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Luca Lusanna - One of the best experts on this subject based on the ideXlab platform.
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Dust in the York Canonical Basis of ADM tetrad gravity: The problem of vorticity
International Journal of Geometric Methods in Modern Physics, 2015Co-Authors: David M. Alba, Luca LusannaAbstract:Brown's formulation of dynamical perfect fluids in Minkowski space-time is extended to ADM tetrad gravity in globally hyperbolic, asymptotically Minkowskian space-times. For the dust, we get the Hamiltonian description in closed form in the York Canonical Basis, where we can separate the inertial gauge variables of the gravitational field in the non-Euclidean 3-spaces of global non-inertial frames from the physical tidal ones. After writing the Hamilton equations of the dust, we identify the sector of irrotational motions and the gauge fixings forcing the dust 3-spaces to coincide with the 3-spaces of the non-inertial frame. The role of the inertial gauge variable York time (the remnant of the clock synchronization gauge freedom) is emphasized. Finally, the Hamiltonian Post-Minkowskian linearization is studied. This formalism is required when one wants to study the Hamiltonian version of cosmological models (for instance back-reaction as an alternative to dark energy) in the York Canonical Basis.
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Hamiltonian expression of curvature tensors in the York Canonical Basis: (I) Riemann tensor and Ricci scalars
International Journal of Geometric Methods in Modern Physics, 2014Co-Authors: Luca Lusanna, Mattia VillaniAbstract:By using the York Canonical Basis of ADM tetrad gravity, in a formulation using radar 4-coordinates for the parametrization of the 3+1 splitting of the space-time, it is possible to write the 4-Riemann tensor of a globally hyperbolic, asymptotically Minkowskian space-time as a Hamiltonian tensor, whose components are 4-scalars with respect to the ordinary world 4-coordinates, plus terms vanishing due to Einstein's equations. Therefore, "on-shell" we find the expression of the Hamiltonian 4-Riemann tensor. Moreover, the 3+1 splitting of the space-time used to define the phase space allows us to introduce a Hamiltonian set of null tetrads and to find the Hamiltonian expression of the 4-Ricci scalars of the Newman–Penrose formalism. This material will be used in the second paper to study the 4-Weyl tensor, the 4-Weyl scalars and the 4-Weyl eigenvalues and to clarify the notions of Dirac and Bergmann observables.
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the einstein maxwell particle system in the york Canonical Basis of adm tetrad gravity iii the post minkowskian n body problem its post newtonian limit in non harmonic 3 orthogonal gauges and dark matter as an inertial effect
Canadian Journal of Physics, 2012Co-Authors: David M. Alba, Luca LusannaAbstract:We conclude the study of the Post-Minkowskian linearization of ADM tetrad gravity in the York Canonical Basis for asymptotically Minkowskian space-times in the family of non-harmonic 3orthogonal gauges parametrized by the York time 3 K(τ,~σ) (the inertial gauge variable, not existing in Newton gravity, describing the general relativistic remnant of the freedom in clock synchronization in the definition of the instantaneous 3-spaces). As matter we consider only N scalar point particles with a Grassmann regularization of the self-energies and with a ultraviolet cutoff making possible the PM linearization and the evaluation of the PM solution for the gravitational field. We study in detail all the properties of these PM space-times emphasizing their dependence on
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the einstein maxwell particle system in the york Canonical Basis of adm tetrad gravity i the equations of motion in arbitrary schwinger time gauges
Canadian Journal of Physics, 2012Co-Authors: David M. Alba, Luca LusannaAbstract:We study the coupling of N charged scalar particles plus the electromagnetic field to Arnowitt–Deser–Misner (ADM) tetrad gravity and its Canonical formulation in asymptotically Minkowskian space–times without super-translations. To regularize the self-energies, both the electric charge and the sign of the energy of the particles are Grassmann-valued. The introduction of the noncovariant radiation gauge allows reformulation of the theory in terms of transverse electromagnetic fields and to extract the generalization of the Coulomb interaction among the particles in the riemannian instantaneous 3-spaces of global noninertial frames, the only ones allowed by the equivalence principle. Then we make the Canonical transformation to the York Canonical Basis, where there is a separation between the inertial (gauge) variables and the tidal ones inside the gravitational field and a special role of the eulerian observers associated with the 3+1 splitting of space–time. The Dirac hamiltonian is weakly equal to the we...
