16024304
Noncommutative gravity: Fuzzy sphere and others
Gravity on noncommutative analogues of compact spaces can give a finite mode truncation of ordinary commutative gravity. We obtain the actions for gravity on the noncommutative two-sphere and on the noncommutative ${\mathbf{CP}}^{2}$ in terms of finite dimensional $(N\ifmmode\times\else\texttimes\fi{}N)$ matrices. The commutative large N limit is also discussed.
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.
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.
119278846
Holonomies of gauge fields in twistor space 4: Functional MHV rules and one-loop amplitudes
Abstract We consider generalization of the Cachazo–Svrcek–Witten (CSW) rules to one-loop amplitudes of N = 4 super Yang–Mills theory in a recently developed holonomy formalism in twistor space. We first reconsider off-shell continuation of the Lorentz-invariant Nair measure for the incorporation of loop integrals. We then formulate an S-matrix functional for general amplitudes such that it implements the CSW rules at quantum level. For one-loop MHV amplitudes, the S-matrix functional correctly reproduces the analytic expressions obtained in the Brandhuber–Spence–Travaglini (BST) method. Motivated by this result, we propose a novel regularization scheme by use of an iterated-integral representation of polylogarithms and obtain a set of new analytic expressions for one-loop NMHV and N 2 MHV amplitudes in a conjectural form. We also briefly sketch how the extension to one-loop non-MHV amplitudes in general can be carried out.
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.
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.
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.
120154304
Evidence for nuclear Landau-Zener effect: New resonance mechanism in heavy-ion reactions
Characteristic resonancelike peaks recently observed in the angle-integrated inelastic cross sections for the /sup 13/C-/sup 17/O system are understood in terms of the Landau-Zener excitation mechanism at energy level crossings. Angle-integrated inelastic cross sections estimated with the Landau-Zener formula show a series of resonancelike peaks as a function of incident energy, each of which is associated with a grazing angular momentum of the relative motion between nuclei. Simple expressions are given for resonance energies and ''widths'' of new ''resonances.'' This resonance mechanism is a new one, which has not been known in nuclear reactions nor in atomic collisions, although it is based on the well-known Landau-Zener promotion mechanism.
18300734
Spin-Alignment and Quasi-Molecular Resonances in Heavy-Ion Collision
Fragment-fragment-$\gamma$ triple coincidence measurements of the $^{28}$Si~$+$~$^{28}$Si reaction at E$_{\rm c.m.}$~=~55.8 MeV, carefully chosen to populate a well known quasi-molecular resonance in $^{56}$Ni, have been performed at the VIVITRON tandem facility by using the Eurogam Phase~II $\gamma$-ray spectrometer. In the $^{28}$Si~$+$~$^{28}$Si reaction, the resonant behavior of the $^{28}$Si $+$ $^{28}$Si exit-channel is clearly observed by the present fragment-fragment coincidence data. The more unexpected result is the spin disalignment of the $^{28}$Si $+$ $^{28}$Si resonance. This has been demonstrated first by the measured angular distributions of the elastic 0$^{+}$, inelastic 2$^{+}$ and mutual excitation channels 2$^{+}-2^{+}$, which are dominated by a unique and pure partial wave with L = 38 ${\rm \hbar}$, and has been confirmed by measuring their particle-$\gamma$ angular correlations with Eurogam Phase II. The spin disalignment supports new molecular model predictions, in which the observed resonance would correspond to the ''Butterfly mode''. A discussion concerning the {\it spin alignment and spin disalignment} for different systems : $^{12}$C~$+$~$^{12}$C, $^{24}$Mg~$+$~$^{24}$Mg and $^{28}$Si~$+$~$^{28}$Si will be given.}
365149
On Theoretical Problems in Synthesis of Superheavy Elements
Towards precise predictions of residue cross sections of the superheavy elements, recent theoretical developments of reaction mechanisms are presented, together with the remaining problems which give rise to ambiguities in absolute values of cross sections predicted.
121781942
Time-dependent mean-field description for multiple electron transfer in slow ion-cluster collisions