119414305
Anomalies, local counter terms and bosonization
We re-examine the issue of local counter terms in the analysis of quantum anomalies. We analyze two-dimensional theories and show that the notion of local counter terms need to be carefully defined depending on the physics contents such as whether one is analyzing gauge theory or bosonization. It is shown that a part of the Jacobian, which is apparently spurious and eliminated by a local counter term corresponding to the mass term of the gauge field in gauge theory, cannot be removed by a local counter term and plays a central role by giving the kinetic term of the bosonized field in the context of path integral bosonization.
119411407
Invariant Regularization of Supersymmetric Chiral Gauge Theory
We present a regularization scheme which respects the supersymmetry and the maximal background gauge covariance in supersymmetric chiral gauge theories. When the anomaly cancellation condition is satisfied, the effective action in the superfield background field method automatically restores the gauge invariance without counterterms. The scheme also provides a background gauge covariant definition of composite operators that is especially useful in analyzing anomalies. We present several applications: The minimal consistent gauge anomaly; the super-chiral anomaly and the superconformal anomaly; as the corresponding anomalous commutators, the Konishi anomaly and an anomalous supersymmetric transformation law of the supercurrent (the ``central extension'' of N=1 supersymmetry algebra) and of the R-current.
15855853
Convergence of Scaled Delta Expansion: Anharmonic Oscillator
We prove that the linear delta expansion for energy eigenvalues of the quantum mechanical anharmonic oscillator converges to the exact answer if the order dependent trial frequency {Omega} is chosen to scale with the order as {Omega}={ital CN}{sup {gamma}}; 1/3{lt}{gamma}{lt}1/2, {ital C}{gt}0 as {ital N} {r_arrow} {infinity}. It converges also for {gamma}=1/3, if {ital C}{ge}{alpha}{sub {ital c}} {ital g}{sup 1/3}, {alpha}{sub {ital c}}{congruent}0.570875, where {ital g} is the coupling constant in front of the operator {ital q}{sup 4}/4. The extreme case with {gamma}=1/3, {ital C}={alpha}{sub {ital c}} {ital g}{sup 1/3} corresponds to the choice discussed earlier by Seznec and Zinn-Justin and, more recently, by Duncan and Jones. {copyright} 1995 Academic Press, Inc.
16738479
Gauge Anomaly Associated with the Majorana Fermion in 8k + 1 Dimensions
Using an elementary method, we show that an odd number of Majorana fermions in 8k + 1 dimensions suffer from a gauge anomaly that is analogous to the Witten global gauge anomaly. This anomaly cannot be removed without sacrificing the perturbative gauge invariance. Our construction of higher-dimensional examples (k > 1) makes use of the SO(8) instanton on S 8 .
17223313
CHIRAL ANOMALIES IN THE REDUCED (OR MATRIX) MODEL
We show that, with an appropriate choice of a Dirac operator, there is a remnant of chiral anomalies in the reduced model in which there is no coordinate dependences of the gauge field. This result is obtained by exploring a topological nature of chiral anomalies associated to Ginsparg-Wilson-type lattice Dirac operators.
102488200
Probability Distribution Functional for Equal-time Correlation Functions in Curved Space
We present a systematic method to calculate the probability distribution functional (PDF) for spatial configuration of an interacting field in curved space-time. As an example, we consider PDF for the minimally coupled massive λΦ4 theory up to the first order of the coupling constant and evaluate it both in Minkowski and de Sitter spacetimes. We observe that PDF has an ultraviolet divergence even after the ultraviolet renormalization. This divergence is unavoidable to reproduce finite expectation values; thus some kind of regularization is necessary to write down PDF. As an application of it, a scaling law among multipoint correlation functions in the de Sitter space is found.
14724846
An approach toward the successful supernova explosion by physics of unstable nuclei
We study the explosion mechanism of collapse-driven supernovae by numerical simulations with a new nuclear EOS based on unstable nuclei. We report new results of simulations of general relativistic hydrodynamics together with the Boltzmann neutrino-transport in spherical symmetry. We adopt the new data set of relativistic EOS and the conventional set of EOS (Lattimer-Swesty EOS) to examine the influence on dynamics of core-collapse, bounce and shock propagation. We follow the behavior of stalled shock more than 500 ms after the bounce and compare the evolutions of supernova core.
