New answers tagged path-integral
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Accepted
Fourier Transform of Vertex function
Let's look at the inverse Fourier transform. Define
$$
{\hat \Gamma}(p_1,\cdots,p_n) = \int d^4 x_1 \cdots d^4 x_n e^{i p_1 \cdot x_1 + \cdots i p_n \cdot x_n } \Gamma (x_1 , \cdots , x_n ) .
$$
For ...
- 27.7k
1
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What are the implications of rejecting the local tomography assumption?
This question was asked quite some time ago, but I came across it just very recently. I meant to post this as a comment; however, I currently lack the capacity of posting comments here. Nevertheless, ...
- 11
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Propagation of the expectation of a function with the path integral
The integral over $x_1$ is an integral over initial conditions, and $\psi(0, x_1)$ is the wavefunction at $t=0$ that weights those initial conditions.
So your path integral computes something like
$$
\...
- 55.3k
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Correct method for splitting path integral in two
In principle, the "trick" of breaking integrals for a few part,
$$\int dx\,dy\,f(x,y)\,=\,\int dx\,\int dy\,f(x,y),$$ is based on applying Fubini's theorem. Clearly, that is allowed for ...
- 1,704
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Differentiate inside path integral
When testing conjectured perturbative formulae (e.g. identities associated with perturbations from Gaussian theories), sometimes it is easier conceptually to work in terms of (finite) multivariable ...
- 3,749
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