کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1896549 | 1044439 | 2011 | 19 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Analogue of the identity Log Det =  Trace Log for resultants
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
فیزیک ریاضی
پیش نمایش صفحه اول مقاله

چکیده انگلیسی
Like evaluation of Gaussian integrals is based on determinants, exact (non-perturbative) evaluation of non-Gaussian integrals is related to algebraic quantities called resultants. Resultant Rr1,â¦,rn defines a condition of solvability for a system of n homogeneous polynomials of degrees r1,â¦,rn in n variables, just in the same way as a determinant does for a system of linear equations. Because of this, resultants are important special functions of upcoming non-linear physics and begin to play a role in various topics related to string theory. Unfortunately, there is a lack of convenient formulas for resultants when the number of variables is large. To cure this problem, we generalize the well-known identity Log Det = Trace Log from determinants to resultants. The generalized identity allows to obtain explicit polynomial formulas for multidimensional resultants: for any number of variables, the resultant is given by a Schur polynomial. We also give several integral representations for resultants, as well as a sum-over-paths representation.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Geometry and Physics - Volume 61, Issue 3, March 2011, Pages 708-726
Journal: Journal of Geometry and Physics - Volume 61, Issue 3, March 2011, Pages 708-726
نویسندگان
A. Morozov, Sh. Shakirov,