Algebraic formulation of the wick’s theorem for symbolic calculations
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BELOUSSOV, Igor. Algebraic formulation of the wick’s theorem for symbolic calculations. In: Materials Science and Condensed Matter Physics, Ed. 8-th Edition, 12-16 septembrie 2016, Chişinău. Chişinău: Institutul de Fizică Aplicată, 2016, Editia 8, p. 59. ISBN 978-9975-9787-1-2.
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Materials Science and Condensed Matter Physics
Editia 8, 2016
Conferința "International Conference on Materials Science and Condensed Matter Physics"
8-th Edition, Chişinău, Moldova, 12-16 septembrie 2016

Algebraic formulation of the wick’s theorem for symbolic calculations


Pag. 59-59

Beloussov Igor
 
Institute of Applied Physics, Academy of Sciences of Moldova
 
Disponibil în IBN: 18 iulie 2019


Rezumat

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 Fermi field operators as a determinant of the matrix is proposed. The proof of this theorem is by induction.   Representations (1) and (2) not only greatly simplify all calculations, but also allow one to perform them using a computer with programs of symbolic mathematics. Development of the methods of symbolic algebra for computing in higher-orders of many-body perturbation theory has been realized for several decades. The SCHOONSCHIP program [1, 2] and other symbolic packages (FEYNCALC [3], HIP [4], REDUCE [5], FORM [6], XLOOPS [7], SNEG [8], etc.) are employed for evaluating Feynman diagrams in quantum electrodynamics and high-energy physics. Similar investigations are under way in quantum chemistry [9] (see also [10] and references therein).   The starting point of symbolic computations is the Wick’s theorem (see, e.g., discussion in [11]). However, there is an alternative approach based on the symbolic replacement rules that are suitable to be used in symbolic algebra [12]. Some of these programs are designed for a narrow range of specific tasks; however, they provide algorithms appropriate for their possible use in other areas. Moreover, they require a certain specific software with mastering add-on packages. Calculations using representations (1) and (2) and subsequent simplifications are possible using standard packages of well-known computing systems such as Mathematica, Maple, Mathcad and so on.