56161879
Construction of Fuzzy Spaces and Their Applications to Matrix Models
Quantization of spacetime by means of finite dimensional matrices is the basic idea of fuzzy spaces. There remains an issue of quantizing time, however, the idea is simple and it provides an interesting interplay of various ideas in mathematics and physics. Shedding some light on such an interplay is the main theme of this dissertation. The dissertation roughly separates into two parts. In the first part, we consider a mathematical aspect of fuzzy spaces, namely, their construction. We begin with a review of the construction of fuzzy complex projective spaces CP^k (k=1,2,...) in relation to geometric quantization. We then present the construction of fuzzy S^4, utilizing the fact that CP^3 is an S^2 bundle over S^4. This method is also applicable to the case of fuzzy S^8. In the second part, we consider applications of fuzzy spaces to physics. We first consider gravitational theories on fuzzy spaces, anticipating that they may offer a novel way of regularizing spacetime dynamics. Particularly we obtain actions for gravity on fuzzy S^2 and fuzzy CP^2. We also discuss application to M(atrix) theory. Introducing extra potentials, we show that the theory has new brane solutions whose transverse directions are described by fuzzy S^4 and fuzzy CP^3. The extra potentials can be interpreted as fuzzy versions of differential forms or fluxes, which enable us to discuss compactification models of M(atrix) theory. Compactification down to fuzzy S^4 is discussed and a physically interesting matrix model in four-dimensions is proposed.
17985110
Holonomies of gauge fields in twistor space 2: Hecke algebra, diffeomorphism, and graviton amplitudes
Abstract We define a theory of gravity by constructing a gravitational holonomy operator in twistor space. The theory is a gauge theory whose Chan–Paton factor is given by a trace over elements of Poincare algebra and Iwahori–Hecke algebra. This corresponds to a fact that, in a spinor-momenta formalism, gravitational theories are invariant under spacetime translations and diffeomorphism. The former symmetry is embedded in tangent spaces of frame fields while the latter is realized by a braid trace. We make a detailed analysis on the gravitational Chan–Paton factor and show that an S-matrix functional for graviton amplitudes can be expressed in terms of a supersymmetric version of the holonomy operator. This formulation will shed a new light on studies of quantum gravity and cosmology in four dimensions.
118650221
Holonomies of gauge fields in twistor space 3: Gravity as a square of N=4 theory
Abstract In a recent paper, we show that an S-matrix functional for graviton amplitudes can be described by an N = 8 supersymmetric gravitational holonomy operator in twistor space. In this paper, we obtain an alternative expression for the gravitational holonomy operator such that it can be interpreted as a square of an N = 4 holonomy operator for frame fields, by taking a sum of certain shuffles over ordered indices. The new expression leads to amplitudes of not only spin-2 gravitons but also spin-0 massless particles. We discuss that the squared model is favored as a theory of quantum gravity.
1494294
Construction of fuzzy S**4
We construct a fuzzy $S^4$, utilizing the fact that ${\bf CP}^3$ is an $S^2$ bundle over $S^4$. We find that a fuzzy $S^4$ can be described by a block-diagonal form whose embedding square matrix represents a fuzzy ${\bf CP}^3$. We discuss some pending issues on fuzzy $S^4$, i.e., precise matrix-function correspondence, associativity of the algebra, and etc. Similarly, we also obtain a fuzzy $S^8$, using the fact that ${\bf CP}^7$ is a ${\bf CP}^3$ bundle over $S^8$.
119304812
Application of abelian holonomy formalism to the elementary theory of numbers
We consider an abelian holonomy operator in two-dimensional conformal field theory with zero-mode contributions. The analysis is made possible by use of a geometric-quantization scheme for abelian Chern-Simons theory on S1 × S1 × R. We find that a purely zero-mode part of the holonomy operator can be expressed in terms of Riemann's zeta function. We also show that a generalization of linking numbers can be obtained in terms of the vacuum expectation values of the zero-mode holonomy operators. Inspired by mathematical analogies between linking numbers and Legendre symbols, we then apply these results to a space of Fp = Z/pZ, where p is an odd prime number. This enables us to calculate “scattering amplitudes” of identical odd primes in the holonomy formalism. In this framework, the Riemann hypothesis can be interpreted by means of a physically obvious fact, i.e., there is no notion of “scattering” for a single-particle system. Abelian gauge theories described by the zero-mode holonomy operators will be usef...
