Feynman diagrams

(0.001 seconds)

10 matching pages

1: 16.24 Physical Applications

… ►

§16.24(ii) Loop Integrals in Feynman Diagrams

►Appell functions are used for the evaluation of one-loop integrals in Feynman diagrams. …

2: 34.9 Graphical Method

… ►The graphical method establishes a one-to-one correspondence between an analytic expression and a diagram by assigning a graphical symbol to each function and operation of the analytic expression. Thus, any analytic expression in the theory, for example equations (34.3.16), (34.4.1), (34.5.15), and (34.7.3), may be represented by a diagram; conversely, any diagram represents an analytic equation. …

3: Bibliography C

… ►

L. G. Cabral-Rosetti and M. A. Sanchis-Lozano (2000) Generalized hypergeometric functions and the evaluation of scalar one-loop integrals in Feynman diagrams. J. Comput. Appl. Math. 115 (1-2), pp. 93–99.

ⓘ

External Links:: ISSN 0377-0427, Document, MathReview (Lorenzo L. Salcedo), ZentralBlatt
Referenced by:: §16.24(ii).
Encodings:: BibTeX

… ►

G. M. Cicuta and E. Montaldi (1975) Remarks on the full asymptotic expansion of Feynman parametrized integrals. Lett. Nuovo Cimento (2) 13 (8), pp. 310–312.

ⓘ

External Links:: MathReview (R. A. Askey)
Referenced by:: §2.3(iii).
Encodings:: BibTeX

…

4: 20.13 Physical Applications

… ►In the singular limit

\Im\tau\rightarrow 0+

, the functions

\theta_{j}\left(z\middle|\tau\right)

j=1,2,3,4

, become integral kernels of Feynman path integrals (distribution-valued Green’s functions); see Schulman (1981, pp. 194–195). …

5: 7.20 Mathematical Applications

…

6: 20.2 Definitions and Periodic Properties

… ►

…

Figure 20.2.1:

z

-plane. …Left-hand diagram is the rectangular case (

\tau

purely imaginary); right-hand diagram is the general case. …

…

7: DLMF Project News

error generating summary

8: Bibliography B

… ►

E. Brézin, C. Itzykson, G. Parisi, and J. B. Zuber (1978) Planar diagrams. Comm. Math. Phys. 59 (1), pp. 35–51.

ⓘ

External Links:: ISSN 0010-3616, Document, MathReview (C. S. Sharma), ZentralBlatt
Referenced by:: §32.15.
Encodings:: BibTeX

…

9: 3.5 Quadrature

… ►

Table 3.5.21: Cubature formulas for disk and square.

► ►►

Diagram	$(x_{j},y_{j})$	$w_{j}$	$R$
…

►

10: Errata

… ►

Table 3.5.21

The correct corner coordinates for the 9-point square, given on the last line of this table, are $(\pm\sqrt{\tfrac{3}{5}}h,\pm\sqrt{\tfrac{3}{5}}h)$ . Originally they were given incorrectly as $(\pm\sqrt{\tfrac{3}{5}}h,0)$ , $(\pm\sqrt{\tfrac{3}{5}}h,0)$ .

\begin{picture}(2.4,3.0)(-1.2,-1.55)\put(0.0,0.0){\line(1,0){0.05}}\put(0.1,0.% 0){\line(1,0){0.05}}\put(0.2,0.0){\line(1,0){0.05}}\put(0.3,0.0){\line(1,0){0.% 05}}\put(0.4,0.0){\line(1,0){0.05}}\put(0.5,0.0){\line(1,0){0.05}}\put(0.6,0.0% ){\line(1,0){0.05}}\put(0.7,0.0){\line(1,0){0.05}}\put(0.8,0.0){\line(1,0){0.0% 5}}\put(0.9,0.0){\line(1,0){0.05}}\put(0.0,0.0){\line(0,1){0.05}}\put(0.0,0.1)% {\line(0,1){0.05}}\put(0.0,0.2){\line(0,1){0.05}}\put(0.0,0.3){\line(0,1){0.05% }}\put(0.0,0.4){\line(0,1){0.05}}\put(0.0,0.5){\line(0,1){0.05}}\put(0.0,0.6){% \line(0,1){0.05}}\put(0.0,0.7){\line(0,1){0.05}}\put(0.0,0.8){\line(0,1){0.05}% }\put(0.0,0.9){\line(0,1){0.05}}\put(0.0,0.0){\line(-1,0){0.05}}\put(-0.1,0.0)% {\line(-1,0){0.05}}\put(-0.2,0.0){\line(-1,0){0.05}}\put(-0.3,0.0){\line(-1,0)% {0.05}}\put(-0.4,0.0){\line(-1,0){0.05}}\put(-0.5,0.0){\line(-1,0){0.05}}\put(% -0.6,0.0){\line(-1,0){0.05}}\put(-0.7,0.0){\line(-1,0){0.05}}\put(-0.8,0.0){% \line(-1,0){0.05}}\put(-0.9,0.0){\line(-1,0){0.05}}\put(0.0,0.0){\line(0,-1){0% .05}}\put(0.0,-0.1){\line(0,-1){0.05}}\put(0.0,-0.2){\line(0,-1){0.05}}\put(0.% 0,-0.3){\line(0,-1){0.05}}\put(0.0,-0.4){\line(0,-1){0.05}}\put(0.0,-0.5){% \line(0,-1){0.05}}\put(0.0,-0.6){\line(0,-1){0.05}}\put(0.0,-0.7){\line(0,-1){% 0.05}}\put(0.0,-0.8){\line(0,-1){0.05}}\put(0.0,-0.9){\line(0,-1){0.05}}\put(-% 1.0,1.0){\line(1,0){2.0}}\put(-1.0,1.0){\line(0,-1){2.0}}\put(1.0,-1.0){\line(% -1,0){2.0}}\put(1.0,-1.0){\line(0,1){2.0}}\put(0.0,0.0){\circle*{0.15}}\put(0.% 7746,0.0){\circle*{0.15}}\put(-0.7746,0.0){\circle*{0.15}}\put(0.0,0.7746){% \circle*{0.15}}\put(0.0,-0.7746){\circle*{0.15}}\put(0.7746,0.7746){\circle*{0% .15}}\put(-0.7746,0.7746){\circle*{0.15}}\put(0.7746,-0.7746){\circle*{0.15}}% \put(-0.7746,-0.7746){\circle*{0.15}}\end{picture}