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the einstein maxwell particle system in the york Canonical Basis of adm tetrad gravity iii the post minkowskian n body problem its post newtonian limit in non harmonic 3 orthogonal gauges and dark matter as an inertial effect
Canadian Journal of Physics, 2012Co-Authors: David M. Alba, Luca LusannaAbstract:We conclude the study of the post-minkowskian (PM) linearization of ADM tetrad gravity in the York Canonical Basis for asymptotically minkowskian space–times in the family of nonharmonic 3-orthogonal gauges parametrized by the York time 3K(τ, s) (the inertial gauge variable, not existing in Newton gravity, describing the general relativistic remnant of the freedom in clock synchronization in the definition of the shape of the instantaneous 3-spaces as 3-submanifolds of space–time). As matter we consider only N scalar point particles with a Grassmann regularization of the self-energies and with an ultraviolet cutoff making possible the PM linearization and the evaluation of the PM solution for the gravitational field. We study in detail all the properties of these PM space–times emphasizing their dependence on the gauge variable 3K(1) = (1/Δ)3K(1) (the nonlocal York time): Riemann and Weyl tensors, 3-spaces, time-like and null geodesics, red-shift, and luminosity distance. Then we study the post-newtonian ...
Weiqiang Wang - One of the best experts on this subject based on the ideXlab platform.
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Character Formulae for Queer Lie Superalgebras and Canonical Bases of Types A/C
Communications in Mathematical Physics, 2017Co-Authors: Shun-jen Cheng, Jae-hoon Kwon, Weiqiang WangAbstract:For the BGG category of $${{\mathfrak{q}}(n)}$$ q ( n ) -modules of half-integer weights, a Kazhdan–Lusztig conjecture à la Brundan is formulated in terms of categorical Canonical Basis of the n th tensor power of the natural representation of the quantum group of type C . For the BGG category of $${{\mathfrak{q}}(n)}$$ q ( n ) -modules of congruent non-integral weights, a Kazhdan–Lusztig conjecture is formulated in terms of Canonical Basis of a mixed tensor of the natural representation and its dual of the quantum group of type A . We also establish a character formula for the finite-dimensional irreducible $${\mathfrak{q}(n)}$$ q ( n ) -modules of half-integer weights in terms of type C Canonical Basis of the corresponding q -wedge space.
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quantum supergroups ii Canonical Basis
arXiv: Quantum Algebra, 2013Co-Authors: Sean Clark, David L Hill, Weiqiang WangAbstract:Following Kashiwara's algebraic approach, we construct crystal bases and Canonical bases for quantum supergroups with no isotropic odd roots and for their integrable modules.
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Canonical Basis for quantum mathfrak osp 1 2
Letters in Mathematical Physics, 2013Co-Authors: Sean Clark, Weiqiang WangAbstract:We introduce a modified quantum enveloping algebra as well as a (modified) covering quantum algebra for the ortho-symplectic Lie superalgebra \({\mathfrak{osp}(1|2)}\). Then we formulate and compute the corresponding Canonical bases, and relate them to the counterpart for \({\mathfrak{sl}(2)}\). This provides a first example of Canonical Basis for quantum superalgebras.
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Canonical Basis for Quantum {\mathfrak{osp}(1|2)}
Letters in Mathematical Physics, 2012Co-Authors: Sean Clark, Weiqiang WangAbstract:We introduce a modified quantum enveloping algebra as well as a (modified) covering quantum algebra for the ortho-symplectic Lie superalgebra \({\mathfrak{osp}(1|2)}\). Then we formulate and compute the corresponding Canonical bases, and relate them to the counterpart for \({\mathfrak{sl}(2)}\). This provides a first example of Canonical Basis for quantum superalgebras.
