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.
12 questions
2 votes
0 answers
52 views
Rigorous definition of euclidean perturbative path integral quantisation of gauge theories
I am trying to understand Witten's localisation argument for topologically twisted theories, specifically $\mathcal{N} = 4$ $d = 4$ Super-Yang-Mills Theory. Since there is in general no Lebesgue ...
- 121
7 votes
2 answers
406 views
The equivalence of stochastic quantization and path integral quantization
I am looking for a reference in which the equivalence of stochastic quantization and path integral quantization has been shown. It would be great if I can see such a relation for a Euclidean quantum ...
- 321
3 votes
1 answer
494 views
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) \ \ ...
- 273
4 votes
1 answer
395 views
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 ...
- 141
35 votes
5 answers
3k views
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 ...
- 1,293
6 votes
0 answers
1k 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 ...
- 61
16 votes
1 answer
890 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 ...
- 9,822
2 votes
1 answer
451 views
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 ...
- 1,026
5 votes
0 answers
235 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 ...
- 5,357
6 votes
1 answer
583 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 ...
- 8,062
11 votes
0 answers
2k views
Yang-Mills theory with non-compact gauge groups G
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-...
- 10.8k
75 votes
5 answers
20k views
Mathematics of path integral: state of the art
I was told that one of the most efficient tools (e.g. in terms of computations relevant to physics, but also in terms of guessing heuristically mathematical facts) that physicists use is the so called ...