for how a perturbation in the form of fresh water release can destabilise the circulation by pushing the velocity below a certain threshold.Comment: Physics department, St Xaviers college, Mumbai and visitor,Institute of Mathematical sciences, Chenna

    Statistical Physics and Dynamical Systems: Models of Phase Transitions

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    This paper explores the connection between dynamical system properties and statistical physics of ensembles of such systems. Simple models are used to give novel phase transitions; particularly for finite N particle systems with many physically interesting examples.Comment: 7 pages, no figures, Physics department, St Xavier's college, Mumbai, India; visitor, Institute of mathematical sciences, Chenna
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