Questions tagged [feynman-integral]
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20 questions
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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 ...
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Normalization of exponential in the context of Feynman integrals from a White noise perspective
I apologize in advance if this question is not suitable for MO (please let me know), but the fact is that since I am not familiar with the theory of Feynman integrals I don't know whether this is a ...
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Forwards Feynman–Kac formula
This might be a simple question, but I'm having trouble with it.
Consider the Cauchy problem with final condition.
\begin{equation}
\begin{cases}
\frac{\partial u}{\partial t}(t,x) + \mathcal{L}u(t,x) ...
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Axiomatic QFT, the reconstruction theorem and functional integrals
Before posting my question, let me make some remarks:
[MS] Salmhofer's book on renormalization begins with a nice discussion on Feynman's path integral. At some point, the author states the following:
...
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A toy model in 0-d QFT
Questions
For any positive integer $r$, compute $$(\frac{d}{dY})^r e^{(Y^2)}| _{Y=0}.$$ The answer should directly relates to a counting problem about Feynman diagrams.
Is there a tutorial for how ...
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One particle irreducible Feynman diagrams
In quantum field theory Feynman has invented a diagrammatic method to encode various terms in the Taylor decomposition of integrals of the following form below which I will write in a baby version as ...
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Gauge integral versus path integral
According to this paper, "The gauge integral [a.k.a. Henstock-Kurzweil integral] provides the only formal framework that is close to the original development of the Feynman path integral", ...
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Feynman diagrams and periods of motives
A recent article in the online science magazine Quanta, Strange Numbers Found in Particle Collisions,
discusses experimental evidence of a connection between Feynman integrals and periods of motives. ...
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Conjecture of relation between residues of Feynman integrals and mixed Tate motives
In many articles (for example in articles given by M.Marcoli) there is statement that there is the following conjecture
Residues of Feynman integrals in scalar field theories are always periods of ...
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Primitive log-divergent graphs and convergence of Feynman amplitudes
To a connected graph $G$, quantum field theory attaches the integral
$$
I_G=\int_{\sigma} \frac{\Omega_G}{\Psi_G^2}
$$ where $N_G$ is the number of edges of the graph, $\sigma$ is the simplex of ...
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Infinite total variation of complex measure in Feynman path integral [closed]
I am trying to understand this: If one tries to define a Feynman path integral as a Wiener integral, then the complex measure could be of infinite total variation. What exactly does this mean? How ...
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Integration by paths formula for Gaussian measures
I have read a paper of J.Bricmont and A. Kupiainen 1994 at [http://iopscience.iop.org/0951-7715/7/2/011], but I didn't understand these calculations concerning to a stochastic process. I hope for kind ...
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Why do polytopes pop up in Lagrange inversion?
I'd be interested in hearing people's viewpoints on this. Looking for an intuitive perspective. See Wikipedia for descriptions of polytopes and the Lagrange inversion theorem/formula (LIF) for ...
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"Modular forms from Feynman integrals "?
I would like to learn more about the background of this talk, but found no text on that theme. Do you know more? Edit: An interesting talk by Miranda Cheng (slides).
Edit: A talk today on the theme, ...
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A 2F1 Hypergeometric identity from a Feynman integral
Using two different approaches to evaluating the dimensionally regularized ($d=4-2\epsilon$ dimensional Euclidean space), equal mass ($x=m^2$), 2-loop vacuum Feynman diagram
$$
\begin{align}
I(x) &...
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