18029655
Influence of the symmetry energy on the birth of neutron stars and supernova neutrinos
We study the influence of the symmetry energy of the equation of state on the thermal evolution of protoneutron stars and the properties of supernova neutrinos by the numerical simulations after the protoneutron stars are formed. As for the equation of state (EOS) of nuclear matter, we take two EOS's with different symmetry energies obtained by the relativistic mean field theory. We find the symmetry energy plays the essential role on the evolution of lepton profiles and the neutrino fluxes.
118431737
A new baryonic equation of state at sub-nuclear densities for core-collapse simulations
We calculate a new equation of state for baryons at sub-nuclear densities meant for the use in core-collapse simulations of massive stars. The abundances of various nuclei are obtained together with the thermodynamic quantities. The formulation is the nuclear statistical equilibrium description and the liquid drop approximation of nuclei. The model free energy to minimize is calculated by relativistic mean field theory for nucleons and the mass formula for nuclei with atomic number up to ~1000. We have also taken into account the pasta phase, thanks to which the transition to uniform nuclear matter in our equation of state (EOS) occurs in the conventional manner: nuclei are not dissociated into nucleons but survive right up to the transition to uniform nuclear matter. We find that the free energy and other thermodynamical quantities are not very different from those given in the H. Shen's EOS, one of the standard EOSs that adopt the single nucleus approximation. On the other hand, the average mass is systematically different, which may have an important ramification to the rates of electron captures and coherent neutrino scatterings on nuclei in supernova cores. It is also interesting that the root mean square of the mass number is not very different from the average mass number, since the former is important for the evaluation of coherent scattering rates on nuclei but has been unavailable so far. The EOS table is currently under construction, which will include the weak interaction rates.
17130454
Dynamics and Neutrino Signal of Black Hole Formation in Nonrotating Failed Supernovae. II. Progenitor Dependence
We study the progenitor dependence of black hole formation and its associated neutrino signal due to the gravitational collapse of a nonrotating massive star, following on our previous study of a single progenitor model. We aim to clarify whether the dynamical evolution toward black hole formation occurs in the same manner for different progenitors and to examine whether the characteristic of neutrino bursts having short duration and rapidly increasing average energies is a general one. We perform numerical simulations using general relativistic neutrino radiation hydrodynamics to follow the dynamical evolution from the collapse of 40 and 50 M☉ presupernova models to black hole formation via contracting proto-neutron stars. For the three progenitor models studied in this paper, we find that black hole formation occurs ~0.4-1.5 s after core bounce through an increase of the proto-neutron star mass, accompanied by a short and energetic neutrino burst. The density profile of the progenitor is important in determining the accretion rate onto the proto-neutron star and, therefore, the duration of the neutrino burst. We compare the neutrino bursts of black hole-forming events from different progenitors and discuss whether they can be used to probe clearly the progenitor and the dense matter.
118715119
EFFECTS OF RESISTIVITY ON MAGNETIZED CORE-COLLAPSE SUPERNOVAE
We studied the role of turbulent resistivity in the core-collapse of a strongly magnetized massive star, carrying out two-dimensional resistive-MHD simulations. Three cases with different initial strengths of magnetic field and rotation are investigated: (1) a strongly magnetized rotating core, (2) a moderately magnetized rotating core, and (3) a very strongly magnetized non-rotating core. In each case, one ideal-MHD model and two resistive-MHD models are computed. As a result of these computations, each model shows an eruption of matter assisted by magnetic acceleration (and also by centrifugal acceleration in the rotating cases). We found that resistivity attenuates the explosion in cases 1 and 2, while it enhances the explosion in case 3. We also found that in the rotating cases, the main mechanisms for the amplification of a magnetic field in the post-bounce phase are an outward advection of the magnetic field and a twisting of poloidal magnetic field lines by differential rotation, which are somewhat dampened down with the presence of resistivity. Although magnetorotational instability seems to occur in the rotating models, it plays only a minor role in magnetic field amplification. Another impact of resistivity is that on the aspect ratio. In the rotating cases, a large aspect ratio of the ejected matter, >2.5, attained in an ideal-MHD model is reduced to some extent in a resistive model. These results indicate that resistivity possibly plays an important role in the dynamics of strongly magnetized supernovae.