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Direct Evaluation of Path Integrals

  • Walter Dittrich
  • Martin Reuter

Abstract

Until now we have always used a trick to calculate the path integral in
$$ \begin{array}{l} K({x_2},\;{t_2};\;{x_1},\;{t_1})\;{\rm{ = }}\;{{\rm{e}}^{(i/\hbar )}}{S_{cl}}[x(t)]\;\;\;\int_{y(t1) = 0}^{y(t2) = 0} {[dy(t)]} \\ \;{\rm{ x exp }}\left\{ {\left. {\frac{i}{\hbar }\;\int_{t1}^{t2} {dt} (a(t){y^2}\; + \;b(t)y\dot y\; + \;c(t){{\dot y}^2})} \right\}} \right.\;\;{\rm{.}} \end{array} $$
(17.1)

Keywords

Classical Action Path Integral Free Particle Direct Evaluation Jacobi Determinant 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Walter Dittrich
    • 1
  • Martin Reuter
    • 2
  1. 1.Institut für Theoretische PhysikUniversität TübingenTübingenFed. Rep. of Germany
  2. 2.Institut für Theoretische PhysikUniversität HannoverHannover 1Fed. Rep. of Germany

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