Quantum scattering from a class of anisotropic potentials

The nonrelativistic quantum scattering problem for a class of 3-dimensional anisotropic, or explicitly angle-dependent potentials, is evaluated. The S-matrix is expressed in terms of the time-dependent propagator and evaluated using earlier results of a path integral solution. The scattering amplitude is then obtained from the S-matrix.     

CGC formalism with two sources

In this work we extend the JIMWLK formalism to the two-source problem. The S-matrix for the forward scattering can be written in a double functional integral representation which involves the usual functional integral for the gluon field and the spin path integral for the external color sources. Modifications needed in the light-cone gauge are discussed. Using our source term we compute the produced gluon field and discuss the duality of the high energy evolution kernel in the pA collision.     

The time-dependent mean-field S-matrix theory in the adiabatic limit

To elucidate the spirit of the recently developed time-dependent mean-field S-matrix theory we apply it to low-energy elastic collisions and solve the corresponding temporally non-local mean-field equation under the assumption that the relative motion proceeds adiabatically. Neglecting the exchange processes this assumption leads to a pure potential scattering picture. The phase shift extracted from the corresponding mean-field S-matrix coincides with the WKB result of potential scattering.     

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.     

The Gell-Mann-Goldberger formula for long-range potential scattering

A derivation of the Gell-Mann-Goldberger (GG) formula and cut-off versions of this formula for the T-matrix involving long-range potentials is given. The derivation is based on the time-dependent and recently developed stationary formalisms for scattering via long-range potentials. A stationary S-operator expression for two-body Coulomb-like scattering is derived. Using the well-known expression for the off-energy-shell “T-matrix” for a pure Coulomb potential the energy-shell limit of this stationary expression is shown to yield the pure Coulomb scattering amplitude. A proof of the convergence of the perturbation series corresponding to the Gell-Mann-Goldberger formula for the two-body Coulomb-like T-matrix is given.     

Action principle of Bogoliubov coefficients

It is shown that the Schwinger action principle uniquely determines the Bogoliubov coefficients connecting in- and out-states for an oscillator with a time-dependent spring constant, and hence for a charged particle field in a constant homogeneous electric field. This allows a complete construction of the S-matrix in the external field approximation. Especially it allows an easy calculation of 〈out∥in〉, the vacuum-to-vacuum amplitude, in this approximation. The method is applied to electromagnetism embedded in a non-abelian gauge group.     

Representation of osp (2, 2) q (2) andS-matrix of super sine-Gordon theory

We investigate the representations of the osp (2, 2) _q ⁽²⁾ algebra, which leads to theS-matrix of super sine-Gordon theory. TheS-matrix has been derived from supersymmetric conformal field theory with some assumptions. We show that the conjecturedS-matrix can be derived from the representation theory using a correspondence between the representations of osp (1, 2) _q and those of sl(2) _q .     

Quark scattering amplitudes with quasi-elastic unitarity

We consider quark-quark scattering at high energies and fixed momentum transfer. In a model where in the s and u channel intermediate states only gluons with sufficiently small transverse momenta are emitted, the scattering amplitudes are expressed in terms of the S-matrix elements for exactly soluble two-dimensional field theories.     

A new approach to potential scattering

An approximate integral-representation of theS-matrix in partial-wave expansion is derived for a scalar Schrödinger particle in a central field. The method consists of linearizingCalogero's Riccati equation for the interpolatingS-matrix in such a way that the solution of the linearized equation deviates as little as possible from the exact one. TheS-matrix thus obtained exhibits exact crossing-symmetry and uniform convergence independent of the coupling constant of the scattering potential. In the weak coupling limit it is especially shown thatour method is more accurate than the second Born approximation. In the second part of the paper we specialize ourS-matrix to low and large energies. At low energies, a general integral for the scattering length is obtained and at large energies the summation over all angular momenta is carried out yielding an expression for the scattering amplitude.     

Particle creation in a time-dependent electric field revisited

We adopt the general formalism for analyzing evolution of gaussian states of quantized fields in time-dependent backgrounds in the Schrodinger picture (presented in detail in Mahajan and Padmanabhan [G. Mahajan, T. Padmanabhan, Gen. Rel. Grav. 40 (2008) 661]) to study the example of a spatially uniform electric field background (in a time-dependent gauge) which is kept turned on for a finite duration of time. In particular, we study the time-dependent particle content, defined in terms of the concept of instantaneous eigenstates, and describe how it captures the time evolution of the quantized field modes. The actual particle creation process occurs over a relatively short interval in time, and the particle content saturates rather quickly. We also compare the power spectrum of the field modes, computed in the asymptotic limit, with the corresponding situation in a cosmological de Sitter background. Particle creation under the influence of a spiked electric field localized in time, as a particular limiting case of the above general model, is also considered.     

