Feynman’s Path Integral Formulation of Schrödinger’s Wave Mechanics
In this final chapter we present an alternative formulation of quantum mechanics operating with new mathematical methods: the so-called path integrals. The first step towards such a description were made by Dirac, but the mathematical foundation and beauty was put forward by Feynman. It contributes essentially to a fundamental understanding of quantum mechanics and allows a derivation of exact equations in complex quantum field theory. It should be noted from the beginning that up to now path integral formulations have not played such an important role for solving certain field-theoretical problems; on the one hand, analytical solutions are only possible in very simple cases, and on the other hand, numerical calculations are extremely computer intense. However, path integrals often allow an approximate solution for physical processes, such as phase transitions, where perturbative methods fail.
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