73 research outputs found
A Covariant Method for Calculating Amplitudes of Processes Involving Polarized Spin 1/2 Particles. Calculation of the Interference Terms in their Cross Sections
A covariant method is proposed for calculating the amplitudes of processes
involving polarized spin 1/2 particles. It is suitable for calculating the
interference terms in the cross sections of such processes. As an illustration,
expressions are given for the amplitudes of electron-electron scattering in the
lowest order of perturbation theory and expressions for the electron current in
the case of emission of two bremsstrahlung photons in the ultrarelativistic
limit.Comment: 12 pages, LaTe
Construction of Orthonormal Bases from the Vectors of the Problem in Minkowski Space
We propose to use the modified Gram -- Schmidt orthonormalization process in
Minkowski space for construction of orthonormal bases from the vectors of the
problem.Comment: LaTeX2e, 6 pages, contribution to the Proceedings of the VI
International School-seminar "Actual Problems of High Energy Physics". Gomel,
Belarus, August 7-16, 200
Method of Covariant Calculation of the Amplitudes of Processes with Polarized Dirac Particles
General scheme for covariant calculation of the amplitudes of processes with
the polarized Dirac particles is considered. It is so concretized that the
obtained expressions can be used for calculation of the amplitudes of processes
with interfering diagrams. As an illustration the expressions for the
amplitudes of processes with massless particles are presented.Comment: 9 pages, LaTex; talk presented at the Joint International Workshop:
VIII Workshop on High Energy Physics and Quantum Field Theory & III Workshop
on Physics at VLEPP. Zvenigorod, Russia, September 15-21, 199
Some Methods of Minimization of Calculations in High Energy Physics
Two approaches to calculations' minimization in High Energy Physics are
considered. The first one is the method of covariant calculations for the
amplitudes of processes with polarized Dirac particles. The second one connects
with the possibility to reduce the expressions for the traces of products of
ten and more Dirac gamma-matrices.Comment: 9 pages, LaTeX, talk presented at the XVIII Workshop on High Energy
Physics and Field Theory. Protvino, Russia, June 26-30,199
Methods of Minimization of Calculations in High Energy Physics: 2. Minimization of number of vectors in problem
The various ways to reduce number of vectors describing condition of
particles for high energy physics problems are presented. In particular
decomposition of any vector with respect to the basis, consisting of any four
linearly independent vectors, including the orthonormal basis; construction of
orthonormal bases from vectors of a problem; expression of one vector of
problem through other is considered.Comment: 9 pages, LaTe
Calculation of the scattering amplitudes
General equations for the calculation of amplitudes are presented. As an
illustration of application of proposed formulae we calculate electron-electron
scattering amplitudes.Comment: 12 pages, LaTeX2E, to appear in the proceedings of 9th Annual RDMS
CMS Collaboration Conference, Minsk, Belarus, November 28 – December 2,
200
Methods of Minimization of Calculations in High Energy Physics: 1. A Covariant Method of the Calculation of Amplitudes of Processes Involving Polarized Dirac Particles
The article deals with a number of the existings variants of direct
calculation of amplitudes of processes with polarized Dirac particles. It is
shown, that all of them are special cases of one and the same mathematical
scheme. The advantages and disadvantages of this scheme are considered. A new
variant of the method of calculation of amplitudes, keeping all the advantages
of this scheme, but free from disadvantages, is proposed. In particular, this
variant is suitable for the evaluation of amplitudes of processes with
interfering diagrams and does not need any additional calculations, that are
necessary in the general case. Expressions for the amplitudes of processes
involving both massive and massless particles are presented. These expressions
make it possible to create in an easy way the computer programs for automatic
calculation of amplitudes. The existing computer programs for calculation of
amplitudes, their limitations and disadvantages are briefly considered.Comment: 38 pages, LaTe
A New Identity in Minkowski Space and Some Applications of It
Schouten's identity is used to obtain a new identity in Minkowski space. Some
applications of the new identity in high-energy physics are considered,
including the possibility of significant shortening of the expressions for the
traces of products of ten and more Dirac gamma-matrices.Comment: 6 pages, LaTe
New Tasks and New Codes for RFQ Beam Simulation
Proton linear accelerator is the base Accelerator Driven Power System (ADS).
Such ADS are dedicated to various purposes: weapon plutonium conversion,
"energy amplifier", transmutation of radionuclear wastes etc. Solution of these
tasks requires proton beams with energy 1 GeV and average current up to 30 mA.
At the moment there are no problems of fundamental nature in such linac
construction. The main problems have economic and technical aspects. Problems
of CW linac will be demonstrated on the base beam dynamics requirements. New
code package LIDOS.RFQ.Designer makes possible to simulate beam dynamics in RF
fields of real vane shape (including gaps between RFQ section) as well as to
determine channel parameters tolerances for reliable operationComment: LINAC'2000 THB1
About calculation of traces of Dirac -matrices contracted with massless vectors in Minkowski space
A new method for calculation of traces of Dirac -matrices contracted
with massless vectors in Minkowski space is discussedComment: 9 pages, LaTeX2
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