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Physical Mathematics by Kevin Cahill

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16

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Path integrals

16.1 Path integrals and classical physics

Since Richard Feynman invented them over 60 years ago, path integrals have been used with increasing frequency in high-energy and condensed-matter physics, in finance, and in biophysics (Kleinert, 2009). Feynman used them to express matrix elements of the time-evolution operator exp(−itH/ħ) in terms of the classical action. Others have used them to compute matrix elements of the Boltzmann operator exp(−H/kT), which in the limit of zero temperature projects out the ground state |E0〉 of the system

(16.1)

a trick used in lattice gauge theory.

Path integrals magically express ...

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