The algebraic formulation of Wick’s theorem that allows one to present the vacuum or thermal
averages of the chronological product of an arbitrary number of field operators as a determinant (permanent)
of the matrix is proposed. Each element of the matrix is the average of the chronological product of only
two operators. This formulation is extremely convenient for practical calculations in quantum field theory,
statistical physics, and quantum chemistry by the standard packages of the well known computer algebra
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Special Matrices is a peer-reviewed, open access electronic journal that publishes original articles of wide significance and originality in all areas of research involving structured matrices present in various branches of pure and applied mathematics and their noteworthy applications in physics, engineering, and other sciences.