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Canonical Basis for quantum osp 1 2
arXiv: Representation Theory, 2012Co-Authors: Sean Clark, Weiqiang WangAbstract:We introduce a modified quantum enveloping algebra as well as a (modified) covering quantum algebra for the ortho-symplectic Lie superalgebra osp(1|2). Then we formulate and compute the corresponding Canonical bases, and relate them to the counterpart for sl(2). This provides a first example of Canonical Basis for quantum superalgebras.
David M. Alba - One of the best experts on this subject based on the ideXlab platform.
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Dust in the York Canonical Basis of ADM tetrad gravity: The problem of vorticity
International Journal of Geometric Methods in Modern Physics, 2015Co-Authors: David M. Alba, Luca LusannaAbstract:Brown's formulation of dynamical perfect fluids in Minkowski space-time is extended to ADM tetrad gravity in globally hyperbolic, asymptotically Minkowskian space-times. For the dust, we get the Hamiltonian description in closed form in the York Canonical Basis, where we can separate the inertial gauge variables of the gravitational field in the non-Euclidean 3-spaces of global non-inertial frames from the physical tidal ones. After writing the Hamilton equations of the dust, we identify the sector of irrotational motions and the gauge fixings forcing the dust 3-spaces to coincide with the 3-spaces of the non-inertial frame. The role of the inertial gauge variable York time (the remnant of the clock synchronization gauge freedom) is emphasized. Finally, the Hamiltonian Post-Minkowskian linearization is studied. This formalism is required when one wants to study the Hamiltonian version of cosmological models (for instance back-reaction as an alternative to dark energy) in the York Canonical Basis.
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the einstein maxwell particle system in the york Canonical Basis of adm tetrad gravity iii the post minkowskian n body problem its post newtonian limit in non harmonic 3 orthogonal gauges and dark matter as an inertial effect
Canadian Journal of Physics, 2012Co-Authors: David M. Alba, Luca LusannaAbstract:We conclude the study of the Post-Minkowskian linearization of ADM tetrad gravity in the York Canonical Basis for asymptotically Minkowskian space-times in the family of non-harmonic 3orthogonal gauges parametrized by the York time 3 K(τ,~σ) (the inertial gauge variable, not existing in Newton gravity, describing the general relativistic remnant of the freedom in clock synchronization in the definition of the instantaneous 3-spaces). As matter we consider only N scalar point particles with a Grassmann regularization of the self-energies and with a ultraviolet cutoff making possible the PM linearization and the evaluation of the PM solution for the gravitational field. We study in detail all the properties of these PM space-times emphasizing their dependence on
-
the einstein maxwell particle system in the york Canonical Basis of adm tetrad gravity i the equations of motion in arbitrary schwinger time gauges
Canadian Journal of Physics, 2012Co-Authors: David M. Alba, Luca LusannaAbstract:We study the coupling of N charged scalar particles plus the electromagnetic field to Arnowitt–Deser–Misner (ADM) tetrad gravity and its Canonical formulation in asymptotically Minkowskian space–times without super-translations. To regularize the self-energies, both the electric charge and the sign of the energy of the particles are Grassmann-valued. The introduction of the noncovariant radiation gauge allows reformulation of the theory in terms of transverse electromagnetic fields and to extract the generalization of the Coulomb interaction among the particles in the riemannian instantaneous 3-spaces of global noninertial frames, the only ones allowed by the equivalence principle. Then we make the Canonical transformation to the York Canonical Basis, where there is a separation between the inertial (gauge) variables and the tidal ones inside the gravitational field and a special role of the eulerian observers associated with the 3+1 splitting of space–time. The Dirac hamiltonian is weakly equal to the we...
