Interpretation of the energy of the vacuum as the sum over zero-point energies

Abstract

It is shown that the energy of the vacuum obtained by functional methods as the one-loop quantum effective potential may be interpreted as the sum over zero-point energies of the quantum modes of the fields provided that f(0), the scale dependence of the quadratic variation of the action, vanishes. This scale dependence does not vanish when one-loop renormalization counterterms are induced in the action by a scale transformation, in which case one has to add to the sum over zero-point energies a term proportional to f (0) to get the correct energy of the vacuum.

On the equivalence between the effective potential and zero-point energy

“…This is a important hypothesis for our derivation as was also observed by Myers [10]. The generalized zeta function associated to the operator M (x, y), defined by (4), can be written, using (7), as…”

“…The inclusion of scale parameter µ in (12) and (13) is an important step since now from (6), (10) and (13) we find the relation between the effective potential and the zero-point energy…”

“…In his paper Myers [10] stressed that the vacuum energy density calculated via an effective potential could be interpreted as the sum over zero-point energies except for an extra term. When this extra term is zero, both definitions of vacuum energy coincide.…”

“…Some years ago E. Myers showed [10] that vacuum energy calculated via the effective potential could be interpreted like zero-point energy except for an extra term. As we shall see this extra term arises when the scale parameter µ is not included in the definition of the generalized zeta function associated to the Hamiltonian operator for the sum over zero-point energy.…”

Unobservable Potentials to Explain Single Photon and Electron Interference

“…In addition, (33) The zero-point energy has been measured through Casimir effect [39][40][41][42][43] . The following circumstance can be identified as a typical setup for the measurement of Casimir effect.…”