http://redberry.cc/ 2026-04-14T15:54:45+00:00 http://redberry.cc/ http://redberry.cc/lib/tpl/redberry/images/favicon.ico text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:tutorials:annihilation_to_muons_in_qed?rev=1448109188&do=diff Annihilation to muons ---------- Code There is only one Feynman diagram responsible for process in the leading order. The following Redberry code produces squared matrix element of this process: Which is a well known formula: See also * Related guides: text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:tutorials:b_c_to_u_bar_d_gamma?rev=1448109188&do=diff B_c \to u \bar d \gamma ---------- Theory ......... Code text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:tutorials:compton_scattering_in_qcd?rev=1448109188&do=diff Compton scattering in QCD ---------- Theory Let us consider Compton scattering in QCD. There are three Feynman diagrams: Since the last diagram contains 3-gluon vertex and in order to avoid ghosts contributions, we will use QCD axial gauge: where text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:tutorials:compton_scattering_in_qed?rev=1448109188&do=diff Compton scattering in QED ---------- Theory Let us consider Compton scattering in spinor QED. There are two Feynman diagrams: The Feynman rules for spinor QED are: where is an electron charge and is Dirac matrix. Using these Feynman rules it is easy to write amplitudes corresponding to the above Feynman diagrams: text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:tutorials:compton_scattering_in_scalar_qed?rev=1448109188&do=diff Compton scattering in scalar QED Theory Let us consider Compton scattering in scalar QED. There are three Feynman diagrams: The Feynman rules for scalar QED are: where is a scalar charge and in the second formula is incoming and outcoming scalar field momentum. text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:tutorials:gravitational_field?rev=1448109188&do=diff Gravitational field ---------- Code Let us consider gravitational field in -family gauge conditions (for details see Sec. 5.5 in Nucl.Phys. B485 (1997) 517-544). The action with gauge-fixing term can be written as follows: where Calculating the second variation and symmetrising over indices by commuting covariant derivatives, it is easy to obtain all text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:tutorials:minimal_fourth_order_operator?rev=1448109188&do=diff Minimal fourth order operator ---------- Code Let' s calculate one-loop counterterms of minimal fourth order operator using methods described in Calculating one-loop counterterms. The operator is: The input quantities needed for the algorithm described in Calculating one-loop counterterms are: The following code produces the result: text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:tutorials:minimal_second_order_operator?rev=1448109188&do=diff Minimal second order operator ---------- Code Let' s calculate one-loop counterterms of minimal second order operator using methods described in Calculating one-loop counterterms. The operator is: The input quantities needed for the algorithm described in Calculating one-loop counterterms are: The following code produces the result: text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:tutorials:spin-3_propagator?rev=1448109188&do=diff Spin-3 propagator ---------- Code The quadratic form of spin-3 Lagrangian in the momentum space is: where is a momentum. The equation for the propagator is: The following Redberry code produces propagator in four dimensions (here we used l for text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:tutorials:squared_vector_field?rev=1448109188&do=diff Squared vector field operator ---------- Code Let' s calculate one-loop counter terms of squared vector field operator using methods described in Calculating one-loop counterterms. The operator is: By commuting covariant derivatives, it is easy to obtain the input quantities needed for the algorithm described in text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:tutorials:vector_field?rev=1448109188&do=diff Vector field ---------- Code Let us consider one-loop counterterms of the the vector field operator, which appears in the theory of the massive vector field: where and . This is a second order operator, and in order to rewrite it in the symmetric form, it is necessary to symmetrize the second term by commutation of the covariant derivatives: