New Phenomenon of Nonlinear Regge Trajectory and Quantum Dual String Theory

The relation between the spin and the mass of an infinite number of particles in a $q$-deformed dual string theory is studied. For the deformation parameter $q$ a root of unity, in addition to the relation of such values of $q$ with the rational conformal field theory, the Fock space of each oscillator mode in the Fubini-Veneziano operator formulation becomes truncated. Thus, based on general physical grounds, the resulting spin-(mass)$^2$ relation is expected to be below the usual linear trajectory. For such specific values of $q$, we find that the linear Regge trajectory turns into a square-root trajectory as the mass increases.Comment: 12 pages, Latex, HU-SEFT R 1994-0

The Hagedorn temperature Revisited

The Hagedorn temperature, T_H is determined from the number of hadronic resonances including all mesons and baryons. This leads to a stable result T_H = 174 MeV consistent with the critical and the chemical freeze-out temperatures at zero chemical potential. We use this result to calculate the speed of sound and other thermodynamic quantities in the resonance hadron gas model for a wide range of baryon chemical potentials following the chemical freeze-out curve. We compare some of our results to those obtained previously in other papers.Comment: 13 pages, 4 figure

Affine Lie Algebras in Massive Field Theory and Form-Factors from Vertex Operators

We present a new application of affine Lie algebras to massive quantum field theory in 2 dimensions, by investigating the $q\to 1$ limit of the q-deformed affine $\hat{sl(2)}$ symmetry of the sine-Gordon theory, this limit occurring at the free fermion point. Working in radial quantization leads to a quasi-chiral factorization of the space of fields. The conserved charges which generate the affine Lie algebra split into two independent affine algebras on this factorized space, each with level 1 in the anti-periodic sector, and level $0$ in the periodic sector. The space of fields in the anti-periodic sector can be organized using level-$1$ highest weight representations, if one supplements the \slh algebra with the usual local integrals of motion. Introducing a particle-field duality leads to a new way of computing form-factors in radial quantization. Using the integrals of motion, a momentum space bosonization involving vertex operators is formulated. Form-factors are computed as vacuum expectation values in momentum space. (Based on talks given at the Berkeley Strings 93 conference, May 1993, and the III International Conference on Mathematical Physics, String Theory, and Quantum Gravity, Alushta, Ukraine, June 1993.)Comment: 13 pages, CLNS 93/125

Two-spin entanglement distribution near factorized states

We study the two-spin entanglement distribution along the infinite $S=1/2$ chain described by the XY model in a transverse field; closed analytical expressions are derived for the one-tangle and the concurrences $C_r$, $r$ being the distance between the two possibly entangled spins, for values of the Hamiltonian parameters close to those corresponding to factorized ground states. The total amount of entanglement, the fraction of such entanglement which is stored in pairwise entanglement, and the way such fraction distributes along the chain is discussed, with attention focused on the dependence on the anisotropy of the exchange interaction. Near factorization a characteristic length-scale naturally emerges in the system, which is specifically related with entanglement properties and diverges at the critical point of the fully isotropic model. In general, we find that anisotropy rule a complex behavior of the entanglement properties, which results in the fact that more isotropic models, despite being characterized by a larger amount of total entanglement, present a smaller fraction of pairwise entanglement: the latter, in turn, is more evenly distributed along the chain, to the extent that, in the fully isotropic model at the critical field, the concurrences do not depend on $r$.Comment: 14 pages, 6 figures. Final versio

Power counting with one-pion exchange

Techniques developed for handing inverse-power-law potentials in atomic physics are applied to the tensor one-pion exchange potential to determine the regions in which it can be treated perturbatively. In S-, P- and D-waves the critical values of the relative momentum are less than or of the order of 400 MeV. The RG is then used to determine the power counting for short-range interaction in the presence of this potential. In the P-and D-waves, where there are no low-energy bound or virtual states, these interactions have half-integer RG eigenvalues and are substantially promoted relative to naive expectations. These results are independent of whether the tensor force is attractive or repulsive. In the 3S1 channel the leading term is relevant, but it is demoted by half an order compared to the counting for the effective-range expansion with only a short-range potential. The tensor force can be treated perturbatively in those F-waves and above that do not couple to P- or D-waves. The corresponding power counting is the usual one given by naive dimensional analysis.Comment: 18 pages, RevTeX (further details, explanation added

Effective boost and "point-form" approach

Triangle Feynman diagrams can be considered as describing form factors of states bound by a zero-range interaction. These form factors are calculated for scalar particles and compared to point-form and non-relativistic results. By examining the expressions of the complete calculation in different frames, we obtain an effective boost transformation which can be compared to the relativistic kinematical one underlying the present point-form calculations, as well as to the Galilean boost. The analytic expressions obtained in this simple model allow a qualitative check of certain results obtained in similar studies. In particular, a mismatch is pointed out between recent practical applications of the point-form approach and the one originally proposed by Dirac.Comment: revised version as accepted for publicatio

On the SO(2,1) symmetry in General Relativity

The role of the SO(2,1) symmetry in General Relativity is analyzed. Cosmological solutions of Einstein field equations invariant with respect to a space-like Lie algebra G_r, with r between 3 and 6 and containing so(2,1) as a subalgebra, are also classified.Comment: 10 pages, latex, no figure

Infinite Symmetry in the Quantum Hall Effect

Free planar electrons in a uniform magnetic field are shown to possess the symmetry of area-preserving diffeomorphisms ($W$-infinity algebra). Intuitively, this is a consequence of gauge invariance, which forces dynamics to depend only on the flux. The infinity of generators of this symmetry act within each Landau level, which is infinite-dimensional in the thermodynamical limit. The incompressible ground states corresponding to completely filled Landau levels (integer quantum Hall effect) are shown to be infinitely symmetric, since they are annihilated by an infinite subset of generators. This geometrical characterization of incompressibility also holds for fractional fillings of the lowest level (simplest fractional Hall effect) in the presence of Haldane's effective two-body interactions. Although these modify the symmetry algebra, the corresponding incompressible ground states proposed by Laughlin are again symmetric with respect to the modified infinite algebra.Comment: 28 page

Information geometry of Gaussian channels

We define a local Riemannian metric tensor in the manifold of Gaussian channels and the distance that it induces. We adopt an information-geometric approach and define a metric derived from the Bures-Fisher metric for quantum states. The resulting metric inherits several desirable properties from the Bures-Fisher metric and is operationally motivated from distinguishability considerations: It serves as an upper bound to the attainable quantum Fisher information for the channel parameters using Gaussian states, under generic constraints on the physically available resources. Our approach naturally includes the use of entangled Gaussian probe states. We prove that the metric enjoys some desirable properties like stability and covariance. As a byproduct, we also obtain some general results in Gaussian channel estimation that are the continuous-variable analogs of previously known results in finite dimensions. We prove that optimal probe states are always pure and bounded in the number of ancillary modes, even in the presence of constraints on the reduced state input in the channel. This has experimental and computational implications: It limits the complexity of optimal experimental setups for channel estimation and reduces the computational requirements for the evaluation of the metric: Indeed, we construct a converging algorithm for its computation. We provide explicit formulae for computing the multiparametric quantum Fisher information for dissipative channels probed with arbitrary Gaussian states, and provide the optimal observables for the estimation of the channel parameters (e.g. bath couplings, squeezing, and temperature).Comment: 19 pages, 4 figure