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This tag is for questions regarding to the boundary conditions (b.c.) which expresses the behaviour of a function on the boundary (border) of its area of definition. The choice of the b.c. is fundamental for the resolution of the computational problem: a bad imposition of b.c. may lead to the divergence of the solution or to the convergence to a wrong solution.
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Green's function for free scalar field theory as an inverse of $-(\partial^2+m^2)$
In his book [QFT in a Nutshell], Zee argues that the functional integral
$$Z= \int D\varphi \; e^{i\int d^4x[ -\frac{1}{2}\varphi(\partial^2+m^2)\varphi + J\varphi]}$$
can be evaluated by discretizing …