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the einstein maxwell particle system in the york Canonical Basis of adm tetrad gravity iii the post minkowskian n body problem its post newtonian limit in non harmonic 3 orthogonal gauges and dark matter as an inertial effect
Canadian Journal of Physics, 2012Co-Authors: David M. Alba, Luca LusannaAbstract:We conclude the study of the post-minkowskian (PM) linearization of ADM tetrad gravity in the York Canonical Basis for asymptotically minkowskian space–times in the family of nonharmonic 3-orthogonal gauges parametrized by the York time 3K(τ, s) (the inertial gauge variable, not existing in Newton gravity, describing the general relativistic remnant of the freedom in clock synchronization in the definition of the shape of the instantaneous 3-spaces as 3-submanifolds of space–time). As matter we consider only N scalar point particles with a Grassmann regularization of the self-energies and with an ultraviolet cutoff making possible the PM linearization and the evaluation of the PM solution for the gravitational field. We study in detail all the properties of these PM space–times emphasizing their dependence on the gauge variable 3K(1) = (1/Δ)3K(1) (the nonlocal York time): Riemann and Weyl tensors, 3-spaces, time-like and null geodesics, red-shift, and luminosity distance. Then we study the post-newtonian ...
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Dust in the York Canonical Basis of ADM Tetrad Gravity: the Problem of Vorticity
arXiv: General Relativity and Quantum Cosmology, 2011Co-Authors: David M. Alba, Luca LusannaAbstract:Brown's formulation of dynamical perfect fluids in Minkowski space-time is extended to ADM tetrad gravity in globally hyperbolic, asymptotically Minkowskian space-times. For the dust we get the Hamiltonian description in closed form in the York Canonical Basis, where we can separate the inertial gauge variables of the gravitational field in the non-Euclidean 3-spaces of global non-inertial frames from the physical tidal ones. After writing the Hamilton equations of the dust, we identify the sector of irrotational motions and the gauge fixings forcing the dust 3-spaces to coincide with the 3-spaces of the non-inertial frame. The role of the inertial gauge variable York time (the remnant of the clock synchronization gauge freedom) is emphasized. Finally the Hamiltonian Post-Minkowskian linearization is studied. The future application of this formalism will be the study of cosmological back-reaction (as an alternative to dark energy) in the York Canonical Basis.
Shuichiro Ebata - One of the best experts on this subject based on the ideXlab platform.
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Systematic investigation of low-lying dipole modes using the Canonical-Basis time-dependent Hartree-Fock-Bogoliubov theory
Physical Review C, 2014Co-Authors: Shuichiro Ebata, Takashi Nakatsukasa, T. InakuraAbstract:Systematic investigations of the electric dipole $(E1)$ modes of excitation are performed using the Canonical-Basis time-dependent Hartree-Fock-Bogoliubov (Cb-TDHFB) theory. The Cb-TDHFB is able to describe dynamical pairing correlations in excited states of nuclear systems. We apply the method to the real-time calculation of linear response in even-even nuclei with Skyrme functionals. Effects of shell structure, neutron skin, deformation, and neutron chemical potential (separation energy) are studied in a systematic way. This reveals a number of characteristic features of the low-energy $E1$ modes. We also find a universal behavior in the low-energy $E1$ modes for heavy neutron-rich isotopes, which suggests the emergence of decoupled $E1$ peaks beyond $N=82$.
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Linear response calculation using the Canonical-Basis TDHFB with a schematic pairing functional
Journal of Physics: Conference Series, 2011Co-Authors: Shuichiro Ebata, Takashi Nakatsukasa, Kazuhiro YabanaAbstract:A Canonical-Basis formulation of the time-dependent Hartree-Fock-Bogoliubov (TDHFB) theory is obtained with an approximation that the pair potential is assumed to be diagonal in the time-dependent Canonical Basis. The Canonical-Basis formulation significantly reduces the computational cost. We apply the method to linear-response calculations for even-even nuclei. E1 strength distributions for proton-rich Mg isotopes are systematically calculated. The calculation suggests strong Landau damping of giant dipole resonance for drip-line nuclei.
