Related papers: Celestial Feynman Rules for Scalars
We present Feynman rules for the strong and $\Delta S = 1$ weak chiral Lagrangian which are relevant for calculating $K\to \pi\pi\pi$ decay amplitudes. Feynman rules for this specific case turn out to be too lengthy to be included in a…
We study in detail the general structure and further properties of the tree-level amplitudes in the SU(N) nonlinear sigma model. We construct the flavor-ordered Feynman rules for various parameterizations of the SU(N) fields U(x), write…
We compute four-point scattering amplitudes in $\mathcal{N}=2$ SCQCD with general external matter configurations using $\mathcal{N}=1$ superspace Feynman diagrams, at one loop in the general case and up to two loops in the fundamental…
Friedmans cosmological equations for the scale factor are analyzed for the Universe containing dark energy. The parameter of the equation of state of the dark energy is treated as an arbitrary constant whose value lies within the interval…
We develop further a new geometrical model of a discretized string, proposed in [1] and establish its basic physical properties. The model can be considered as the natural extention of the usual Feynman amplitude of the random walks to…
Propagation of elastic waves along the axis of cylindrical shells is of great current interest due to their ubiquitous presence and technological importance. Geometric imperfections and spatial variations of properties are inevitable in…
We show that the one-loop on-shell four-point scattering amplitude of massless $\phi^4$ scalar field theory in 4D Minkowski space time, when Mellin transformed to the Celestial sphere at infinity, transforms covariantly under the global…
Beyond standard model (BSM) particles should be included in effective field theory in order to compute the scattering amplitudes involving these extra particles. We formulate an extension of Higgs effective field theory which contains…
We study celestial amplitudes in string theory at one-loop. Celestial amplitudes describe scattering processes of boost eigenstates and relate to amplitudes in the more standard basis of momentum eigenstates through a Mellin transform. They…
The field-theoretic wavefunction has received renewed attention with the goal of better understanding observables at the boundary of de Sitter spacetime and studying the interior of Minkowski or general FLRW spacetime. Understanding the…
The Cachazo-He-Yuan (CHY) formula for on-shell scattering amplitudes are extended off-shell. The off-shell amplitudes are M\"obius invariant, and have the same momentum poles as the on-shell amplitudes. The same technique is also used to…
We present an approach to analyze the scalar integrals of any Feynman diagrams in detail here. This method not only completely recovers some well-known results in the literature, but also produces some brand new results on the $C_{_0}$…
Post-Newtonian theory was instrumental in conducting the critical experimental tests of general relativity and in building the astronomical ephemerides of celestial bodies in the solar system with an unparalleled precision. The cornerstone…
We transform the one-loop four-point type $\mathrm{I}$ open superstring gluon amplitude to correlation functions on the celestial sphere including both the (non-)orientable planar and non-planar sector. This requires a Mellin transform with…
It is argued that the amplitudes of the production of $n$ soft scalar particles by one or a few energetic ones in theories like $\lambda\phi^4$ has the exponential form, $A_n\propto\sqrt{n!}\exp[{1\over\lambda}F(\lambda n,\epsilon)]$, in…
Exploiting the analytic properties of the scattering amplitude, we provide an alternative but equivalent definition of the standard Mellin transform used to obtain celestial correlation functions. From this representation, we identify a…
Representations are derived for the basic scalar one-loop vertex Feynman integrals as meromorphic functions of the space-time dimension $d$ in terms of (generalized) hypergeometric functions $_2F_1$ and $F_1$. Values at asymptotic or…
The tensor Feynman amplitudes are reduced to scalar integrals by a procedure of Passarino and Veltman. We provide an alternative approach based on the causal formalism.
The scalar three-point function appearing in one-loop Feynman diagrams is compactly expressed in terms of a generalized hypergeometric function of two variables. Use is made of the connection between such Appell function and dilogarithms…
Possible formulations of the problem of cosmic rays acceleration in the interstellar galactic medium are considered with the use of fractional differential equations. The applied technique has been physically justified. A Fermi result has…