The scattering amplitude for four off-shell tachyons from functional integrals

We use functional integral techniques to calculate the scattering amplitude for four open off-shell tachyons in Witten's string field theory and show that the residues of the first three poles agree with those obtained using oscillator methods.     

Multi-loop Feynman integrals and conformal quantum mechanics

New algebraic approach to analytical calculations of D-dimensional integrals for multi-loop Feynman diagrams is proposed. We show that the known analytical methods of evaluation of multi-loop Feynman integrals, such as integration by parts and star-triangle relation methods, can be drastically simplified by using this algebraic approach. To demonstrate the advantages of the algebraic method of analytical evaluation of multi-loop Feynman diagrams, we calculate ladder diagrams for the massless φ³ theory. Using our algebraic approach we show that the problem of evaluation of special classes of Feynman diagrams reduces to the calculation of the Green functions for specific quantum mechanical problems. In particular, the integrals for ladder massless diagrams in the φ³ scalar field theory are given by the Green function for the conformal quantum mechanics.     

The singularities of the integrals in Mayer's ionic solution theory

The terms of the expression previously obtained by Friedman for the cluster integral sum in Mayer's theory are examined as to order in total ion concentration, c, at the limit, c = 0. The order of the singularity at c = 0 is calculated for several of those terms of the irreducible cluster integrals that correspond to graphs of low connectivity but with an arbitrary number of vertices. On the basis of these calculations and two postulates concerning the relation of the singularities of these integrals to others, it is concluded that the terms of the cluster integral sum, when arranged in order of increasing index, are also in increasing order of concentration, and that the first term, κ ³/12π, has a lower order than any other. The order in concentration of the higher terms depends on whether the third moment of the concentration of charge types, σc₈z₈ ³, vanishes, as it does in solutions of electrolytes of symmetrical charge type.     

Point-like structure and off-shell dual strings

We argue that in a consistent off-shell dual formalism the amplitude for the emission of a scalar off-shell state by a string consists of two components. One of these contains the particle poles in the off-shell leg and the other is intimately related to the insertion of a point-like energy density on the string. As a result, the amplitude for a string to emit a zero momentum scalar state into the vacuum (which may be relevant for spontaneous symmetry breaking) is described by the amplitude for a finite fraction of the energy in the string to collapse to a spatial point at some time (this fraction and its space-time position being integrated over). The off-shell amplitudes have an elegant formulation in terms of a set of “confined modes” which can be assigned quark flavour quantum numbers to reproduce the Chan-Paton scheme.We suggest the dual model be modified by allowing for the coupling of scalar closed strings to the vacuum and the resulting effect on the space-time structure of dual Green functions is described.We find that even the emission of a single zero-momentum closed string modifies the elastic amplitude in a significant manner, leading to a power-behaved fixed-angle cross section in contrast to the usual exponential decrease of the dual model. This arises from point-like scattering between energy densities accumulating in the colliding strings. The relationship between the fixed angle and Regge limits is discussed. The fixed angle behaviour is found to be the asymptotic limit in momentum transfer of a fixed pole that arises in the Regge limit.     

Exclusive deuteron electrodisintegration and off-shell effects

In the framework of a covariant formalism relying on a relativistic deuteron wave function (RDWF) with one nucleon on the mass shell one deals with an exclusive deuteron electrodisintegration process in the impulse approximation. The influence of the off-shell effect of the RDWF on possible analytic and dynamic cross-section factorizations is investigated. Contributions of direct and interference electrodisintegration amplitudes have been calculated taking into account the off-shell behavior of the electromagnetic nucleon vertex. Corresponding results are compared with data on three kinematics of the SaclayD(e, é p)n experiments. It is shown that off-shell effects both of the RDWF and electromagnetic nucleon vertex must be considered properly in order to get reliable information on the high-momentum component of the RDWF.     

Particles and events in classical off-shell electrodynamics

Despite the many successes of the relativistic quantum theory developed by Horwitz et al., certain difficulties persist in the associated covariant classical mechanics. In this paper, we explore these difficulties through an examination of the classical. Coulomb problem in the framework of off-shell electrodynamics. As the local gauge theory of a covariant quantum mechanics with evolution paratmeter τ, off-shell electrodynamics constitutes a dynamical theory of ppacetime events, interacting through five τ-dependent pre-Maxwell potentials. We present a straightforward solution of the classical equations of motion, for a test event traversing the field induced by a “fixed” event (an event moving uniformly along the time axis at a fixed point in space). This solution is seen to be unsatisfactory, and reveals the essential difficulties in the formalism at the classical levels. We then offer a new model of the particle current—as a certain distribution of the event currents on the worldline—which eliminates these difficulties and permits comparison of classisical off-shell electrodynamics with the standard Maxwell theory. In this model, the “fixed” event induces a Yukawa-type potential, permitting a semiclassical identification of the pre-Maxwell time scale λ with the inverse mass of the intervening photon. Numerical solutions to the equations of motion are compared with the standard Maxwell solutions, and are seen to coincide when λ≳10⁻⁶ seconds, providing an initial estimate of this parameter. It is also demonstrated that the proposed model provides a natural interpretation for the photon mass cut-off required for the renormalizability of the off-shell quantum electrodynamics.     

