Abstract
Unfortunately, path integrals can be evaluated explicitly only for very simple systems like the free particle, harmonic oscillator, or topological field theories. More complicated systems are analyzed via perturbation theory (e.g., semi-classical expansion, perturbative expansion in powers of the interaction strength, strong-coupling expansion, high- and low-temperature expansions) or by numerical methods.
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Notes
- 1.
For a discussion and proof of this law, see p. 46.
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Wipf, A. (2021). High-Dimensional Integrals. In: Statistical Approach to Quantum Field Theory. Lecture Notes in Physics, vol 992. Springer, Cham. https://doi.org/10.1007/978-3-030-83263-6_3
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