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- W4309907029 abstract "The roles of Lie groups in Feynman's path integrals in non-relativistic quantum mechanics are discussed. Dynamical as well as geometrical symmetries are found useful for path integral quantization. Two examples having the symmetry of a non-compact Lie group are considered. The first is the free quantum motion of a particle on a space of constant negative curvature. The system has a group SO(d,1) associated with the geometrical structure, to which the technique of harmonic analysis on a homogeneous space is applied. As an example of a system having a non-compact dynamical symmetry, the d-dimensional harmonic oscillator is chosen, which has the non-compact dynamical group SU(1,1) besides its geometrical symmetry SO(d). The radial path integral is seen as a convolution of the matrix functions of a compact group element of SU(1,1) on the continuous basis." @default.
- W4309907029 created "2022-11-30" @default.
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- W4309907029 date "2016-09-27" @default.
- W4309907029 modified "2023-09-28" @default.
- W4309907029 title "Path Integrals and Lie Groups" @default.
- W4309907029 doi "https://doi.org/10.48550/arxiv.1609.08526" @default.
- W4309907029 hasPublicationYear "2016" @default.
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