14286968
An interpretation of multigraviton amplitudes
Abstract We obtain alternative expressions for the multigraviton tree level amplitudes and discuss their general properties. In particular, by analogy with Yang–Mills theory, we find that some combinatoric structure can be carried by a Chan–Paton factor of general relativity as a gauge theory.
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...
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.
119222076
On the deconfining limit in (2+1)-dimensional Yang–Mills theory
Abstract We consider ( 2 + 1 ) -dimensional Yang–Mills theory on S 1 × S 1 × R in the framework of a Hamiltonian approach developed by Karabali, Kim and Nair. The deconfining limit in the theory can be discussed in terms of one of the S 1 radii of the torus ( S 1 × S 1 ), while the other radius goes to infinity. We find that the limit agrees with the previously known result for a dynamical propagator mass of a gluon. We also make comparisons with numerical data.
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 $S^8$.
44215083
Fuzzy S(4) and its construction
We present construction of fuzzy S, utilizing the fact that CP is an S bundle over S. Fuzzy S is obtained by imposing an additional algebraic constraint on fuzzy CP. Hence, as in the case of fuzzy CP = SU(4)/U(3), fuzzy S is globally defined on R with the additional constraint on top of the construction of fuzzy CP. We consider the commutative limit of fuzzy S and find that it naturally gives commutative S in terms of homogeneous coordinates on CP. We also discuss exact matrix-function correspondence of fuzzy S. In conclusion, it is proposed that fuzzy S is described by a certain form of block-diagonal matrix whose embedding square matrix represents fuzzy CP.
18150688
Theory of Nuclear Reactions Leading to Superheavy Elements
Dynamical reaction theory is presented for synthesis of superheavy elements. Characteristic features of formation and surviving are discussed, which combinedly determine final residue cross sections of superheavy elements. Preliminary results on Z=114 are also given.
53058436
WHAT CAN WE LEARN FROM THE FISSION TIME OF THE SUPER-HEAVY ELEMENTS?
Recent experiments performed at GANIL with a crystal blocking technique have shown direct evidences of long fission times in the Super-Heavy Elements (SHE) region. Aimed to localize the SHE island of stability, can these experiments give access to the fission barrier and then to the shell-correction energy? In this paper, we calculate the fission time of heavy elements by using a new code, KEWPIE2, devoted to the study of the SHE. We also investigate the effect of potential structure beyond the saddle on the fission time.
122223146
Limitation on heavy ion fusion and nuclear level density at high excitation energies
Over a wide energy range, the limitation on fusion is interpreted from the properties of the compound nuclear level density obtained by taking into account the finiteness of the nucleus. The essential point is to use the shell model single particle bound states in the calculation of the grand partition function. The critical angular momentum for fusion is estimated in connection with the critical temperature for fusion.
121781942
Time-dependent mean-field description for multiple electron transfer in slow ion-cluster collisions
121106621
Diffusion mechanism for synthesis of superheavy elements
The fusion-fission process in heavy systems is analyzed by the Smoluchowski equation with the finite-range droplet model potential of no pocket and the temperature-dependent shell correction energy which generates the pocket around the spherical shape. The evaporation residue cross sections of superheavy elements have been shown to have an optimum value at a certain initial temperature, due to the balance between the diffusibility for fusion at high temperature and the restoration of the shell correction energy against fission at low temperature. {copyright} {ital 1997} {ital The American Physical Society}