From Euclidean to Minkowski space with the Cauchy-Riemann equations



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Llanes Estrada, Felipe José and Gimeno Segovia, Mercedes (2008) From Euclidean to Minkowski space with the Cauchy-Riemann equations. European Physical Journal C, 56 (4). pp. 557-569. ISSN 1434-6044

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We present an elementary method to obtain Green’s functions in non-perturbative quantum field theory in Minkowski space from Green’s functions calculated in Euclidean space. Since in non-perturbative field theory the analytical structure of amplitudes often is unknown, especially in the presence of confined fields, dispersive representations suffer from systematic uncertainties. Therefore, we suggest to use the Cauchy–Riemann equations, which perform the analytical continuation without assuming global information on the function in the entire complex plane, but only in the region through which the equations are solved. We use as example the quark propagator in Landau gauge quantum chromodynamics, which is known from lattice and Dyson Schwinger studies in Euclidean space. The drawback of the method is the instability of the Cauchy–Riemann equations against high-frequency noise,which makes it difficult to achieve good accuracy. We also point out a few curious details related to the Wick rotation.

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© Springer-Verlag

Uncontrolled Keywords:Dyson-Schwinger Equations, Renormalization-Group, Scalar Theories, Bethe-Salpeter
Subjects:Sciences > Physics
ID Code:22903
Deposited On:23 Sep 2013 14:52
Last Modified:31 Dec 2020 00:01

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