We apply the δ-expansion perturbation scheme to the λφ4 self-interacting scalar field theory in 3+1 D at finite temperature. In the δ-expansion the interaction term is written as λ(φ2)1+δ and δ is considered as the perturbation parameter. We compute within this perturbative approach the renormalized mass at finite temperature at a finite order in δ. The results are compared with the usual loop-...

A conserved cosmological perturbation is associated with each quantity whose local evolution is determined entirely by the local expansion of the Universe. It may be defined as the appropriately normalised perturbation of the quantity, defined using a slicing of spacetime such that the expansion between slices is spatially homogeneous. To first order, on super-horizon scales, the slicing with u...

In L(R), we consider the unperturbed Stark operator H0 (i.e., the Schrödinger operator with a linear potential) and its perturbation H = H0 + V by an infinitely smooth compactly supported potential V . The large energy asymptotic expansion for the modified perturbation determinant for the pair (H0, H) is obtained and explicit formulae for the coefficients in this expansion are given. By a stand...

Perturbation–iteration theory is systematically generated for both linear and nonlinear second-order differential equations and applied to Bratu-type equations. Different perturbation–iteration algorithms depending upon the number of Taylor expansion terms are proposed. Using the iteration formulas derived using different perturbation–iteration algorithms, new solutions of Bratu-type equations ...