Related papers: A Group-Theoretical Method for Natanzon Potentials…
This work studies in detail the possibility of defining a one-to-one mapping from charge densities as obtained by the time-dependent Schr\"odinger equation to external potentials. Such a mapping is provided by the Runge-Gross theorem and…
We set up a method for a recursive calculation of the effective potential which is applied to a cubic potential with imaginary coupling. The result is resummed using variational perturbation theory (VPT), yielding an exponentially fast…
The Polchinski exact renormalization group equation for a scalar field theory in arbitrary dimensions is translated, by means of a covariant Hamiltonian formalism, into a partial differential equation for an effective Hamiltonian density…
We describe a prescription for constructing conformal blocks in conformal field theories in any space-time dimension with arbitrary quantum numbers. Our procedure reduces the calculation of conformal blocks to constructing certain group…
We introduce some general and special formulations of general position theorem for parametrized families of fractals and explain the techniques of its application to prove the existence of self-similar sets with prescribed special…
Combining an optimized expansion scheme in the spirit of the background field method with the Coleman's normal-ordering renormalization prescription, we calculate the effective potential of sine-Gordon field theory beyond the Gaussian…
The derivation of effective equations for group field theories is discussed from a variational point of view, with the action being determined by the fidelity of the trial state with respect to the exact state. It is shown how the…
Some exact analytical formulas are derived for the potential and mass ratio as a function of Lagrangian points position, in the classical Roche model of the close binary stars.
We consider quantum inverse scattering with singular potentials and calculate the Sine-Gordon model effective potential in the laboratory and centre-of-mass frames. The effective potentials are frame dependent but closely resemble the…
Based on the decomposition of SU(2) gauge field, we derive a generalization of the decomposition theory for the SU(N) gauge field. We thus obtain the invariant electro-magnetic tensors of SU(N) groups and the extended Wu-Yang potentials.…
The concept of moment differentiation is extended to the class of moment summable functions, giving rise to moment differential properties. The main result leans on accurate upper estimates for the integral representation of the moment…
We derive the field-dependent masses in Fermi gauges for arbitrary scalar extensions of the Standard Model. These masses can be used to construct the effective potential for various models of new physics. We release a flexible…
A supersymmetric technique for the solution of the effective mass Schr\"{o}% dinger equation is proposed. Exact solutions of the Schroedinger equation corresponding to a number of potentials are obtained. The potentials are fully…
The present work draws on the understanding how notions of general potential theory - as set up, e.g., by Fuglede - explain existence and some basic results on the "magical" rendezvous numbers. We aim at a fairly general description of…
The inhomogeneous wave equations for the scalar, vector, and Hertz potentials are derived starting from retarded charge, current, and polarization densities and then solved in the reciprocal (or k-) space to obtain general solutions, which…
We derive a formula describing the transformation of the Hawking-Hayward quasi-local energy under a conformal rescaling of the spacetime metric. A known formula for the transformation of the Misner-Sharp-Hernandez mass is recovered as a…
We consider the $\Omega$-deformed $\mathcal{N}=2$ $SU(2)$ gauge theory in four dimensions with $N_{f}=4$ massive fundamental hypermultiplets. The low energy effective action depends on the deformation parameters $\varepsilon_{1},…
We compute the one-loop non-holomorphic effective potential for the N=4 SU(n) supersymmetric Yang-Mills theory with the gauge symmetry broken down to the maximal torus. Our approach remains powerful for arbitrary gauge groups and is based…
We formulate the equations which determine a potential function in an $\mathcal{N}=1$ higher derivative supersymmetric mechanics compatible with the $osp(2|1)\oplus so(d)$ symmetry and provide a few explicit examples.
Representations of the symmetry group D_n of the n-sided regular polygon have generic multiplication rules if n is prime. Using D_n with n=5 or greater, a particular well-known form of the Majorana neutrino mass matrix is derived.