Calculating the Fierz Transformation for Higher Orders

We consider the higher-order Fierz transformation, which corresponds to expanding a product of $\bar\psi\Gamma\psi$ terms into a sum of products of Dirac densities and currents. It is shown that the Fierz transformation can be obtained by solving a large system of linear equations with fractional complex coefficients, which is practical at least up to fourth power.Comment: 6 pages, 3 table

On different actions for the vacuum of bosonic string field theory

We study a family of kinetic operators in string field theory describing the theory around the closed string vacuum. Those operators are based on the analytical classical solutions of Takahashi and Tanimoto and are analogous to the pure ghost action usually referred to as "vacuum string field theory," but are much more general, and less singular than the pure ghost operator. The closed string vacuum is related to the D-brane vacuum by large, singular, gauge transformations or field redefinition, and all those different representations are related to each other by small gauge transformations. We try to clarify the nature of this singular gauge transformation. We also show that by choosing the Siegel gauge one recovers the propagator proposed in hep-th/0207266 that generates closed string surfaces.Comment: 15 page

Closed String Amplitudes from Gauge Fixed String Field Theory

Closed string diagrams are derived from cubic open string field theory using a gauge fixed kinetic operator. The basic idea is to use a string propagator that does not generate a boundary to the world sheet. Using this propagator and the closed string vertex, the moduli space of closed string surfaces is covered, so closed string scattering amplitudes should be reproduced. This kinetic operator could be a gauge fixed form of the string field theory action around the closed string vacuum.Comment: 10 pages, revtex, 3 figures. Discussion on the covering of moduli expanded, version to appear in PR

Brane Decay and Death of Open Strings

We show how open strings cease to propagate when unstable D-branes decay. The information on the propagation is encoded in BSFT two-point functions for arbitrary profiles of open string excitations. We evaluate them in tachyon condensation backgrounds corresponding to (i) static spatial tachyon kink (= lower dimensional BPS D-brane) and (ii) homogeneous rolling tachyon. For (i) the propagation is restricted to the directions along the tachyon kink, while for (ii) all the open string excitations cease to propagate at late time and are subject to a collapsed light cone characterized by Carrollian contraction of Lorentz group.Comment: 19 pages, published version (typos corrected, a reference added

Time Dependent Solution in Cubic String Field Theory

We study time dependent solutions in cubic open string field theory which are expected to describe the configuration of the rolling tachyon. We consider the truncated system consisting of component fields of level zero and two, which are expanded in terms of cosh n x^0 modes. For studying the large time behavior of the solution we need to know the coefficients of all and, in particular, large n modes. We examine numerically the coefficients of the n-th mode, and find that it has the leading n-dependence of the form (-\beta)^n \lambda^{-n^2} multiplied by a peculiar subleading part with peaks at n=2^m=4,8,16,32,64,128,.... This behavior is also reproduced analytically by solving simplified equations of motion of the tachyon system.Comment: 22 pages, 12 figures, LaTeX2e, v3:minor correction

Statistical methods applied to composition studies of ultrahigh energy cosmic rays

The mass composition of high energy cosmic rays above $10^{17}$ eV is a crucial issue to solve some open questions in astrophysics such as the acceleration and propagation mechanisms. Unfortunately, the standard procedures to identify the primary particle of a cosmic ray shower have low efficiency mainly due to large fluctuations and limited experimental observables. We present a statistical method for composition studies based on several measurable features of the longitudinal development of the CR shower such as $N_{max}$, $X_{max}$, asymmetry, skewness and kurtosis. Principal component analysis (PCA) was used to evaluate the relevance of each parameter in the representation of the overall shower features and a linear discriminant analysis (LDA) was used to combine the different parameters to maximize the discrimination between different particle showers. The new parameter from LDA provides a separation between primary gammas, proton and iron nuclei better than the procedures based on $X_{max}$ only. The method proposed here was successfully tested in the energy range from $10^{17}$ to $10^{20}$ eV even when limitations of shower track length were included in order to simulate the field of view of fluorescence telescopes

Spin oscillations in transient diffusion of a spin pulse in n-type semiconductor quantum wells

By studying the time and spatial evolution of a pulse of the spin polarization in $n$-type semiconductor quantum wells, we highlight the importance of the off-diagonal spin coherence in spin diffusion and transport. Spin oscillations and spin polarization reverse along the the direction of spin diffusion in the absence of the applied magnetic field are predicted from our investigation.Comment: 5 pages, 4 figures, accepted for publication in PR

The Tachyon Potential in the Sliver Frame

We evaluate the tachyon potential in the Schnabl gauge through off-shell computations in the sliver frame. As an application of the results of our computations, we provide a strong evidence that Schnabl's analytic solution for tachyon condensation in open string field theory represents a saddle point configuration of the full tachyon potential. Additionally we verify that Schnabl's analytic solution lies on the minimum of the effective tachyon potential.Comment: v1: 19 pages, 1 figure, 1 table; v2: 20 pages, 1 figure, 2 tables, 1 reference added, comments added; v3: 21 pages, 1 figure, 2 tables, 4 references added, comments adde

Specific heat and high-temperature series of lattice models: interpolation scheme and examples on quantum spin systems in one and two dimensions

We have developed a new method for evaluating the specific heat of lattice spin systems. It is based on the knowledge of high-temperature series expansions, the total entropy of the system and the low-temperature expected behavior of the specific heat as well as the ground-state energy. By the choice of an appropriate variable (entropy as a function of energy), a stable interpolation scheme between low and high temperature is performed. Contrary to previous methods, the constraint that the total entropy is log(2S+1) for a spin S on each site is automatically satisfied. We present some applications to quantum spin models on one- and two- dimensional lattices. Remarkably, in most cases, a good accuracy is obtained down to zero temperature.Comment: 10 pages (RevTeX 4) including 11 eps figures. To appear in Phys. Rev.

Patterns in Open String Field Theory Solutions

In open string field theory the kinetic operator mixes matter and ghost sectors, and thus the ghost structure of classical solutions is not universal. Nevertheless, we have found from numerical analysis that certain ratios of expectation values for states involving pure ghost excitations appear to be universal. We give an analytic expression for these ratios and find good evidence that they are common to all known solutions of open string field theory, including the tachyon vacuum solution, lump solutions and string fields representing marginal deformations. We also draw attention to a close correspondence between the expectation values for the pure matter components in the tachyon vacuum solution and those in the solution of a simpler equation for a ghost number zero string field. Finally we observe that the action of L_0 on the tachyon condensate gives a state that is approximately factorized into a matter and a ghost part.Comment: 21 pages, LaTe