"The path integral is a formulation of quantum mechanics equivalent to the standard formulations, offering a new way of looking at the subject which is, arguably, more intuitive than the usual approaches. Applications of path integrals are as vast as those of quantum mechanics itself, including the quantum mechanics of a single particle, statistical mechanics, condensed matter physics and quantum field theory. ... It is in quantum field theory, both relativistic and nonrelativistic, that path integrals (functional integrals is a more accurate term) play a much more important role, for several reasons. They provide a relatively easy road to quantization and to expressions for s, which are closely related to amplitudes for physical processes such as scattering and decays of particles. The path integral treatment of gauge field theories (non-abelian ones, in particular) is very elegant: and ghosts appear quite effortlessly. Also, there are a whole host of nonperturbative phenomena such as solitons and that are most easily viewed via path integrals. Furthermore, the close relation between statistical mechanics and quantum mechanics, or and quantum field theory, is plainly visible via path integrals."
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Richard MacKenzie:
https://en.wikiquote.org/wiki/Statistical_mechanics
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Statistical mechanics
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