Related papers: A Group-Theoretical Method for Natanzon Potentials…
Effective superpotentials obtained by integrating out matter in super Yang-Mills and conformal supergravity backgrounds in N=1 SUSY theories are considered. The pure gauge and supergravity contributions (generalizing Veneziano-Yankielowicz…
We outline a general method of obtaining exact solutions of Schroedinger equations with a position dependent effective mass. Exact solutions of several potentials including shape invariant potentials have also been obtained.
An exact differential equation is derived for the evolution of the Liouville effective action with the mass parameter. This derivation is based on properties of the exponential potential and some consequences of the equation are discussed.
We study the one-loop quantum corrections for higher-derivative superfield theories, generalizing the approach for calculating the superfield effective potential. In particular, we calculate the effective potential for two versions of…
We present a new framework for a Lagrangian description of conformal field theories in various dimensions based on a local version of d+2-dimensional conformal space. The results include a true gauge theory of conformal gravity in d=(1,3)…
We present a novel way to compute the one-loop ring-improved effective potential numerically, which avoids the spurious appearence of complex expressions and at the same time is free from the renormalization ambiguities of the…
The renormalization-group improved effective potential ---to leading-log and in the linear curvature approximation--- is constructed for ``finite'' theories in curved spacetime. It is not trivial and displays a quite interesting,…
It is shown that for a class of position dependent mass Schroedinger equation the shape invariance condition is equivalent to a potential symmetry algebra. Explicit realization of such algebras have been obtained for some shape invariant…
Motivated by questions arising in the study of harmonic maps and Yang Mills theory, we study new techniques for producing optimal monotonicity relations for geometric partial differential equations. We apply these results to sharpen epsilon…
The gauge parameter dependence of the effective potential is determined by partial differential equations involving also the Higgs boson field expectation value. Solving these equations by the method of characteristics leads to complete…
The optimized effective potential method is formulated as a convex minimization problem. This formulation does not require assumptions about $v$-representability nor functional differentiability. The formulation provides a natural framework…
The energy eigenvalues and the corresponding eigenfunctions of the one-dimensional Klein-Gordon equation with q-parameter Poschl-Teller potential are analytically obtained within the position-dependent mass formalism. The parametric…
The superposition of atomic potentials (SAP) approach has recently been shown to be a simple and efficient way to initialize electronic structure calculations [S. Lehtola, J. Chem. Theory Comput. 15, 1593 (2019)]. Here, we study the…
The exact bound state spectrum of rationally extended shape invariant real as well as $PT$ symmetric complex potentials are obtained by using potential group approach. The generators of the potential groups are modified by introducing a new…
The second functional derivative of the effective potential of pure fermionic field theories is rewritten in a factorized form which facilitates the evaluation of the renormalisation flow rate of the effective action in the Wetterich…
We present a general method to obtain a closed, finite formula for the exponential map from the Lie algebra to the Lie group, for the defining representation of the orthogonal groups. Our method is based on the Hamilton-Cayley theorem and…
In this paper we calculate the leading divergences of the effective potential for an arbitrary scalar theory on a curved spacetime background. Based on the recurrence relation between the leading poles following from the locality condition,…
We consider compact objects in a classical and non-relativistic generalisation of Newtonian gravity, dubbed bootstrapped Newtonian theory, which includes higher-order derivative interaction terms of the kind generically present in the…
The radial part of the Klein-Gordon equation for the generalized Woods-Saxon potential is solved by using the Nikiforov-Uvarov method in the case of spatially dependent mass within the new approximation scheme to the centrifugal potential…
We present the second part of a paper series devoted to the study of the multi-loop effective potential evolution in $\varphi^4$-theory using the conformal symmetry. In this paper, we demonstrate that the conformal symmetry can still be…