On the evaluation of Matsubara sums
| dc.creator | Espinosa, Olivier | |
| dc.date | 2009-05-20 | |
| dc.date.accessioned | 2026-07-07T13:16:52Z | |
| dc.date.available | 2026-07-07T13:16:52Z | |
| dc.description | Given a connected (multi)graph G, consisting of V vertices and I lines, we consider a class of multidimensional sums constructed in the following way: - orient the lines of the graph in some (arbitrary) fashion - assign to each line i a positive variable q_i and an integer summation variable n_i - assign to each vertex v an integer variable N_v - construct the following rational function: -- the denominator is a product of factors (n^2+q^2), one for each line of the graph; -- the numerator is a product of Kronecker deltas, one for each vertex of the graph. For each vertex, the Kronecker delta imposes a linear constraint among the summation variables n_i of the lines incident upon the vertex, requiring that the sum of the variables n_i of the lines coming out of vertex minus the sum of the variables n_i of the lines coming into the vertex be equal to the integer variable N assigned to that vertex. - sum over all the n_i variables from minus infinity to infinity The sums thus constructed, called Matsubara sums, are functions of the I real positive variables q_i and the V integer variables N_v. It is shown any Matsubara sum can be evaluated in closed form by applying a linear operator to an integral closely associated with the sum. | |
| dc.description | 18 pages, 5 figures | |
| dc.identifier | https://arxiv.org/abs/0905.3366 | |
| dc.identifier | http://arxiv.org/abs/0905.3366 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/230933 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Mathematical Physics | |
| dc.subject | 33E20; 33F99 | |
| dc.title | On the evaluation of Matsubara sums | |
| dc.type | text |