# Questions tagged [path-integral]

The path integral formulation of quantum mechanics is a description of quantum theory that generalizes the action principle of classical mechanics. It replaces the classical notion of a single, unique classical trajectory for a system with a sum, or functional integral, over an infinity of quantum-mechanically possible trajectories to compute a quantum amplitude. This formulation has proven crucial to the subsequent development of theoretical physics.

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### Double integral in a polygon domain

I want to compute a integral of a polynomial $f(x, y)$ over a polygon domain $D$ of $n$ sides. $$I(f) = \int_{D} f(x, \ y) \ dx \ dy$$ The vertex of this polygon are \vec{p}_{i} = (x_i, \ y_i) \ \ ...
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### Reference request: path integral approach to Gaussian processes

Are there any good, rigorous and preferably modern books or papers on path integral approach to Gaussian processes? I am interested in both introductory level and deeper monographs on the subject. I ...
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### Looking for some interesting complex integration contours

I am currently working on some tools to make contour integration in a proof assistant less painful and I'm looking for interesting examples of contours in the complex plane used in the literature. I ...
647 views

### Condensed/liquid vector spaces and path integrals

[Edited to take into account comments.] Background One approach to the problem of making rigorous various measures on spaces of paths (for example, the Wiener or Feynman measure) is the time-slicing ...
717 views

### Peter Freyd on path Integral?

In the issue Electronic Notes in Theoretical Computer Science Volume 29, 1999, Page 79 there is a very intriguing abstract by Peter Freyd. Path Integrals, Bayesian Vision, and Is Gaussian Quadrature ...
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### Ratios of Gaussian integrals with a positive semidefinite matrix

Cross-post from MSE https://math.stackexchange.com/questions/4118128/ratios-of-gaussian-integrals-with-a-positive-semidefinite-matrix Generally speaking, I’m wondering what the usual identities for ...
153 views

### References for computing $n$-point correlations in Chern-Simons theory

I am interested in learning how to compute $n$-point correlation functions in Chern-Simons theory, thought of as a TQFT (similar to Witten's work linking that theory to knot theory). I am mostly ...
345 views

### Path integral as quantum mechanics on the tangent bundle

Let $X$ be a configuration space, a finite-dimensional manifold. By "quantum mechanics on $X$" I mean a linear evolution equation on complex-valued functions on $X$, determined by a ...
Physicists are familiar working with Yang-Mills theory with compact and semi-simple gauge groups $G$ (Lie groups). However, it is not entirely clear the formulation of Yang-Mills theory with non-...