Diagram	$(x_{j},y_{j})$	$w_{j}$
$\begin{picture}(2.4,3.0)(-1.2,-1.55)\put(0.0,0.0){\line(1,0){0.05}}\put(0.1,0.% 0){\line(1,0){0.05}}\put(0.2,0.0){\line(1,0){0.05}}\put(0.3,0.0){\line(1,0){0.% 05}}\put(0.4,0.0){\line(1,0){0.05}}\put(0.5,0.0){\line(1,0){0.05}}\put(0.6,0.0% ){\line(1,0){0.05}}\put(0.7,0.0){\line(1,0){0.05}}\put(0.8,0.0){\line(1,0){0.0% 5}}\put(0.9,0.0){\line(1,0){0.05}}\put(0.0,0.0){\line(0,1){0.05}}\put(0.0,0.1)% {\line(0,1){0.05}}\put(0.0,0.2){\line(0,1){0.05}}\put(0.0,0.3){\line(0,1){0.05% }}\put(0.0,0.4){\line(0,1){0.05}}\put(0.0,0.5){\line(0,1){0.05}}\put(0.0,0.6){% \line(0,1){0.05}}\put(0.0,0.7){\line(0,1){0.05}}\put(0.0,0.8){\line(0,1){0.05}% }\put(0.0,0.9){\line(0,1){0.05}}\put(0.0,0.0){\line(-1,0){0.05}}\put(-0.1,0.0)% {\line(-1,0){0.05}}\put(-0.2,0.0){\line(-1,0){0.05}}\put(-0.3,0.0){\line(-1,0)% {0.05}}\put(-0.4,0.0){\line(-1,0){0.05}}\put(-0.5,0.0){\line(-1,0){0.05}}\put(% -0.6,0.0){\line(-1,0){0.05}}\put(-0.7,0.0){\line(-1,0){0.05}}\put(-0.8,0.0){% \line(-1,0){0.05}}\put(-0.9,0.0){\line(-1,0){0.05}}\put(0.0,0.0){\line(0,-1){0% .05}}\put(0.0,-0.1){\line(0,-1){0.05}}\put(0.0,-0.2){\line(0,-1){0.05}}\put(0.% 0,-0.3){\line(0,-1){0.05}}\put(0.0,-0.4){\line(0,-1){0.05}}\put(0.0,-0.5){% \line(0,-1){0.05}}\put(0.0,-0.6){\line(0,-1){0.05}}\put(0.0,-0.7){\line(0,-1){% 0.05}}\put(0.0,-0.8){\line(0,-1){0.05}}\put(0.0,-0.9){\line(0,-1){0.05}}\put(-% 1.0,1.0){\line(1,0){2.0}}\put(-1.0,1.0){\line(0,-1){2.0}}\put(1.0,-1.0){\line(% -1,0){2.0}}\put(1.0,-1.0){\line(0,1){2.0}}\put(0.0,0.0){\circle{0.15}}\put(0.% 7746,0.0){\circle{0.15}}\put(-0.7746,0.0){\circle{0.15}}\put(0.0,0.7746){% \circle{0.15}}\put(0.0,-0.7746){\circle{0.15}}\put(0.7746,0.7746){\circle{0% .15}}\put(-0.7746,0.7746){\circle{0.15}}\put(0.7746,-0.7746){\circle{0.15}}% \put(-0.7746,-0.7746){\circle*{0.15}}\end{picture}$
$(0,0)$	$\tfrac{16}{81}$	$O\left(h^{6}\right)$
$(\pm\sqrt{\tfrac{3}{5}}h,0)$ , $(0,\pm\sqrt{\tfrac{3}{5}}h)$	$\tfrac{10}{81}$
$(\pm\sqrt{\tfrac{3}{5}}h,\pm\sqrt{\tfrac{3}{5}}h)$	$\tfrac{25}{324}$

Reported 2014-01-13 by Stanley Oleszczuk.

…