Related papers: Recursive equations for Majorana currents
The reduction formulas for Dirac fermions are derived, using the exact solutions of free Dirac equation on de Sitter spacetime. In the framework of the perturbation theory one studies the Green functions and derive the scatering amplitude…
This paper deals with the inverse problem of recovering an arbitrary number of fractional damping terms in a wave equation. We develop several approaches on uniqueness and reconstruction, some of them relying on Tauberian theorems on the…
Differential calculus on the space of asymptotically linear curves is developed. The calculus is applied to the vortex filament equation in its Hamiltonian description. The recursion operator generating the infinite sequence of commuting…
We demonstrate that the use of on-shell methods, involving calculation of the discontinuity across the t-channel cut associated with the exchange of a pair of massless particles, can be used to evaluate loop contributions to both the…
We present a novel framework for deriving on-shell recursion relations, with a specific focus on biadjoint and pure Yang-Mills theories. Starting from the double-cover CHY factorization formulae, we identify a suitable set of independent…
We construct exact functional renormalization group (RG) flow equations for non-relativistic fermions in arbitrary dimensions, taking into account not only mode elimination but also the rescaling of the momenta, frequencies and the…
This thesis presents an overview of the flow equations recently introduced by Wegner. The little known mathematical framework of the flow in the manifold of unitarily equivalent matrices, as discovered in the mathematical literature before…
The problem of fermion dynamics is studied using the Q-function for fermions. This is a probabilistic phase-space representation, which we express using Majorana operators, so that the phase-space variable is a real antisymmetric matrix. We…
We explore whether one can $T \overline{T}$ deform a collection of theories that are already $T \overline{T}$-deformed. This allows us to define classes of irrelevant deformations that know about subsystems. In some basic cases, we explore…
The scattering of Dirac fermions in the background fields of topological solitons of the $(2+1)$-dimensional $\mathbb{CP}^{N-1}$ model is studied using analytical and numerical methods. It is shown that the exact solutions for fermionic…
The Taylor expansion of wave fields with respect to shape parameters has a wide range of applications in wave scattering problems, including inverse scattering, optimal design, and uncertainty quantification. However, deriving the high…
We apply the method of flow equations to describe quantum systems subject to a time-periodic drive with a time-dependent envelope. The driven Hamiltonian is expressed in terms of its constituent Fourier harmonics with amplitudes that may…
We compare different methods used for non-perturbative calculations in strongly interacting fermionic systems. Mean field theory often shows a basic ambiguity related to the possibility to perform Fierz transformations. The results may then…
The generalized Dirac equation of the third order, describing particles with spin 1/2 and three mass states, is analyzed. We obtain the first order generalized Dirac equation in the 24-dimensional matrix form. The mass and spin projection…
We compute the $n_h$ terms to the massive three loop vector-, axialvector-, scalar- and pseudoscalar form factors in a direct analytic calculation using the method of large moments. This method has the advantage, that the master integrals…
We develop a systematic method to derive the Majorana representation of the Dirac equation in (1+3)-dimensions. We compare with similar approach in (2+2)-dimensions . We argue that our formalism can be useful to have a better understanding…
An iterative scheme is presented to solve analytically the relativistic fluid dynamics equations. The scheme is applied to longitudinal expansion, transversal symmetric and transversal asymmetric (triaxial) expansion as well. Within this…
Recently, an extension of the BCFW on-shell recursion relation suitable to compute gauge invariant scattering amplitudes with off-shell particles has been presented for Yang-Mills theories with fermions. In particular, 4- and 5-point…
We give an outline of a formalism for the solution of the evolution equations for off-forward parton distributions in leading and next-to-leading orders based on partial conformal wave expansion and orthogonal polynomials reconstruction.
In front-form dynamics a current operator for systems of interacting particles, which fulfills Poincar\'e, parity and time reversal covariance, together with hermiticity, can be defined. The electromagnetic form factors can be extracted…