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Canonical-Basis Time-Dependent Hartree-Fock-Bogoliubov Theory and Linear-Response Calculation for Light to Heavy Nuclei
2011Co-Authors: Shuichiro EbataAbstract:We have developed a new theory to study excited states and dynamics of atomic nuclei, which we call the Canonical-Basis time-dependent Hartree-Fock-Bogoliubov (Cb-TDHFB). The CbTDHFB is a simplified theory of the full TDHFB theory, treating pairing energy functional with a BCS-like approximation which is assumed to be diagonal in the Canonical Basis. Implementing the theory with a real-space and real-time method, we can describe nuclear excitations and dynamics taking account of deformation effects and pairing correlations, even for heavy nuclei with a reasonable computational costs. In this thesis, we first present a derivation of the CbTDHFB theory and we apply the method to linear-response calculations for even-even light to heavy nuclei and demonstrate its capability and accuracy by comparing our results with recent calculations of the quasi-particle random-phase approximation (QRPA) which is equivalent to the small amplitude limit of TDHFB, with Skyrme functionals. We derived the Cb-TDHFB equations starting with the full TDHFB equations, introducing a simplified form for the pairing energy functional. In the derivation, we start with the ordinary TDHFB equation written in terms of the time-dependent generalized density matrix R(t) which is composed of the time-dependent normal density matrix ρ(t) and the pairing tensor κ(t). We then rewrite the equation in the Canonical Basis, which diagonalize ρ(t). The derived TDHFB equations in the Canonical Basis has a very simple form. However, they are not useful practically for a general case since it costs much to obtain the Canonical Basis themselves at each time. Solving the time-dependent equation for the Canonical Basis is as difficult as solving the full TDHFB equation. This difficulty disappears if we employ a simplified pairing energy density functional, which is equivalent to that employed in the BCS approximation for ground state calculations. For linear response calculations, we present results of the Cb-TDHFB calculations for excited states of some spherical and deformed nuclei to show performance of the method. We show strength functions of isovector dipole and isoscalar quadrupole excitations for some spherical and deformed nuclei. First, we show the comparison results of Cb-TDHFB with the QRPA in order to confirm the justification of Canonical-Basis formulation and the reduction of computational cost with this new framework. We show isoscalar quadrupole strength functions of neutron-rich nucleus 34Mg for confirmation of our new method, and also discuss full self-consistent calculations of 24Mg as an example of light nucleus and 208Pb and 154Sm as an example of heavy nuclei, in order to be clear, especially, the effects of spin-orbit and Coulomb residual interaction. Next, in order to show typical strength functions for spherical and deformed nuclei, we discuss isovector dipole and isoscalar quadrupole mode for 34Si as an example of spherical nucleus, for 34Mg as an example of prolate deformed nucleus and for 24Ne as an example of oblate deformed nucleus. For a confirmation of computational cost of the calculation using Cb-TDHFB, we isovector dipole strength functions of deformed heavy nuclei 172Yb and 236−240U. We show then the comparison our results with experimental data for photo-nuclear reaction cross sections. And we also show systematic calculations low-energy E1 strength which is often called Pygmy dipole resonance and which is well-known as a important strength to understand nucleosynthesis. In this thesis, we discuss the appearance of low-energy E1 strength functions of C, O, Ne, Mg, Si, S, Ar and Ca isotopes which are relatively light nuclei.
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Canonical-Basis time-dependent Hartree-Fock-Bogoliubov theory and linear-response calculations
Physical Review C, 2010Co-Authors: Shuichiro Ebata, Takashi Nakatsukasa, Tsunenori Inakura, Kenichi Yoshida, Yukio Hashimoto, Kazuhiro YabanaAbstract:We present simple equations for a Canonical-Basis (Cb) formulation of the time-dependent Hartree-Fock-Bogoliubov (TDHFB) theory. The equations are obtained from the TDHFB theory with an approximation that the pair potential is assumed to be diagonal in the Cb. The Cb formulation significantly reduces the computational cost. We apply the method to linear-response calculations for even-even light nuclei and demonstrate its capability and accuracy by comparing our results with recent calculations of the quasiparticle random-phase approximation with Skyrme functionals. We show systematic studies of E1 strength distributions for Ne and Mg isotopes. The evolution of the low-lying pygmy strength seems to be determined by the interplay of several factors, which include the neutron excess, the separation energy, the neutron-shell effects, the deformation, and the pairing.
