Trace of the product of Pauli matrices occurring as a/sub r/ = a/sub ri/ sigma/sub i/ + ia/sub r4/ and that of the product of Dirac matrices, and the interconnection between them
Sasabindu Sarkar · OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · 1973
The sigma /sub i/u sigma /sub i/, sigma /sub i/ sigma /sub j/u sigma / sub i/ sigma /sub j/,and Tr( s/sub i/u)Tr( sigma /sub i/v), Tr( sigma /sub i/ sigma /sub j/v) and Tr(u) where u and v involve Pauli matrices sigma /sub i/, and the 2 x 2 unit matrix in the form of products of elements of the type a/sub r/ = a/sub ri/ sigma /sub i/ + ia/sub r4/ are evaluated with the help of the results of the trace calculation involving Dirac matrices. The gamma /sub v/,U gamma /sub v/, gamma /sub u/, gamma /sub v/ gamma , U gamma y gamma /sub v/, Tr( gamma /sub u/ S) Tr( gamma /sub u/ S'), Tr( gamma /sub u/ gamma ,U)Tr( gamma /sub u/ gamma ,V), Tr( gamma /sub 5/V), Tr ( gamma /sub 5/U) and Tr(U) are evaluated. Here U, V are products of an even number of elements and S, S' are products of an odd number of elements of the type A - (A/sub ru/ gamma /sub u/) The cases in which the dummy suffixes i and mu occurring in some of the above expressions are replaced by a'' which assume any specificmore » value instead of implying a summation are dealt with. The evaluation of the above-mentioned traces when the term, 1 plus or minus gamma /sub 5/, occurs within the trace brackets is considered; this is required in the calculation of the traces involving sigma /sub i/; and the unit 2 x 2 matrix. It was shown that the problem of the trace calculation involving Dirac matrices can be reduced to one involving three Pauli matrices sigma /sub i/ and the unit 2 x 2 matrix. (auth)« less