56161879
Construction of Fuzzy Spaces and Their Applications to Matrix Models
Quantization of spacetime by means of finite dimensional matrices is the basic idea of fuzzy spaces. There remains an issue of quantizing time, however, the idea is simple and it provides an interesting interplay of various ideas in mathematics and physics. Shedding some light on such an interplay is the main theme of this dissertation. The dissertation roughly separates into two parts. In the first part, we consider a mathematical aspect of fuzzy spaces, namely, their construction. We begin with a review of the construction of fuzzy complex projective spaces CP^k (k=1,2,...) in relation to geometric quantization. We then present the construction of fuzzy S^4, utilizing the fact that CP^3 is an S^2 bundle over S^4. This method is also applicable to the case of fuzzy S^8. In the second part, we consider applications of fuzzy spaces to physics. We first consider gravitational theories on fuzzy spaces, anticipating that they may offer a novel way of regularizing spacetime dynamics. Particularly we obtain actions for gravity on fuzzy S^2 and fuzzy CP^2. We also discuss application to M(atrix) theory. Introducing extra potentials, we show that the theory has new brane solutions whose transverse directions are described by fuzzy S^4 and fuzzy CP^3. The extra potentials can be interpreted as fuzzy versions of differential forms or fluxes, which enable us to discuss compactification models of M(atrix) theory. Compactification down to fuzzy S^4 is discussed and a physically interesting matrix model in four-dimensions is proposed.
119374559
Predictions of the residue cross-sections for the elements Z = 113 and Z = 114
Abstract.A good reproduction of experimental excitation functions is obtained for the 1n reactions producing the elements with Z = 108, 110, 111 and 112 by the combined usage of the two-step model for fusion and the statistical decay code KEWPIE. Furthermore, the model provides reliable predictions of productions of the elements with Z = 113 and Z = 114 which will be a useful guide for plannings of experiments.
121241167
Collisions between metal clusters and multiply charged ions
SummaryMetal clusters are electrically charged by collisions with charged ions through electron transfer reactions from the clusters to the ions. The reaction processes are studied by the time-dependent mean field theory with the usual Local Density Approximation for the exchange-correlation potential. Preliminary results show the interesting feature that collisions with large impact parameters make ionized clusters with relatively low excitation, which gives important new information on the stability of metal clusters against fission.
115177201
Perspectives of nuclear fission
6712709
FROM DI-NUCLEUS TO MONO-NUCLEUS: NECK EVOLUTION IN FUSION OF MASSIVE SYSTEMS
Dynamics of the neck degree of freedom during fusioning process between heavy ions is studied. Time scales of the three degrees of freedom (the relative distance, the neck and the mass-asymmetry) are studied, showing an early equilibration of the neck. This means that a di-nucleus formed by the incident combination of ions quickly forms a mono-nucleus with a superdeformation during the fusion process and that the other two degrees of freedom have to be solved in a coupled way. A brief introduction of Langevin approach and dissipation-fluctuation dynamics is also given and of the application to the synthesis of the superheavy elements.
121916152
On stochastic approaches of nuclear dynamics
Abstract We present recent developments of stochastic descriptions of nuclear dynamics. We focus on the newly introduced microscopic descriptions, such as stochastic extensions of currently used kinetic equations, as well as on more phenomenological, macroscopic approaches. We show to what extent these stochastic descriptions may offer a proper picture of nuclear dynamics both in strongly out of equilibrium situations, such as the ones encountered in energetic heavy-ion collisions or in closer to equilibrium situations such as the deexcitation of hot nuclei by thermal fission. In Section 1 we present a pedestrian introduction to the stochastic description of dynamical systems. We start from the elementary Brownian motion and introduce the Langevin and Fokker-Planck descriptions of the motion on that occasion. A few words are then spent to discuss the numerical methods developed for simulating stochastic equations. Section 2 of the paper is devoted to a formal introduction and discussion of both macroscopic and microscopic stochastic descriptions of nuclear dynamics. After a brief introduction reminding general concepts of equilibrium statistical physics we focus on microscopic descriptions of the many-body problem. We introduce here the Boltzmann Langevin equation which will provide a basis for many subsequent discussions. After having discussed the obtention of this equation from various points of view (from density matrix and Green's function techniques in particular), we consider reduced versions of this equation as well as a Fokker-Planck alternative. Section 3 is devoted to an analysis of fission by means of Langevin or Fokker-Planck-like approaches. We mainly discuss phenomenological approaches and spend some time in a detailed presentation of the ingredients entering these models. We present results obtained in these dynamical calculations when a proper account of particle evaporation is included for describing the fission of hot nuclei. Critical comparisons with experimental data are also provided. In Section 4 we focus on the application of the Boltzmann Langevin Equation to various situations encountered in energetic nuclear collisions. We first remind some typical examples for which this stochastic approach is both necessary and well suited. Typical applications are nuclear multifragmentation and subthreshold particle production, such as in particular kaon production. We discuss possible simulations of this equation and present some results in realistic calculations of collisions. We particularly focus on the dynamics of collective variables such as the quadrupole moment of the momentum distribution. We finally discuss other numerical simulations developed in the field. The last section before conclusion is devoted to extensions presently developed in the field of microscopic stochastic descriptions of nuclear dynamics. We present as a first step a relativistic version of the theory, then focus on fluid dynamics reductions. We finally discuss in some detail the recently introduced Stochastic time-dependent Hartree-Fock theory, which could provide new interesting developments.