# Questions tagged [feynman-integral]

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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 ...
727 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 ...
249 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 "...
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. ...
531 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 ...
198 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 ...
151 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 ...
223 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 ...
2k 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 ...
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, ...
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) &...
416 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 ...
985 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) ...
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 $n$ ...