scholarly journals A REPRESENTATION OF THE S MATRIX ELEMENT FOR A HIGHLY SINGULAR POTENTIAL

1966 ◽  
Vol 22 (9) ◽  
pp. 1038
Author(s):  
CHQU LON-SHIANG
Keyword(s):  
Matrix Element ◽  
Singular Potential ◽  
S Matrix

scholarly journals A REPRESENTATION OF THE S MATRIX ELEMENT FOR A HIGHLY SINGULAR POTENTIAL

1965 ◽  
Vol 21 (5) ◽  
pp. 983
Author(s):  
DAI YUAN-BEN
Keyword(s):  
Matrix Element ◽  
Singular Potential ◽  
S Matrix

A Multichannel “Potential Curves Hopping” Model for Inelastic Collisions

1986 ◽  
Vol 41 (5) ◽  
pp. 704-714
Author(s):  
D. Campos ◽  
J. M. Tejeiro ◽  
F. Cristancho
Keyword(s):  
Matrix Element ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Inelastic Collisions ◽  
Interaction Matrix ◽  
Quantum Mechanical ◽  
Interaction Matrix Element ◽  
S Matrix ◽  
Hopping Model ◽  
Potential Curves

We introduce a multichannel “potential curves hopping” model and obtain the exact quantum mechanical S-matrix by solving the associated set of coupled second-order ordinary differential equations that describes the inelastic collisions between atomic particles. The only assumption is that the interaction matrix element between each pair of channels (say, γ and β) is of the form Uγβ(r) = Uβγ(r) =: Uγβ δ( r - rγβ), where δ (c) is the Dirac deltafunction, and rγβ and Uγβ are parameters which can be chosen freely.Semiclassical techniques can be incorporated directly in the theory if the Schrödinger equations for the uncoupled channels allow this treatment. The formulation is particularized to the two-channel problem and illustrated with a semiclassical example the He+ + Ne problem at 70.9 eV.

scholarly journals Elimination of Primitive Divergents from Field Theory by Means of Complex Coupling Constants

1973 ◽  
Vol 26 (6) ◽  
pp. 703
Author(s):  
AF Nicholson
Keyword(s):  
Field Theory ◽  
Matrix Element ◽  
Spinor Field ◽  
Scalar Fields ◽  
Coupling Constants ◽  
Quantum Fields ◽  
Iteration Theory ◽  
Spinor Fields ◽  
S Matrix ◽  
Physical Particle

LSZ. iteration theory is extended to accommodate quantum fields coupled by complex constants, while retaining a positive metric and a Hermitian Hamiltonian. Interpolating and particle (~in, out) fields are linked by an operator U(t) which is nonunitary, so that Haag's theorem may be avoided. It is shown that U(t) may be rendered sufficiently well-behaved as t -+ � 00 to allow development of the iteration series for the T function. For certain combinations of fields the coupling constants and masses can then be chosen so as to eliminate the primitive divergents from the iteration series for any S-matrix element. The theory is illustrated by two models: four spinor plus two scalar fields, and the electromagnetic plus several spinor fields. In the second model not every spinor field corresponds to a stable physical particle, and the LSZ formalism is extended to allow for this.

Linear eigenvalue -S matrix element relations for the regular polyhedra

1982 ◽  
Vol 29 (2) ◽  
pp. 76-81 ◽  
Author(s):  
G. Riblet
Keyword(s):  
Matrix Element ◽  
Regular Polyhedra ◽  
S Matrix

scholarly journals Effective action of type II superstring theories at order α′3: NS-NS couplings

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Mohammad R. Garousi
Keyword(s):  
Matrix Element ◽  
Effective Action ◽  
Sigma Model ◽  
Linear Sigma Model ◽  
Type Ii ◽  
Gauge Invariant ◽  
Duality Transformations ◽  
S Matrix ◽  
Minimum Number ◽  
Superstring Theories

Abstract Recently, it has been shown that the minimum number of gauge invariant couplings for B-field, metric and dilaton at order α′3 is 872. These couplings, in a particular scheme, appear in 55 different structures. In this paper, up to an overall factor, we fix all parameters in type II supertirng theories by requiring the reduction of the couplings on a circle to be invariant under T-duality transformations. We find that there are 445 non-zero couplings which appear in 15 different structures. The couplings are fully consistent with the partial couplings that have been found in the literature by the four-point S-matrix element and by the non-linear Sigma model methods.

Threshold behaviour in quantum field theory

1952 ◽  
Vol 210 (1102) ◽  
pp. 388-404 ◽  
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Matrix Element ◽  
Rest Mass ◽  
Momentum Conservation ◽  
Quantum Field ◽  
Branch Points ◽  
Threshold Values ◽  
Physical Assumption ◽  
S Matrix

The elements of the S matrix are functions of the energies and momenta of a set of incident particles. For sufficiently high relative energies of the incident particles new particles of non-zero rest mass can be created. At the thresholds for such creation processes the S matrix will have a complicated behaviour. This behaviour is investigated when the S matrix is calculated by means of renormalized quantum field theory. For a typical matrix element there are thresholds of two main types. The first is a creation threshold below which the element is zero on account of energy-momentum conservation; mathematically this is due to a Dirac S function factor. The second is an interference threshold above which a competing process has non-zero probability. Interference thresholds are closely connected with the appearance of displaced poles in the integration. It is shown that a matrix element will always contain a term having a branch point at an interference threshold; the path of analytic continuation round these branch points is obtained from the physical assumption that particles interact through their retarded fields. Between the threshold values it is shown that the S matrix elements are analytic functions of the energies and momenta of the incident particles.

EVALUATION OF ELASTIC NΔ SCATTERING AMPLITUDE FROM INELASTIC pp→NΔ AMPLITUDE

1990 ◽  
Vol 05 (03) ◽  
pp. 207-214 ◽  
Author(s):  
N. HIROSHIGE ◽  
M. KAWASAKI ◽  
W. WATARI ◽  
M. YONEZAWA
Keyword(s):  
Matrix Element ◽  
Scattering Amplitudes ◽  
Partial Wave ◽  
Energy Region ◽  
Scattering Amplitude ◽  
Transition Amplitude ◽  
Channel Approximation ◽  
S Matrix

In the dibaryon energy region we have evaluated the NΔ→NΔ (5S2) partial-wave S-matrix element from recently obtained pp→NΔ transition amplitude by combining with the information on pp→pp, pp→πd, and πd→πd scattering amplitudes in the three-channel approximation. One of the two solutions allowed by the unitarity shows an anticlockwise rotating behavior.

scholarly journals S -matrix element of two R-R and one NS states

2017 ◽  
Vol 96 (6) ◽  
Author(s):  
Mojtaba Mohammadzadeh ◽  
Mohammad R. Garousi
Keyword(s):  
Matrix Element ◽  
S Matrix
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