Summary
The entanglement between chains imposes a topological constraint which makes the functional integral description of a system of loops yet completely open. The problem is here formulated in the sense of piecewise linear category, leading to an algorithm viable for either analytical or numerical evaluation of the generating function. For simplicity only the two-loop case is discussed.
Riassunto
L'aggrovigliamento fra le catene costituisce un vincolo topologico che rende la descrizione in termini di integrali funzionali di un sistema di oggetti lineari estesi chiusi un problema ancora completamente aperto. Tale problema è qui formulato nel senso della categoria PL (lineare a tratti), ciò che porta ad un algoritmo che consente la valutazione analitica o numerica della funzione generatrice. Per semplicità si discute solo il caso di un sistema di due catene.
Резюме
Скрученность между цепями предполагает топологическое ограничение, которое делает описание системы петеля в терминах функциональных интегралов полностью открытой проблемой. В этой работе эта проблема формулируется с помощью кусочно-линейных категорий, предложенный алгоритм приводит либо к аналитическому, либо численному вычислению производящей функции. Для простоты обсуждается случай только двух петель.
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Also Gruppo Nazionale di Struttura della Materia del C.N.R., U.R. 24, Torino and Istituto Nazionale di Fisica Nucleare, Gruppo IV, Torino, Italia.
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Agnes, C., Rasetti, M. Piecewise-linear-category approach to entanglement. Il Nuovo Cimento D 3, 121–136 (1984). https://doi.org/10.1007/BF02452207
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DOI: https://doi.org/10.1007/BF02452207