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LINEAR RESPONSE CALCULATION USING Canonical-Basis TDHFB WITH A SCHEMATIC PAIRING FUNCTIONAL
Modern Physics Letters A, 2010Co-Authors: Shuichiro Ebata, Takashi Nakatsukasa, T. Inakura, Y. Hashimoto, Kazuhiro YabanaAbstract:We derive the Canonical-Basis Time-Dependent Hartree-Fock-Bogoliubov (CbTDHFB) equations using time-dependent variational principle with a special pairing energy functional. We obtain the isoscalar quadrupole strength functions for Magnesium isotopes with small-amplitude CbTDHFB calculation in the three-dimensional coordinate-space representation.
Kazuhiro Yabana - One of the best experts on this subject based on the ideXlab platform.
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Linear response calculation using the Canonical-Basis TDHFB with a schematic pairing functional
Journal of Physics: Conference Series, 2011Co-Authors: Shuichiro Ebata, Takashi Nakatsukasa, Kazuhiro YabanaAbstract:A Canonical-Basis formulation of the time-dependent Hartree-Fock-Bogoliubov (TDHFB) theory is obtained with an approximation that the pair potential is assumed to be diagonal in the time-dependent Canonical Basis. The Canonical-Basis formulation significantly reduces the computational cost. We apply the method to linear-response calculations for even-even nuclei. E1 strength distributions for proton-rich Mg isotopes are systematically calculated. The calculation suggests strong Landau damping of giant dipole resonance for drip-line nuclei.
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Canonical-Basis time-dependent Hartree-Fock-Bogoliubov theory and linear-response calculations
Physical Review C, 2010Co-Authors: Shuichiro Ebata, Takashi Nakatsukasa, Tsunenori Inakura, Kenichi Yoshida, Yukio Hashimoto, Kazuhiro YabanaAbstract:We present simple equations for a Canonical-Basis (Cb) formulation of the time-dependent Hartree-Fock-Bogoliubov (TDHFB) theory. The equations are obtained from the TDHFB theory with an approximation that the pair potential is assumed to be diagonal in the Cb. The Cb formulation significantly reduces the computational cost. We apply the method to linear-response calculations for even-even light nuclei and demonstrate its capability and accuracy by comparing our results with recent calculations of the quasiparticle random-phase approximation with Skyrme functionals. We show systematic studies of E1 strength distributions for Ne and Mg isotopes. The evolution of the low-lying pygmy strength seems to be determined by the interplay of several factors, which include the neutron excess, the separation energy, the neutron-shell effects, the deformation, and the pairing.
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LINEAR RESPONSE CALCULATION USING Canonical-Basis TDHFB WITH A SCHEMATIC PAIRING FUNCTIONAL
Modern Physics Letters A, 2010Co-Authors: Shuichiro Ebata, Takashi Nakatsukasa, T. Inakura, Y. Hashimoto, Kazuhiro YabanaAbstract:We derive the Canonical-Basis Time-Dependent Hartree-Fock-Bogoliubov (CbTDHFB) equations using time-dependent variational principle with a special pairing energy functional. We obtain the isoscalar quadrupole strength functions for Magnesium isotopes with small-amplitude CbTDHFB calculation in the three-dimensional coordinate-space representation.
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Linear Response Calculation using Canonical‐Basis TDHFB with a schematic pairing functional
2010Co-Authors: Shuichiro Ebata, Takashi Nakatsukasa, T. Inakura, Y. Hashimoto, Kazuhiro YabanaAbstract:We derive the Canonical‐Basis Time‐Dependent Hartree‐Fock‐Bogoliubov (CbTDHFB) equations using time‐dependent variational principle with a special pairing energy functional. We obtain the isoscalar quadrupole strength functions for Neon isotopes with small‐amplitude CbTDHFB calculation in the three‐dimensional coordinate‐space representation.