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In mathematics, variational perturbation theory (VPT) is a mathematical method to convert divergent power series in a small expansion parameter, say , into a convergent series in powers , where is a critical exponent (the so-called index of "approach to scaling" introduced by Franz Wegner). This is possible with the help of variational parameters, which are determined by optimization order by order in . The partial sums are converted to convergent partial sums by a method developed in 1992.

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  • نظرية التغاير(بالإنجليزية: Variational theory)‏ هي طريقة حسابية مبسطة لحساب قيم الطاقة لمستويات مختلفة، أهمها طاقة المستوى الأرضي.ونقول: , في سلسلة متقاربة في القوى:,حيث هو (ما يسمى مؤشر «نهج لتوسيع نطاق» الذي عرضته ). هذا هو ممكن مع مساعدة من ، والتي يتم تحديدها من قبل النظام الأمثل في . The partial sums are حيث يتم تحويلها إلى مبالغ جزئية متقاربة بواسطة طريقة تم تطويرها في عام 1992. (ar)
  • In mathematics, variational perturbation theory (VPT) is a mathematical method to convert divergent power series in a small expansion parameter, say , into a convergent series in powers , where is a critical exponent (the so-called index of "approach to scaling" introduced by Franz Wegner). This is possible with the help of variational parameters, which are determined by optimization order by order in . The partial sums are converted to convergent partial sums by a method developed in 1992. Most perturbation expansions in quantum mechanics are divergent for any small coupling strength . They can be made convergent by VPT (for details see the first textbook cited below). The convergence is exponentially fast. After its success in quantum mechanics, VPT has been developed further to become an important mathematical tool in quantum field theory with its anomalous dimensions. Applications focus on the theory of critical phenomena. It has led to the most accurate predictions of critical exponents.More details can be read here. (en)
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  • نظرية التغاير(بالإنجليزية: Variational theory)‏ هي طريقة حسابية مبسطة لحساب قيم الطاقة لمستويات مختلفة، أهمها طاقة المستوى الأرضي.ونقول: , في سلسلة متقاربة في القوى:,حيث هو (ما يسمى مؤشر «نهج لتوسيع نطاق» الذي عرضته ). هذا هو ممكن مع مساعدة من ، والتي يتم تحديدها من قبل النظام الأمثل في . The partial sums are حيث يتم تحويلها إلى مبالغ جزئية متقاربة بواسطة طريقة تم تطويرها في عام 1992. (ar)
  • In mathematics, variational perturbation theory (VPT) is a mathematical method to convert divergent power series in a small expansion parameter, say , into a convergent series in powers , where is a critical exponent (the so-called index of "approach to scaling" introduced by Franz Wegner). This is possible with the help of variational parameters, which are determined by optimization order by order in . The partial sums are converted to convergent partial sums by a method developed in 1992. (en)
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  • نظرية التغاير (ar)
  • Variational perturbation theory (en)
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