Search Results for « S-matrix theory »

Intense-field many-body S -matrix theory (IM S T) provides a systematic ab initio approach to investigate the dynamics of atoms and molecules interacting with intense laser radiation. We review the derivation of IM S T as well as its diagrammatic representation and point out its advantage over the conventional 'prior' and 'post' expansions which are shown to be special cases of IM S T. The practicality and usefulness of the theory is illustrated by its application to a number of current problems of atomic and molecular ionization in intense fields. We also present a consistent S -matrix formulation of the quantum amplitude for high harmonic generation (HHG) and point out some of the most general properties of HHG radiation emitted by a single atom as well as its relation to coherent emission from many atoms. Experimental results for single and double (multiple) ionization of atoms and the observed distributions of coincidence measurements are analysed and the dominant mechanisms behind them are discussed. Ionization of more complex systems such as diatomic and polyatomic molecules in intense laser fields is analysed as well using IM S T and the results are discussed with special attention to the role of molecular orbital symmetry and molecular orientation in space. The review ends with a summary and a brief outlook.

We formulate an $S$-matrix theory in which localization effects of the particle interactions involved in a scattering process are consistently taken into account. In the limit of an infinite spread of all interactions, the $S$-matrix assumes its standard form. To better understand the significance of the emerging quantum phenomena in this formalism, we consider a solvable field-theoretic model with spatial Gaussian spreads at the interaction vertices. This solvable model, which was previously introduced in the literature, enables accurate descriptions of detection regions that are either close to or far from the source. In close analogy with light diffraction in classical optics, we call these two regions near-field and far-field zones, or the Fresnel and Fraunhofer regions. We revisit the question whether mixed mediators produce an oscillating pattern if their detection occurs in the Fresnel region. Besides corroborating certain earlier findings of the $S$-matrix amplitude in the forward Fresnel and Fraunhofer regimes, we observe several novel features with respect to its angular dependence which have not been accounted before in the literature. In particular, we obtain a ``quantum obliquity factor'' that suppresses particle propagation in the backward direction, thereby providing an explicit quantum field-theoretic description for its origin in diffractive optics. Present and future colliders, as well as both short and long baseline neutrino experiments, would greatly benefit from the many predictions that can be offered from such a holistic localized $S$-matrix theory.

Contents: 1. Introduction. 2. The Early Years. 2.1 Living Without Field Theory. 2.2 Initial Postulates. 2.3 Further Postulates. 2.4 QCD and a Final Postulate. 2.5 Analyticity in Field Theory. 3. Axiomatic S-Matrix Theory. 3.1 Unitarity, Bubble Diagrams and Landau Diagrams. 3.2 The Landau Equations and the ``$+~ α$'' Condition. 3.3 Macrocausality and Essential Support. 3.4 The Structure Theorem. 3.5 Local Discontinuity Formulae. 3.6 Good and Bad Functions and the Steinmann Relations. 3.7 Global Discontinuity Formulae. 3.8 CPT, Hermitian Analyticity, etc. 3.9 Holonomy. 4. Asymptotic S-Matrix Theory. 4.1 The Elastic Scattering Asymptotic Dispersion Relation. 4.2 Multiparticle Kinematics and Analyticity Domains. 4.3 Multiparticle Asymptotic Dispersion Relations. 4.4 Classification of Multiple Discontinuities. 5. Multi-Regge Theory. 5.1 Partial-Wave Expansions. 5.2 Froissart-Gribov Continuations. Sommerfeld-Watson Representations. 5.4 Reggeon Unitarity. 6. Reggeon Field Theory. 6.1 Pomeron Phase-Space and the Effective Lagrangian. 6.2 The Critical Pomeron. 6.3 The Super-Critical Pomeron. 7. QCD and the Critical Pomeron. 7.1 Reggeon Diagrams in QCD. 7.2 Color Superconductivity and the Super-Critical Pomeron. 7.3 Quark Saturation and an Infra-Red Fixed Point. 7.4 Uniqueness of the S-Matrix ?

We give a model-independent exact solution in $S$-matrix terms to the problem of relating proper vertex functions and physical scattering amplitudes, a problem studied extensively by Ida. The solution is of the Omn\`es type, supplemented by the solution of some algebraic equations. We use conventional definitions of the renormalization constants ${Z}_{1}$ and ${Z}_{2}$ to study the composite limit (${Z}_{1}={Z}_{2}=0$) in $S$-matrix theory. A model-independent discussion of the same problem is given in terms of the Dyson equations, where essentially the same results are recovered, in a different language. Possible applications to the electromagnetic mass shifts of composite particles are briefly discussed, including problems of gauge invariance.