Applications

2017 ◽  
Author(s):  
Laurent Baulieu ◽  
John Iliopoulos ◽  
Roland Sénéor
Keyword(s):  
Phase Space ◽  
Cross Sections ◽  
Scattering Amplitude ◽  
Field Theories ◽  
Tree Approximation ◽  
General Field ◽  
Feynman Rules

Physical applications. Introduction of the scattering amplitude and cross sections. The phase space integrals. Explicit calculations of QED processes in the tree approximation. Derivation of the Feynman rules for general field theories.

HADRON SPIN-FLIP AMPLITUDE AND SLOPE OF DIFFERENTIAL CROSS-SECTIONS

1999 ◽  
Vol 14 (03) ◽  
pp. 223-230 ◽  
Author(s):  
O. V. SELYUGIN
Keyword(s):  
Experimental Data ◽  
Cross Sections ◽  
Differential Cross ◽  
Scattering Amplitude ◽  
Previous Analysis ◽  
Differential Cross Sections ◽  
Spin Flip ◽  
Flip Amplitude

A possibility to obtain restrictions of the magnitude of the elastic spin-flip hadron scattering amplitude from accurately measured experimental data on the differential cross-sections of elastic hadron–hadron scattering is shown. Appropriate estimations confirm the previous analysis of experimental data at [Formula: see text] GeV and a probable contribution of the hadron spin-flip amplitude.

scholarly journals High energy scattering of Dirac particles on smooth potentials

2016 ◽  
Vol 31 (23) ◽  
pp. 1650126 ◽  
Author(s):  
Nguyen Suan Han ◽  
Le Anh Dung ◽  
Nguyen Nhu Xuan ◽  
Vu Toan Thang
Keyword(s):  
Dirac Equation ◽  
Cross Sections ◽  
Differential Cross ◽  
Scattering Amplitude ◽  
High Energy ◽  
Type Representation ◽  
Dirac Particles ◽  
Energy Scattering ◽  
Two Component ◽  
High Energy Scattering

The derivation of the Glauber type representation for the high energy scattering amplitude of particles of spin 1/2 is given within the framework of the Dirac equation in the Foldy–Wouthuysen (FW) representation and two-component formalism. The differential cross-sections on the Yukawa and Gaussian potentials are also considered and discussed.

scholarly journals Quantum Field Theory over $\mathbb{F}_q$

10.37236/589 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Oliver Schnetz
Keyword(s):  
Field Theory ◽  
Perturbation Series ◽  
The Other ◽  
Field Theories ◽  
Roots Of Unity ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Feynman Rules ◽  
Graph Hypersurfaces ◽  
Prime 2

We consider the number $\bar N(q)$ of points in the projective complement of graph hypersurfaces over $\mathbb{F}_q$ and show that the smallest graphs with non-polynomial $\bar N(q)$ have 14 edges. We give six examples which fall into two classes. One class has an exceptional prime 2 whereas in the other class $\bar N(q)$ depends on the number of cube roots of unity in $\mathbb{F}_q$. At graphs with 16 edges we find examples where $\bar N(q)$ is given by a polynomial in $q$ plus $q^2$ times the number of points in the projective complement of a singular K3 in $\mathbb{P}^3$. In the second part of the paper we show that applying momentum space Feynman-rules over $\mathbb{F}_q$ lets the perturbation series terminate for renormalizable and non-renormalizable bosonic quantum field theories.

Interacting Fields

2021 ◽  
pp. 237-252
Author(s):  
J. Iliopoulos ◽  
T.N. Tomaras
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Perturbation Expansion ◽  
Field Theories ◽  
Green Functions ◽  
Quantum Field ◽  
Minkowski Space Time ◽  
Dimensional Minkowski Space ◽  
Feynman Rules ◽  
Wightman Axioms

We present a simple form of the Wightman axioms in a four-dimensional Minkowski space-time which are supposed to define a physically interesting interacting quantum field theory. Two important consequences follow from these axioms. The first is the invariance under CPT which implies, in particular, the equality of masses and lifetimes for particles and anti-particles. The second is the connection between spin and statistics. We give examples of interacting field theories and develop the perturbation expansion for Green functions. We derive the Feynman rules, both in configuration and in momentum space, for some simple interacting theories. The rules are unambiguous and allow, in principle, to compute any Green function at any order in perturbation.

