FEYNMAN GRAPH RULES FOR IINN-INTERACTION AND MATRIX ELEMENTS FOR A SIMPLIFIED pπ0 → pπ0 MODEL IN 5-DIMENSIONAL CONFORMAL QFT

1989 ◽  
Vol 04 (20) ◽  
pp. 5411-5432
Author(s):  
G. A. LUNA-ACOSTA
Keyword(s):  
Feynman Graph ◽  
Matrix Elements ◽  
Hadron Spectra ◽  
Feynman Graphs ◽  
Matter Interaction ◽  
Interesting Possibility ◽  
The Matrix ◽  
The Individual ◽  
Energy Dependent ◽  
Infinite Sum

Recently we reported a successful fitting of the kinematic predictions of the Mass Theory of 5-dimensional Conformal Relativity to the Hadron Spectra. We use results obtained there to study the dynamical properties of the trilinear boson-matter interaction Lagrangian implied by isospin SU(2) gauge invariance. The isovector massive gauge boson allows for two interpretations: a J = 1 field and the 5-D derivative of a J = 0 field. We construct the Feynman Graphs for the ΠNN-interaction and show that (1) any given graph is actually an infinite sum of similar graphs, one for each member of the Conformal Family Field of the virtual Hadron and (2) that the individual coupling of each of these members depends on its mass, giving rise to an effectively energy-dependent coupling. Based on these features, we speculate on the interesting possibility that Perturbation Theory may be usable for hadron processes and calculate the matrix elements for a simplified model of pπ0 → pπ0 to second order. Useful comparisons are made with the analogous treatment in ordinary QFT.

The electronic states of composite systems

1956 ◽  
Vol 235 (1203) ◽  
pp. 537-543 ◽  
Keyword(s):  
Density Operator ◽  
Spectroscopic Data ◽  
Composite System ◽  
Three Dimensional ◽  
Transition Density ◽  
Matrix Elements ◽  
Multipole Moments ◽  
Composite Systems ◽  
The Matrix ◽  
The Individual

In order to relate the electronic eigenstates of a composite system to those of its constituent parts one requires the matrix elements of the interaction Hamiltonian between the unperturbed states of the system . It is shown that in the absence of electron exchange these matrix elements, which are usually approximated as multipole series, may be accurately expressed as electrostatic repulsion energies between three-dimensional electric distributions localized on the subsystems. These distributions are them selves the matrix elements of the electric density operator between the eigenstates of the individual subsystems, and their multipole moments are identified as the permanent moments of the subsystems in their various states and the transition moments between these states. The name ‘transition density' is proposed for the off-diagonal elements of the electric density operator, and an examination of its properties suggests that the transition density may be a useful concept for summarizing and systematizing spectroscopic data on atomic and molecular assemblies.

scholarly journals On the Modular Operator of Mutli-component Regions in Chiral CFT

2021 ◽  
Author(s):  
Stefan Hollands
Keyword(s):  
Field Theory ◽  
Integral Equation ◽  
Hilbert Problem ◽  
Matrix Elements ◽  
New Approach ◽  
Conformal Field ◽  
The Matrix ◽  
Kms Condition ◽  
Modular Operator ◽  
Riemann Hilbert Problem

AbstractWe introduce a new approach to find the Tomita–Takesaki modular flow for multi-component regions in general chiral conformal field theory. Our method is based on locality and analyticity of primary fields as well as the so-called Kubo–Martin–Schwinger (KMS) condition. These features can be used to transform the problem to a Riemann–Hilbert problem on a covering of the complex plane cut along the regions, which is equivalent to an integral equation for the matrix elements of the modular Hamiltonian. Examples are considered.

scholarly journals Analytical angular solutions for the atom–diatom interaction potential in a basis set of products of two spherical harmonics: two approaches

2021 ◽  
Author(s):  
Mariusz Pawlak ◽  
Marcin Stachowiak
Keyword(s):  
Spherical Harmonics ◽  
Interaction Potential ◽  
Chem Phys ◽  
Basis Set ◽  
Matrix Elements ◽  
Trigonometric Functions ◽  
Variational Theory ◽  
Molecular Collision ◽  
The Matrix ◽  
Analytical Expressions

AbstractWe present general analytical expressions for the matrix elements of the atom–diatom interaction potential, expanded in terms of Legendre polynomials, in a basis set of products of two spherical harmonics, especially significant to the recently developed adiabatic variational theory for cold molecular collision experiments [J. Chem. Phys. 143, 074114 (2015); J. Phys. Chem. A 121, 2194 (2017)]. We used two approaches in our studies. The first involves the evaluation of the integral containing trigonometric functions with arbitrary powers. The second approach is based on the theorem of addition of spherical harmonics.

