Abstract
Some 67 years ago (1951), Wolfgang Pauli noted that the net zero-point energy density could be set to zero by a carefully fine-tuned cancellation between bosons and fermions. In the current article, I will argue in a slightly different direction: the zero-point energy density is only one component of the zero-point stress energy tensor, and it is this tensor quantity that is in many ways the more fundamental object of interest. I shall demonstrate that Lorentz invariance of the zero-point stress energy tensor implies finiteness of the zero-point stress energy tensor, and vice versa. Under certain circumstances (in particular, but not limited to, the finite quantum field theories (QFTs)), Pauli’s cancellation mechanism will survive the introduction of particle interactions. I shall then relate the discussion to beyond standard model (BSM) physics, to the cosmological constant, and to Sakharov-style induced gravity.
Highlights
In his ETH lectures of 1951, Wolfgang Pauli noted that the net zero-point energy density could be set to zero by imposing a carefully fine-tuned cancellation between bosons and fermions [1]
The degeneracy factor g includes an additional factor of 2 when particle and antiparticle are distinct, and an additional factor of 3 due to colour. one sums over all particle species indexed by n. It is the physical relevance of this sum over the entire particle physics spectrum that is Pauli’s key insight. (In related discussion in Ref. [2], the (−1)2S has been absorbed into the degeneracy factor g.) Later on, in the article, we shall directly relate the zero-point energy density ρzpe to the contentious issue of particle-physics estimates of the cosmological constant (See, for instance, Refs. [3,4,5,6,7,8,9,10,11,12,13,14], but, for let us focus on the the zero-point energy density itself)
N (This fourth, logarithmic-in-mass condition, is completely independent of the arbitrary but fixed parameter μ∗, due to one already having imposed the third polynomial-in-mass condition.) This enforced vanishing of the zero-point energy density certainly requires an extremely delicate fine-tuning of the particle physics spectrum
Summary
In his ETH lectures of 1951 (transcribed and translated into English in 1971), Wolfgang Pauli noted that the net zero-point energy density could be set to zero by imposing a carefully fine-tuned cancellation between bosons and fermions [1]. [2], the (−1)2S has been absorbed into the degeneracy factor g.) Later on, in the article, we shall directly relate the zero-point energy density ρzpe to the contentious issue of particle-physics estimates of the cosmological constant We shall see various ways of evading the need for any hard momentum cutoff Using this integral, Pauli observed that the total zero-point energy density vanishes if and only if we first impose the three polynomial-in-mass conditions. N (This fourth, logarithmic-in-mass condition, is completely independent of the arbitrary but fixed parameter μ∗, due to one already having imposed the third polynomial-in-mass condition.) This enforced vanishing of the zero-point energy density certainly requires an extremely delicate fine-tuning of the particle physics spectrum. A somewhat similar formula for the zero-point stress-energy tensor is given in Equation (3) of Ref. The physical framework considering those articles is somewhat different from that considered in the current article
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