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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
$$ K\left( {{x_{2}},\,{t_{2}};\,{x_{1}},\,{t_{1}}} \right) = {{\text{e}}^{{\left( {{\text{i/}}\hbar } \right){S_{{{\text{cl}}}}}\left[ {x\left( t \right)} \right]}}}\int_{{y\left( {{t_{1}}} \right) = 0}}^{{y\left( {{t_{2}}} \right) = 0}} {\left[ {dy\left( t \right)} \right]} {\text{ }} \times \exp \left\{ {\frac{{\text{i}}}{\hbar }\int_{{{t_{1}}}}^{{{t_{2}}}} {dt\left( {a\left( t \right){y^{2}} + b\left( t \right)y\dot{y} + c\left( t \right){{\dot{y}}^{2}}} \right)} } \right\}. $$
(17.1)

Keywords

Path Integral Phase Factor Free Particle Integration Measure Direct Evaluation 
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 1994

Authors and Affiliations

  • Walter Dittrich
    • 1
  • Martin Reuter
    • 2
  1. 1.Institut für Theoretische PhysikUniversität TübingenTübingenGermany
  2. 2.Deutsches Elektronen-Synchrotron DESYHamburgGermany

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