Weigel reports about his development of an efficient method, based on scattering data (spectral method) about a scalar field configuration of given topology (static solution to the classical equation of motion), to compute its one-loop effective potential (or

vacuum polarization energy, VPE) in a 1 + 1D [[phi].sup.6] (nonrenormalizable) theory where fluctuations do not naturally decompose into parity eigenstates since the background field may connect inequivalent vacua (not related by a parity transformation).

In this paper, we will focus on the vacuum polarization by scalar field and its testing.

[delta][[PHI].sub.5D] ~ 0, and the effect on the vacuum polarization may be extremely difficult to detect.

However, thermal contributions to electric permittivity, magnetic permeability, and dielectric constant of the medium are derived from the vacuum polarization. Some of the important parameters of QED plasma such as Debye shielding length, plasma frequency, and the phase transitions can be obtained from the properties of the medium itself.

Calculations of the vacuum polarization tensor show that the real part of the [9, 10] longitudinal and transverse components of the polarization tensors can be evaluated, in the limit [omega] [right arrow] 0, as

The

vacuum polarization by a scalar field has been studied in the Schwarzschild spacetime [10], in a waveguide [11], in the de Sitter spacetime with the presence of global monopole [12], and in a homogeneous space with an invariant metric [13].

For that reason, the quantum correction to the classical energy is called

vacuum polarization energy (VPE).

We should note that these energy conditions are violated by certain states of quantum fields, amongst which one may refer to the Casimir energy, Hawking evaporation, and

vacuum polarization [5-12].

Again, the first and second ratios in (3) and (4) are

vacuum polarization and curvature forces respectively.

The ([e.sub.*]) in (2) belongs to the free-space proton and the (-[e.sub.*]) to the separate Planck particles of the PV, where the first and second ratios in (2) are the

vacuum polarization and curvature forces respectively.

Suppression of singularities by the [9.sup.55] field with mass and classical

vacuum polarization in a classical Kaluza-Klein theory.

As in a review by Gross [7], the point could further be made that a "

vacuum polarization" screens the point-chargelike electron in such a way that its effective electrostatic force vanishes at large distances.