Lorentz invariance and the zero-point stress-energy tensor

Abstract

Some 65 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 QFTs), Pauli's cancellation mechanism will survive the introduction of particle interactions. I shall then relate the discussion to BSM physics, to the cosmological constant, and to Sakharov-style induced gravity.

V1: 11 pages; V2: 11 pages, 5 references added; V3: 12 pages, 3 references added; V4: 16 pages, 7 references, extra discussion. V5: 18 pages; new sections added on the renormalization group flow of the Pauli sum rules and net zero point energy. V6: 1 reference added. V7: now 24 pages, more discussion, many references added. Closely corresponds to published version

References in corpus (17)

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• Renormalization of Lorentz violating theories
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• Vacuum energy and spectral function sum rules
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• The Cosmological Constant and Lorentz Invariance of the Vacuum State
• Renormalization Of High-Energy Lorentz Violating Four Fermion Models
• Vacuum energy, Standard Model physics and the $750\mathrm{GeV}$ Diphoton Excess at the LHC
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Cited by in corpus (23)

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• Running vacuum in quantum field theory in curved spacetime: renormalizing ${\rho }_{vac}$ without $\sim m^4$ terms
• Palatini frames in scalar-tensor theories of gravity
• Probing topological superconductors with emergent gravity
• Cosmological acceleration
• Gravitational collapse with quantum fields
• Reference level of the vacuum energy density of the Universe and astrophysical data
• Cosmological Constant and Vacuum Zero Point Energy in Black Hole Backgrounds
• Vacuum polarization instead of "dark matter" in a galaxy
• Comment about the vanishing of the vacuum energy in the Wess-Zumino model
• AEther as an Inevitable Consequence of Quantum Gravity
• The Pauli sum rules imply BSM physics
• Wave optics of quantum gravity for massive particles
• Pauli-Villars regularization of Kaluza-Klein Casimir energy with Lorentz symmetry
• Vacuum Zero Point Energy and its Statistical Correlations in dS Background
• The equation of vacuum state and the structure formation in universe
• The strong CP problem, general covariance, and horizons
• Geometric and computational aspects of chiral topological quantum matter
• The H0 tension: did a QCD meV axion emerge?
• About the measure of the bare cosmological constant
• Quantum fields in boson star spacetime
• Beyond the standard model with sum rules
• Scalar Product for a Version of Minisuperspace Model with Grassmann Variables