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

Sine 

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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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