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Springer eBooks

An Introduction to Feynman Path Integrals

K.K. Thornber

Published Jan 1, 1978• 1 citation
Publisher
DOI
10.1007/978-1-4684-9140-1_1

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This chapter introduced the concept of the wavenumber operator rather than employing the standard notion of the momentum operator. The introduction and usage of the wavenumber operator were hailed as a significant achievement. Indeed the introduction of the wavenumber operator significantly simplifies the discussion. The Feynman path integral was derived using the Trotter product formula. The chapter presented schemes for the symmetrization and then the generalization of the standard Trotter product rule, which is the quintessential tool in establishing the Feynman path integral. The proposed symmetrization improves the convergence rate of the calculations by one order. The standard Trotter product rule merely involves two operators. The proposed generalization admits the involvement of any finite number of operators. The introduction of the wavenumber operator and the symmetrization and generalization of the Trotter product formula have been presented in this chapter for the first time. The reader may consult the references [1-16] further below to deepen their understanding and hopefully appreciate the simplifications and generalizations achieved in this chapter.

Institution of Engineering and Technology eBooks•Dec 18, 2023•0 citations
This chapter introduced the concept of the wavenumber operator rather than employing the standard notion of the momentum operator. The introduction and usage of the wavenumber operator were hailed as a significant achievement. Indeed the introduction of the wavenumber operator significantly simplifies the discussion. The Feynman path integral was derived using the Trotter product formula. The chapter presented schemes for the symmetrization and then the generalization of the standard Trotter product rule, which is the quintessential tool in establishing the Feynman path integral. The proposed symmetrization improves the convergence rate of the calculations by one order. The standard Trotter product rule merely involves two operators. The proposed generalization admits the involvement of any finite number of operators. The introduction of the wavenumber operator and the symmetrization and generalization of the Trotter product formula have been presented in this chapter for the first time. The reader may consult the references [1-16] further below to deepen their understanding and hopefully appreciate the simplifications and generalizations achieved in this chapter.