Waldmann-Snider Collision Integrals and Nonspherical Molecular Interaction. I. Collision Integrals for Pure Gases

1974 ◽  
Vol 29 (12) ◽  
pp. 1705-1716 ◽  
Author(s):  
W. E. Köhler
Keyword(s):  
Angular Momentum ◽  
Cross Sections ◽  
Molecular Interaction ◽  
Scattering Amplitude ◽  
Collision Operator ◽  
Positive Definiteness ◽  
Collision Integrals ◽  
General Properties ◽  
Relaxation Coefficients ◽  
Rotational Angular Momentum

Collision integrals of the linearized Waldmann-Snider collision operator for pure gases are defined. General properties due to invariances of the molecular interaction are discussed. Effective cross sections are introduced and expressed in terms of convenient bracket symbols. The positive definiteness of the relaxation coefficients is proved. The approximation of small nonsphericity for the scattering amplitude is explained and consequences for the collision integrals are investigated. Molecular cross sections describing the orientation and reorientation of the molecular rotational angular momentum are defined. Expressions for effective cross sections relevant for the various nonequilibrium alignment phenomena are presented.

An experimental investigation of small angle photon elastic scattering

1979 ◽  
Vol 57 (3) ◽  
pp. 343-352 ◽  
Author(s):  
N. Ramanathan ◽  
T. J. Kennett ◽  
W. V. Prestwich
Keyword(s):  
Experimental Investigation ◽  
Elastic Scattering ◽  
Cross Sections ◽  
Small Angle ◽  
Differential Cross ◽  
Bound States ◽  
Scattering Amplitude ◽  
Form Factors ◽  
Differential Cross Sections

The differential cross sections for photon elastic scattering have been determined for targets of Cu, Cd, Ta, and Pb, at angles of 2.4, 3.5, 5.1., 6.0, 8.0, and 10.0° and incident energies of 244.7, 344.3, 443.9, 778.9, 964.0, 1085.8, 1112.0, 1274.2, and 1408.0 keV. The data indicate that presently calculated form factors may be too large, and suggest that intermediate bound states may influence the scattering amplitude.

scholarly journals Removing phase-space restrictions in factorized cross sections

2015 ◽  
Vol 91 (9) ◽  
Author(s):  
Ilya Feige ◽  
Matthew D. Schwartz ◽  
Kai Yan
Keyword(s):  
Phase Space ◽  
Cross Sections

SECOND-ORDER LAGRANGIAN DYNAMICS IN THE PHASE-SPACE: SOME EXAMPLES

2012 ◽  
Vol 27 (10) ◽  
pp. 1250062
Author(s):  
CONSTANTIN BIZDADEA ◽  
MARIA-MAGDALENA BÂRCAN ◽  
MIHAELA TINCA MIAUTĂ ◽  
SOLANGE-ODILE SALIU
Keyword(s):  
Phase Space ◽  
Scalar Field ◽  
Finite Number ◽  
Configuration Space ◽  
Degrees Of Freedom ◽  
Hamiltonian Formulation ◽  
Second Order ◽  
Lagrangian Formulation ◽  
Field Theories ◽  
Lagrangian Dynamics

By means of a class of nondegenerate models with a finite number of degrees of freedom, it is proved that given a Hamiltonian formulation of dynamics, there exists an equivalent second-order Lagrangian formulation whose configuration space coincides with the Hamiltonian phase-space. The above result is extended to scalar field theories in a Lorentz-covariant manner.

First-order exchange approximation

1963 ◽  
Vol 276 (1366) ◽  
pp. 346-353 ◽  
Keyword(s):  
Elastic Scattering ◽  
Cross Sections ◽  
Born Approximation ◽  
Scattering Amplitude ◽  
Wave Functions ◽  
Hydrogen Atoms ◽  
Final State ◽  
First Order ◽  
Exchange Approximation ◽  
Exchange Scattering

It is shown that when the Born approximation is applied to rearrangement collisions in the customary way, terms of the first order in the interaction energy between the colliding particles are omitted from the exchange scattering amplitude. If these terms are retained the arbitrariness which arises from the lack of orthogonality between the initial and final state wave functions is removed. The first-order exchange approximation derived in the present paper is employed to calculate the cross-sections for the 1 s -2 s and 1 s -2 p excitations of hydrogen atoms by electron impact and the elastic scattering of electrons by hydrogen atoms.

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