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is, therefore, the textbook example for the use of statistical-physics meth- ods. To evaluate the sum over Matsubara frequencies we need to add a con- vergence factor which can be proved by contour integration in the following way. The.
 Although not crucial to the practice of functional field integration, in the construction of. the many–body .. In the last line, the integration measure is defined as d( ??, ?) ?. ?i .. Consider a single Matsubara frequency summation,. S ? ?n.
 10 Feb 2012 From searching in the literature, I know that contour integration is Yes, for this particular Matsubara sum you mentioned, taking different limits will lead to two results differed by 1. which can be seen from the following integral (the continuous limit . For example, if one tries to calculate 1??n1(i?n??)2,.
 In thermal quantum field theory, the Matsubara frequency summation (named after Takeo . The contour integral picks up the residue of these poles, which is equivalent to .. For example, the free energy is obtained by the integral of logarithm,.
 29 Oct 1993 involves (integration over loops, regularization and renormalization), some others arise because of the sums Its allowed values are the so-called Matsubara frequencies: i 2n?/? for Finally, some examples are worked out by using such program. Let us sum 2 coth(?z/2) and C is the contour in fig. 1(a).
 Partition function in the path integral formalism. 7. IV. Real non-interacting scalar field. 9. A. Summation over bosonic Matsubara frequencies. 11. B. Pressure of a
 This is just a simple example to point out the importance of perturbative methods in finite the so-called Matsubara frequencies: i2n'n//3 for bosons and i(2n + 1)'rr//3 for Using the contours in Fig. lc, we can write the integrals in (3) as fi~" =~c
 24 Jun 2017 In thermal quantum field theory, the Matsubara frequency summation The contour integral picks up the residue of these poles, which is
 25 Feb 2010 to work operationally for such Matsubara frequency sums. 1e-mail address: This summation are evaluated in [12] using contour integration and in. [11, 13] using . It is shown to be true for one known example. For more
 16 Jun 2014 One way to do this Matsubara sum that only involves standard results is the following. First, write A=T?n1?2n+a2=T?nei?n0+?2n+a2,.
     
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