Taming the off-shell Higgs boson

Journal of Experimental and Theoretical Physics - We study the off-shell Higgs data in the process pp → h (*) → Z (*) Z (*) → 4l, to constrain deviations of the Higgs couplings....     

Nuclear matter with off-shell propagation

Symmetric nuclear matter is studied within the conserving, self-consistent T-matrix approximation. This approach involves off-shell propagation of nucleons in the ladder diagrams. The binding energy receives contributions from the background part of the spectral function, away from the quasiparticle peak. The Fermi energy at the saturation point fulfills the Hugenholz-Van Hove relation. In comparison to the Brueckner-Hartree-Fock approach, the binding energy is reduced and the equation of state is stiffer. Received: 16 April 2002 / Accepted: 10 June 2002 / Published online: 26 November 2002 RID="a" ID="a"e-mail: bozek@sothis.ifj.edu.pl Communicated by A. Molinari     

Self-consistent approach to off-shell transport

The properties of two forms of the gradient expanded Kadanoff-Baym equations, i.e., the Kadanoff-Baym and Botermans-Malfliet forms, suitable for describing the transport dynamics of particles and resonances with broad spectral widths, are discussed in context of conservation laws, the definition of a kinetic entropy, and the possibility of numerical realization. Recent results on exact conservations of charge and energy-momentum within Kadanoff-Baym form of quantum kinetics based on local coupling schemes are extended to two cases relevant in many applications. These concern the interaction via a finite-range potential and, relevant in nuclear and hadron physics, e.g., for the pion-nucleon interaction, the case of derivative coupling.     

The Lorentz force and energy-momentum for off-shell electromagnetism

The kinematics of pre-Maxwell electrodynamics is examined and interpretations of these fields is found through an examination of the associated Lorentz force and the structure of the energy-momentum tensor.     

Green's functions for off-shell electromagnetism and spacelike correlations

The requirement of gauge invariance for the Schwinger-DeWitt equations, interpreted as a manifestly covariant quantum theory for the evolution of a system in spacetime, implies the existence of a five-dimensional pre-Maxwell field on the manifold of spacetime and proper time . The Maxwell theory is contained in this theory; integration of the field equations over restores the Maxwell equations with the usual interpretation of the sources. Following Schwinger's techniques, we study the Green's functions for the five-dimensional hyperbolic field equations for both signatures ± [corresponding to O(4, 1) or O(3, 2) symmetry of the field equations] of the proper time derivative. The classification of the Green's functions follows that of the four-dimensional theory for massive fields, for which the mass squared may be positive or negative, respectively. The Green's functions for the five-dimensional field are then given by the Fourier transform over the mass parameter. We derive the Green's functions corresponding to the principal part _P and the homogeneous function ₁ ; all of the Green's functions can be expressed in terms of these, as for the usual field equations with definite mass. In the O(3, 2) case, the principal part function has support for x²², corresponding to spacelike propagation, as well as along the light cone x²=0 (for =0). There can be no transmission ofinformation in spacelike directions, with this propagator, since the Maxwell field, obtained by integration over , does not contain this component of the support. Measurements are characterized by such an integration. The spacelike field therefore can dynamically establish spacelike correlations.     

A remark on off-shell phase-shift analysis

We consider the ππ → ππ amplitude that is extracted from πN → ππN experiments, and show that off-mass-shell unitarity can only be used to resolve phase-shift ambiguities if no inelasticity is present. If there is inelasticity in the two-pion subsystem, the off-mass-shell structure does not reduce the on-mass-shell continuum ambiguities in any way. Similar remarks apply to electroproduction, considered as off-shell photoproduction.     

On- and off-shell Jost functions and their integral representations

By judicious exploitation of the transpose operator relation in conjunction with the differential equations of special functions of mathematical physics, integral representations of the on- and off-shell Jost functions are derived from the particular integrals of the inhomogeneous Schrödinger equation. Using the particular integral of the inhomogeneous Schrödinger equation, exact analytical expressions for the Coulomb and Coulomb plus Yamaguchi off-shell Jost solutions are constructed in the maximal reduced form. As a case study, the limiting behaviours and the on-shell discontinuities of the Coulomb plus Yamaguchi Jost solutions are verified numerically.     

Pion-nucleon vertex function with an off-shell nucleon

We present a model calculation for the π-N vertex function in the case in which there is a single off-mass-shell nucleon and a (nearly) on-mass-shell pion. We find very strong effects due to the P₁₁ resonance at 1470 MeV. We provide a simple parametrization of the vertex function in the case that at least one nucleon is on its mass shell.