C. Rebbi

Quantum dynamics of a massless relativistic string

Abstract We develop the classical and quantum mechanics of a massless relativistic string, the light string, which is characterized by an action proportional to the area of the world sheet swept out by the string in space time. We show that, classically, there are only D -2 dynamically independent components among the D functions x μ ( σ , τ ) which represent the world sheet ( D is the dimension of space time). Quantizing only these independent components, we find that the angular momentum operators suggested by the correspondence principle generate O( D -1,1) only when the first excited state is a photon, i.e., a spin-one massless state, and when D = 26. By allowing additional degrees of freedom in the quantum mechanics, we are able to quantize the string in a Lorentz covariant manner for any value of D and any mass for the first excited state. In this latter scheme the full Fock space contains negative norm states. However, when D ⩽ 26 for a massless first excited state and D ⩽ 25 for a real massive first excited state, the physical states span a positive subspace of the Fock space. The excitation spectrum of the light string coincides with the space of physical states in the dual resonance model for unit intercept of the leading Regge trajectory. We point out the connection of this work to previous studies of the physical states in dual models.

A proposal for Monte Carlo simulations of fermionic systems

Abstract We suggest a possible extension of the Monte Carlo technique to systems with fermionic degrees of freedom. We study in detail the application to an elementary example.

Monte Carlo computations in lattice gauge theories

Abstract The formulation of gauge theories on Euclidean space-time lattices and the application of the Monte Carlo computational technique to the ensuing systems are reviewed. A variety of numerical results obtained for lattice gauge theories are presented and discussed.

Dual models and relativistic quantum strings

Abstract The string picture of the dual resonance model is reviewed. It is shown that, if we assume for a relativistic string propagating through space time an action proportional to the area of the surface of evolution, the spectrum of states of the corresponding quantum system coincides with the spectrum of states of the conventional dual resonance model and contains only transverse excitations if suitable consistency conditions are met. It is shown also how an interaction among strings can be introduced so as to obtain the dual amplitudes as quantum mechanical transition amplitudes. The main properties of the spectrum of the closed string (Pomeron sector of the conventional dual model) and a generalization to include spin degrees of freedom are discussed. Throughout the article, the results obtained in the theory of the string are compared with the results obtained in the conventional approach to dual models. The reader is assumed to have some familiarity with the general properties of dual models. The review of G. Veneziano in Physics Reports, for instance, may provide the required introduction.

SU(2) String Tension, Glueball Mass and Interquark Potential by Monte Carlo Computations

Monte Carlo simulations of the SU(2) gauge system on a large (164) lattice and with high statistics are performed to determine several quantities of physical interest. Previous evaluations of the ratio between string tension, σ, and scale constant, Λ0, are confirmed. The mass of the glueball is found to be approximately 3√σ and the potential between static charges at very small separation is measured.

Monte Carlo Simulation of the Massive Schwinger Model

Abstract In this article we apply a previously proposed defermionization method to the study of two-dimensional QED (massive Schwinger model). We find good evidence for the spontaneous breaking of axial symmetry, i.e., 〈 ψ ψ〉≠0 in the massless limit.

Numerical simulations of quantum chromodynamics

Abstract A previously proposed method to perform Monte Carlo simulations with dynamical fermions is applied to lattice QCD. The main features of the computational technique are reviewed and results for some selected quantities, such as the average plaquette action and the quark condensate 〈 ψ ψ〉 are presented. Both the dependence on the quark mass and on the number of flavors are considered. An estimate of the scale parameter in the presence of fermions is given.

Hadron masses in quenched quantum chromodynamics

Abstract Hadron masses are calculated by numerical methods in the quenched approximation to lattice QCD. The analysis is performed at β =6.0 on a large (16 3 ×32) lattice, with Kogut-Susskind fermions and bare quark masses down to m q a =0.01. The results are in satisfactory agreement with experimental data and the value of the scale parameter, determined by fixing the mass of the ϱ-meson, is consistent with independent estimates based on the calculation of the string tension.

The phase structure of a non-abelian gauge Higgs field system

Abstract The phase structure of a non-abelian gauge Higgs field system is studied by Monte Carlo (MC) simulations. The analysis is done on a 4 4 lattice and approximating both the gauge group and the Higgs manifold by the icosahedral subgroup of SU(2). Results are presented for a Higgs field in the fundamental representation, in which case the symmetry is completely broken for sufficiently strong coupling, and for a Higgs field in the adjoint representation, in which case a U(1) symmetry (approximated by Z 10 ) survives. No evidence for a “Coulomb pocket” is found.

CONSIDERATIONS ON NUMERICAL ANALYSIS OF QCD

Abstract We discuss the strategy to remove the quenched approximation and to minimize systematical and statistical errors occurring in the numerical simulation of lattice QCD. We suggest a way to compute the flavour singlet sector of the mass spectrum, and comment about the relation between the fluctuations of the mass values and the scattering amplitudes.