3 research outputs found
Symmetry Factors of Feynman Diagrams for Scalar Fields
The symmetry factor of Feynman diagrams for real and complex scalar fields is
presented. Being analysis of Wick expansion for Green functions, the mentioned
factor is derived in a general form. The symmetry factor can be separated into
two ones corresponding to that of connected and vacuum diagrams. The
determination of symmetry factors for the vacuum diagrams is necessary as they
play a role in the effective action and phase transitions in cosmology. In the
complex scalar theory the diagrams different in topology may give the same
contribution, hence inverse of the symmetry factor (1/S) for total contribution
is a summation of each similar ones (1/S_i), i.e., 1/S = \sum_i (1/S_i).Comment: Journal version, new references adde
Recursive Graphical Solution of Closed Schwinger-Dyson Equations in phi^4-Theory -- Part1: Generation of Connected and One-Particle Irreducible Feynman Diagrams
Using functional derivatives with respect to the free correlation function we
derive a closed set of Schwinger-Dyson equations in phi^4-theory. Its
conversion to graphical recursion relations allows us to systematically
generate all connected and one-particle irreducible Feynman diagrams for the
two- and four-point function together with their weights.Comment: Author Information under http://www.physik.fu-berlin.de/~pelster