scholarly journals Synthesis and Characterization of a Bioartificial Polymeric System with Potential Antibacterial Activity: Chitosan-Polyvinyl Alcohol-Ampicillin

Molecules ◽  
2018 ◽  
Vol 23 (12) ◽  
pp. 3109 ◽  
Author(s):  
Andres Bernal-Ballen ◽  
Jorge Lopez-Garcia ◽  
Martha-Andrea Merchan-Merchan ◽  
Marian Lehocky
Keyword(s):  
Antibacterial Activity ◽  
Polyvinyl Alcohol ◽  
Statistical Significance ◽  
Antibacterial Properties ◽  
Intermolecular Forces ◽  
Polymeric System ◽  
Bacterial Strains ◽  
Natural Polymers ◽  
The Matrix ◽  
The Individual

Bio-artificial polymeric systems are a new class of polymeric constituents based on blends of synthetic and natural polymers, designed with the purpose of producing new materials that exhibit enhanced properties with respect to the individual components. In this frame, a combination of polyvinyl alcohol (PVA) and chitosan, blended with a widely used antibiotic, sodium ampicillin, has been developed showing a moderate behavior in terms of antibacterial properties. Thus, aqueous solutions of PVA at 1 wt.% were mixed with acid solutions of chitosan at 1 wt.%, followed by adding ampicillin ranging from 0.3 to 1.0 wt.% related to the total amount of the polymers. The prepared bio-artificial polymeric system was characterized by FTIR, SEM, DSC, contact angle measurements, antibacterial activity against Staphylococcus aureus and Escherichia coli and antibiotic release studies. The statistical significance of the antibacterial activity was determined using a multifactorial analysis of variance with ρ < 0.05 (ANOVA). The characterization techniques did not show alterations in the ampicillin structure and the interactions with polymers were limited to intermolecular forces. Therefore, the antibiotic was efficiently released from the matrix and its antibacterial activity was preserved. The system disclosed moderate antibacterial activity against bacterial strains without adding a high antibiotic concentration. The findings of this study suggest that the system may be effective against healthcare-associated infections, a promising view in the design of novel antimicrobial biomaterials potentially suitable for tissue engineering applications.

Notizen: The Dipole Moment Function of HF Molecule Using Morse Potential

1977 ◽  
Vol 32 (8) ◽  
pp. 897-898 ◽  
Author(s):  
Y. K. Chan ◽  
B. S. Rao
Keyword(s):  
Wave Equation ◽  
Dipole Moment ◽  
Potential Function ◽  
Electric Dipole ◽  
Morse Potential ◽  
Moment Function ◽  
Matrix Elements ◽  
The Matrix ◽  
Vibration Rotation ◽  
Experimental Values

Abstract The radial Schrödinger wave equation with Morse potential function is solved for HF molecule. The resulting vibration-rotation eigenfunctions are then used to compute the matrix elements of (r - re)n. These are combined with the experimental values of the electric dipole matrix elements to calculate the dipole moment coefficients, M 1 and M 2.

Leach Behavior of SRL TDS-131 Defense Waste Glass in Water at High&Low Flow Rates

1983 ◽  
Vol 26 ◽  
Author(s):  
Aaron Barkatt ◽  
William Sousanpour ◽  
Alisa Barkatt ◽  
Morad A. Boroomand ◽  
Pedro B. Macedo
Keyword(s):  
Contact Time ◽  
Protective Layer ◽  
High Flow ◽  
Low Flow ◽  
Matrix Elements ◽  
Flow Rates ◽  
Low Concentrations ◽  
Controlling Mechanism ◽  
The Matrix ◽  
Leach Behavior

ABSTRACTLeach tests carried out on SRL TDS-131 Defense Waste Class indicate that at high flow rates the controlling mechanism is simple corrosion. The matrix elements (Si, Al) are leached out at rates similar to those of the leaching of the alkalis and of boron, and the leaching process is nearly linear with time. At slow flow rates (below 1 m/yr) leaching becomes controlled by the build-up of a protective layer. Al and most of the Si remain in the leached surface layer. The leach rates decrease in the course of the test before leveling off at constant values which are almost inversely proportional to the contact time, indicating that leachate concentrations have become solubility-limited. The low concentrations observed at this stage indicate the formation of alteration products.

Sign in / Sign up

Export Citation Format

Share Document