%0 Journal Article %1 Freedman:1991tk %A Freedman, Daniel Z. %A Johnson, Kenneth %A Latorre, Jose I. %D 1992 %J Nucl. Phys. %K imported %P 353-414 %T Differential regularization and renormalization: A New method of calculation in quantum field theory %V B371 %X Most primitively divergent Feynman diagrams are well defined in x-space but too singular at short distances for transformation to p-space. A new method of regularization is developed in which singular functions are written as derivatives of less singular functions which contain a logarithmic mass scale. The Fourier transform is then defined by formal integration by parts. The procedure is extended to graphs with divergent subgraphs. No explicit cutoff or counter-terms are required, and the method automatically delivers renormalized amplitudes which satisfy Callan-Symanzik equations. These features are thoroughly explored in massless ?4 theory through 3-loop order, and the method yields explicit functional forms for all amplitudes with less difficulty than conventional methods which use dimensional regularization in p-space. The procedure also appears to be compatible with gauge invariance and the chiral structure of the standard model. This aspect is tested in extensive 1-loop calculations which include the Ward identity in quantum electrodynamics, the chiral anomaly, and the background field algorithm in non-abelian gauge theories.

@article{Freedman:1991tk, abstract = {Most primitively divergent Feynman diagrams are well defined in x-space but too singular at short distances for transformation to p-space. A new method of regularization is developed in which singular functions are written as derivatives of less singular functions which contain a logarithmic mass scale. The Fourier transform is then defined by formal integration by parts. The procedure is extended to graphs with divergent subgraphs. No explicit cutoff or counter-terms are required, and the method automatically delivers renormalized amplitudes which satisfy Callan-Symanzik equations. These features are thoroughly explored in massless ?4 theory through 3-loop order, and the method yields explicit functional forms for all amplitudes with less difficulty than conventional methods which use dimensional regularization in p-space. The procedure also appears to be compatible with gauge invariance and the chiral structure of the standard model. This aspect is tested in extensive 1-loop calculations which include the Ward identity in quantum electrodynamics, the chiral anomaly, and the background field algorithm in non-abelian gauge theories.}, added-at = {2011-03-12T05:52:28.000+0100}, author = {Freedman, Daniel Z. and Johnson, Kenneth and Latorre, Jose I.}, biburl = {https://www.bibsonomy.org/bibtex/2e1245070f722de41408bf280fa0c1252/corneliu}, file = {sdarticle5.pdf:sdarticle5.pdf:PDF}, interhash = {7b3c56cf768d41ced18afe66d45cab25}, intrahash = {e1245070f722de41408bf280fa0c1252}, journal = {Nucl. Phys.}, keywords = {imported}, pages = {353-414}, slaccitation = {%%CITATION = NUPHA,B371,353;%%}, timestamp = {2011-03-12T05:52:32.000+0100}, title = {{D}ifferential regularization and renormalization: {A} {N}ew method of calculation in quantum field theory}, volume = {B371}, year = 1992 }