Abstract
We show that a non-zero renormalised value of the zero-point energy in λϕ4-theory over Minkowski spacetime is in tension with the scalar-field equation at two-loop order in perturbation theory.
Highlights
Quantum fields give rise to an infinite vacuum energy density [1,2,3,4], which arises from quantum-field fluctuations taking place even in the absence of matter
In the presence of matter, there are quantum effects occurring in nature, which cannot be understood without quantum-field fluctuations. These are the spontaneous emission of a photon by excited atoms, the Lamb shift, the anomalous magnetic moment of the electron, and so forth [5]. This means quantum-field fluctuations do manifest themselves in nature and, the zero-point energy poses a serious problem
Lorentz symmetry implies that vacuum stress-energy tensor is proportional to the metric tensor [2]
Summary
Quantum fields give rise to an infinite vacuum energy density [1,2,3,4], which arises from quantum-field fluctuations taking place even in the absence of matter. In the presence of matter, there are quantum effects occurring in nature, which cannot be understood without quantum-field fluctuations. These are the spontaneous emission of a photon by excited atoms, the Lamb shift, the anomalous magnetic moment of the electron, and so forth [5]. This means quantum-field fluctuations do manifest themselves in nature and, the zero-point energy poses a serious problem. The vacuum energy density must equal a quarter of the stress-tensor trace.
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