That path integral measure factor is famously known as Feynman's fudge factor. It makesensures that the Lagrangian free Gaussian (=free) Lagrangian path integral (i) has a finite value, and (ii) is form invariant-invariant wrt. to extra intermediate Gaussian integrations, cf. e.g. my Phys.SE answer here.
As OP already noted, Feynman's fudge factor can be derived from the Hamiltonian phase space path integral by integrating out the momentum variables. See also this related Phys.SE post.
That path integral measure factor is famously known as Feynman's fudge factor. It makes the Lagrangian free Gaussian path integral form invariant wrt. to extra intermediate Gaussian integrations, cf. e.g. my Phys.SE answer here.
As OP already noted, Feynman's fudge factor can be derived from the Hamiltonian phase space path integral by integrating out the momentum variables. See also this related Phys.SE post.
That path integral measure factor is famously known as Feynman's fudge factor. It ensures that the Gaussian (=free) Lagrangian path integral (i) has a finite value, and (ii) is form-invariant wrt. to extra intermediate Gaussian integrations, cf. e.g. my Phys.SE answer here.
As OP already noted, Feynman's fudge factor can be derived from the Hamiltonian phase space path integral by integrating out the momentum variables. See also this related Phys.SE post.
That path integral measure factor is famously known as Feynman's fudge factor. It makes the Lagrangian free Gaussian path integral form invariant wrt. to extra intermediate Gaussian integrations, cf. e.g. my Phys.SE answer here.
As OP already noted, Feynman's fudge factor can be derived from the Hamiltonian phase space path integral by integrating out the momentum variables. See also this related Phys.SE post.