A Particle-Picture Approach to Anomalies in Chiral Gauge Theories

The system of a chiral fermion field coupled to a background gauge field is considered. By taking what we call the particle picture and carefully defining the S-matrix in the Heisenberg picture, we investigate anomalous phenomena in this system. It is shown by explicit calculations that the gauge-field configuration with nonvanishing topological-charge causes anomalous production of particles that is directly responsible for the chiral U(1) anomaly. Unlike the chiral U(1) anomaly, the gauge anomaly, that is, gauge non-invariance of the S-matrix is a problem that arises in the phase of the S-matrix. It is shown that this phase is related to the freedom existing in the quantization method, and that a suitably chosen phase which of course is consistent with the equation of motion can remove the gauge anomaly. Finally, a modified form of path-integral quantization for this system is proposed.     

Statistical reactions with memory and thermalized-nonequilibrated nuclear states

Starting from the Feshbach S-matrix pole expansion we modify the standard statistical model for compound reactions by introducing correlations between fluctuating S-matrix elements with different J (total spin) and π (parity) values. The S-matrix (J, π)-correlations are obtained at the expense of introducing infinitesimally small entrance-exit channel off-diagonal (J, π)-correlations between the random variables of the statistical model. Although later on these correlations are switched off by means of a properly applied limiting procedure, the S-matrix (J, π)-correlations do not vanish and can be strong. The physical origin of the S-matrix (J, π)-correlations resembles the effect of spontaneous symmetry breaking while S-matrix (J, π)-decoherence is due to quantum chaos. Novel reaction mechanism results in the excitation of peculiar nuclear states: The intermediate system is thermalized so that the shape of the spectrum is angle-independent and Maxwellian with angle-independent slope, yet the intermediate nucleus is not equilibrated since the angular distribution is forward-peaked, i.e., memory of the direction of the initial beam is not lost. The existence of thermalized-nonequilibrated nuclear states is supported by data on the 50–100% forward peaking of neutrons in the typically evaporation (1–3.5 MeV) part of the spectrum observed in the ⁹³ N b(n, n′) scattering with E _n = 7 MeV.     

Algebraic solution of the Hubbard model on the infinite interval

We develop the quantum inverse scattering method for the one-dimensional Hubbard model on the infinite line at zero density. This enables us to diagonalize the Hamiltonian algebraically. The eigenstates can be classified as scattering states of particles, bound pairs of particles and bound states of pairs. We obtain the corresponding creation and annihilation operators and calculate the S-matrix. The Hamiltonian on the infinite line is invariant under the Yangian quantum group Y(su(2)). We show that the n-particle scattering states transform like n-fold tensor products of fundamental representations of Y(su(2) ) and that the bound states are Yangian singlet.     

Classical quantization condition in the generalized coherent-state representation with application to many-body systems

On the basis of the ansatz of the single-valuedness for the classically approximated wave function, a classical quantization rule is derived for a dynamical system described by a general class of coherent states. The classical wave function, which is defined on the manifold parametrizing the coherent states, is constructed by an application of the stationary phase approximation to the coherent-state path integral. The general form of the quantization rule for the time-dependent Hartree-Fock solutions is obtained as a particular case.     

Time independent description of thet(d,n)α fusion reaction in the presence of a muon

We describe the (α n μ)—(d t μ) continuum above and below thed+(t μ)₁ s threshold using theR-matrix formalism. The continuum is explicitly constructed in an adiabatic approximation, and the asymptotic phase shifts and amplitudes in all channels are obtained. The energy eigenstates are used to compute the fusion reaction cross section for in-flightd+(t μ) fusion, and fusion reaction rates involving transitions from thed+(t μ)₁ s continuum to be below threshold continuum states.     

P-Matrix and J-Matrix Approaches: Coulomb Asymptotics in the Harmonic Oscillator Representation of Scattering Theory

The relation between the R- and P-matrix approaches and the harmonic oscillator representation of the quantum scattering theory (J-matrix method) is discussed. We construct a discrete analogue of the P-matrix that is shown to be equivalent to the usual P-matrix in the quasiclassical limit. A definition of the natural channel radius is introduced. As a result, it is shown to be possible to use a well-developed technique of R- and P-matrix theory for calculation of resonant states characteristics, scattering phase shifts, etc., in the approaches based on harmonic oscillator expansions, e.g., in nuclear shell-model calculations. The P-matrix is used also for formulation of the method of treating Coulomb asymptotics in the scattering theory in oscillator representation.