Polarization-Free Quantum Fields and Interaction

A new approach to the inverse scattering problem proposed by Schroer, is applied to two-dimensional integrable quantum field theories. For any two-particle S-matrix S ₂ which is analytic in the physical sheet, quantum fields are constructed which are localizable in wedge-shaped regions of Minkowski space and whose two-particle scattering is described by the given S ₂. These fields are polarization-free in the sense that they create one-particle states from the vacuum without polarization clouds. Thus they provide examples of temperate polarization-free generators in the presence of nontrivial interaction.     

Ordered hadron S-Matrix

An ordered hadron S-matrix is developed that accommodates an arbitrary number of “neighbors” for each particle. Automatic features are baryon-number conservation and zero triality. The ordered Hilbert space splits into a set of non-communicating sectors each characterized by a “skeleton” graph whose external edges can be given aquark interpretation. Selection rules are found that generalize the OZI rules.     

On the Connection between Particles and Poles of the S-Matrix

In axiomatic S-matrix theory it is usually assumed that stable particles give rise to simple poles of the S-matrix for real negative energies while unstable particles give rise to poles close to the real axis on an unphysical sheet of the energy Riemann surface. The stable particle — pole association has been known for a long time not to be always true. For example in potential scattering what is relevant in this case in fact is not the S-matrix but the Jost function. The zeroes of this function for real negative energies are in fact in one-to-one correspondence with the bound states, while the correspondence may break down for the poles of the S-matrix. On the other hand it has recently been pointed out that there also is in general no connection between unstable particles and poles of the S-matrix.     

Strong Coupling Problems of S-Matrix Equations

The analytic continuation of the solutions of nonlinear S-matrix equations for large values of a coupling parameter is investigated.     

Causality and Dispersion Relations and the Role of the S-Matrix in the Ongoing Research

The adaptation of the Kramers-Kronig dispersion relations to the causal localization structure of QFT led to an important project in particle physics, the only one with a successful closure. The same cannot be said about the subsequent attempts to formulate particle physics as a pure S-matrix project. The feasibility of a pure S-matrix approach are critically analyzed and their serious shortcomings are highlighted. Whereas the conceptual/mathematical demands of renormalized perturbation theory are modest and misunderstandings could easily be corrected, the correct understanding about the origin of the crossing property requires the use of the mathematical theory of modular localization and its relation to the thermal KMS condition. These new concepts, which combine localization, vacuum polarization and thermal properties under the roof of modular theory, will be explained and their potential use in a new constructive (nonperturbative) approach to QFT will be indicated. The S-matrix still plays a predominant role but, different from Heisenberg’s and Mandelstam’s proposals, the new project is not a pure S-matrix approach. The S-matrix plays a new role as a “relative modular invariant”.     

Factorizable S-Matrix and Symmetry Operator With Toroidal Rapidity Values

We constructed the factorizable S-matrix and obtained the symmetry operator which commutes with the S-matrix and has a new form of "coproduct",the elements of which depend on the parameters defining the toroidal rapidity surface.By defining a new operator which commutes with the symmetry operator the Yang-Baxter equation can be obtained.Finally,the relation between the broken Z_N symmetric model and the chiral Potts model was expressed explicitly in the selfdual genus zero limit.     

Dirac Formalism for Arbitrary Spin in S-Matrix Theory

The S-matrix formalism is built up from the beginning, for particles with and without mass, through systematic use of the representation D_s,0 D_0,s of the homogeneous Lorentz group. Only concepts referring to space and time are considered. Within the framework of the formalism, the close interdependence between CPT, spin and statistics, crossing symmetry and unitarity is explicitly emphasized. The concepts of intrinsic parity, spin-flip and particle conjugation are re-examined. A comparison is made with conventional field-theoretic formalism.     

Compositeness Criteria of Particles in Quantum Field Theory and S-Matrix Theory

A review is given of recent developments in compositeness arguments of particles in the framework of Lagrangian field theory and S-matrix theory.     

S-Matrix singularities in scattering of charged particles on hydrogen-like targets

The scattering of a charged particle on an excited degenerate state of a hydrogen-like system is considered. The threshold and angular singularities of binary scattering amplitudes in this problem are studied. For these singularities closed-form analytical representations are obtained.     

S-Matrix formalism for particles interacting with phonon fields: Coherent state representation

We apply the quasiparticle picture to the interaction between a fermion and a boson field using a coherent states representation of theS matrix. Its matrix elements between single particle states are explicitly evaluated in terms of a path integral. The method is extended to include dispersion in the excitation spectrum and applied to the case of a metal with electron-hole symmetry. Its relation with perturbation theory is discussed and the second order perturbative result for polarons in insulators is recovered.     

S-Matrix formalism calculation of atomic transition probabilities with inclusion of polarization effects

A universal, semi-empirical procedure is proposed for including polarization of the core by the outer electrons of an atom in calculations of radiative transition probabilities based on the S-matrix approach. A calculation was carried out of dipole transition probabilities between low lying configurations of sodium-like ions for nuclear charges Z = 16 to 40 and for aluminum-like ions with nuclear charges Z = 21 to 40.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, Vol. 32, No. 12, pp. 73–77, December, 1989.     

A Novel Formulation of the Fourier Model Method in S-Matrix Form for Arbitrary Shaped Gratings

A new formula has been proposed for analyzing arbitrary shaped-gratings. The formula is in very simple form, is always suitable for all the gratings of arbitrary profiles, any depth, and any permittivity. The new formula has a character of satisfying rigorously the energy-flux conservation. The effectiveness and its characters have been confirmed by numerical examples. The numerical examples have shown that the new formula is superior to the classical formulas with Fourier series technique in convergence, computing precision, and stability.     

Lorentz Generators for the Maxwell Field and Gauge Fixing

We propose a direct derivation of the Lorentz generators for the four-potential of electrodynamics on the basis of Wigner's theorem. The derivation relies on a study of the behaviour of polarisation vectors under k-space differentiation. The Coulomb and Lorenz gauges are discussed in that respect, and gauge invariance under Poincare′transformations is examined. The Poincar′e generators given by Bia lynicki-Birula and Bia lynicka-Birula are found to correspond to the Coulomb gauge case.     

η-Weak-Pseudo-Hermiticity Generators and Radially Symmetric Hamiltonians

A class η-weak-pseudo-Hermiticity generators for spherically symmetric non-Hermitian Hamiltonians are presented. An operators-based procedure is introduced so that the results for the 1D Schrödinger Hamiltonian may very well be reproduced. A generalization beyond the nodeless states is proposed. Our illustrative examples include η- weak-pseudo-Hermiticity generators for the non-Hermitian weakly perturbed 1D and radial oscillators, and the non-Hermitian perturbed radial Coulomb.     

Generators of nuclear collisions at the LHC energy

Current versions of the most popular generators of ultrarelativistic heavy-ion collisions are used to simulate central (b<3 fm) Pb + Pb collisions at the LHC energy, $\sqrt s = 6A$ TeV. The charged-particle density predicted by the generators for the mid-rapidity range, dN _ch/dη, varies in a wide range, from about 2000 to about 6000. Moreover, even for a given generator, it depends strongly on model parameters and can vary from 10 to 100%.