About calculation of traces of Dirac $γ$-matrices contracted with massless vectors in Minkowski space
A new method for calculation of traces of Dirac $γ$-matrices contracted with massless vectors in Minkowski space is discussed
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arXiv subjects
Alexander L. Bondarev
Publications and source records attributed to Alexander L. Bondarev.
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.
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A new method for calculation of traces of Dirac $γ$-matrices in Minkowski space
This paper presents some relations for orthonormal bases in the Minkowski space and isotropic tetrads constructed from the vectors of these bases. As an example of an application of the obtained formulae, in particular recursion relations, a new method is proposed to calculate traces of Dirac $γ$-matrices in the Minkowski space. Compared to the classical algorithms, the new method results in more compact expressions for the traces. Specifically, it may be easily implemented as a simple yet efficient computer algorithm.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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