Questions tagged [feynman-integral]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
5 votes
0 answers
593 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 ...
user avatar
1 vote
0 answers
38 views

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 ...
user avatar
  • 475
1 vote
1 answer
200 views

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) ...
user avatar
11 votes
2 answers
736 views

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: ...
user avatar
  • 2,809
12 votes
2 answers
875 views

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 ...
user avatar
  • 4,005
8 votes
4 answers
1k views

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 ...
user avatar
  • 19k
5 votes
2 answers
530 views

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", and also "...
user avatar
  • 37.4k
9 votes
1 answer
2k views

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. ...
user avatar
  • 8,968
7 votes
1 answer
559 views

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 ...
user avatar
  • 777
5 votes
1 answer
229 views

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 ...
user avatar
  • 51
3 votes
0 answers
162 views

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 ...
user avatar
0 votes
0 answers
235 views

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 ...
user avatar
25 votes
0 answers
3k views

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 ...
13 votes
2 answers
2k views

"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, ...
user avatar
  • 10.5k
11 votes
1 answer
1k views

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) &...
user avatar
  • 441
8 votes
1 answer
429 views

Singularity structure of integrals of rational functions

Suppose I have a convergent integral of the form $\int_0^1dx_1\dots\int_0^1 dx_n \frac{P(x_i)}{Q(x_i)}$, where $P$ and $Q$ are polynomial functions of $n$ nonnegative real variables $x_i$. Let the ...
user avatar
  • 363
12 votes
1 answer
1k views

Degree of Transcendentality and Feynman Diagrams

Physicists computing multiloop Feynman diagrams have introduced various techniques and conjectures that involve the notion of Degree of Transcendentality (DoT). From what I understand one defines 1) ...
user avatar
  • 5,133
14 votes
3 answers
1k views

Finite dimensional Feynman integrals

In a sense this is a follow up question to The mathematical theory of Feynman integrals although by all rights it should precede that question. Let $S$ be a polynomial with real coefficients in $n$ ...
user avatar
  • 22.5k
91 votes
1 answer
9k views

The mathematical theory of Feynman integrals

It is well known that Feynman integrals are one of the tools that physicists have and mathematicians haven't, sadly. Arguably, they are the most important such tool. Briefly, the question I'd like to ...
user avatar
  • 22.5k
16 votes
8 answers
4k views

Path integrals outside QFT

The main application of Feynman path integrals (and the primary motivation behind them) is in Quantum Field Theory - currently this is something standard for physicists, if even the mathematical ...
user avatar