RT Journal Article
T1 From Euclidean to Minkowski space with the Cauchy-Riemann equations
A1 Llanes Estrada, Felipe José
A1 Gimeno Segovia, Mercedes
AB 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.
PB Springer
SN 1434-6044
YR 2008
FD 2008-08
LK https://hdl.handle.net/20.500.14352/50787
UL https://hdl.handle.net/20.500.14352/50787
LA eng
NO © Springer-Verlag
NO Comunidad de Madrid
NO Accion Integrada Hispano-Lusa
DS Docta Complutense
RD 10 abr 2025