1997/06/12 by Stephen L. Adler
Physics and Astronomy · #Action (physics) #Black Holes and Theoretical Physics #Classical mechanics #Cosmological constant #Cosmology and Gravitation Theories #Effective action #Geometry #Mathematical physics #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Operator (biology) #Physics #Primordial fluctuations #Quantum field theory #Quantum mechanics #Scale invariance #TRACE (psycholinguistics) #Tensor (intrinsic definition) #Theoretical physics #hep-th
paper · pdf · doi:10.1023/a:1018897011431
published as Gen.Rel.Grav. 29 (1997) 1357-1362 · Second award in the Gravity Research Foundation Essay Competition for 1997; to appear in General Relativity and Gravitation. Plain Tex, no figures
arxiv created 1997/06/12 · openalex publication_date 1997/11/01 · arxiv updated 2015/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Recent work has shown that complex quantum field theory emerges as a statistical mechanical approximation to an underlying noncommutative operator dynamics based on a total trace action. In this dynamics, scale invariance of the trace action becomes the statement 0=Re Tr Tμμ, with Tμν the operator stress energy tensor, and with Tr the trace over the underlying Hilbert space. We show that this condition implies the vanishing of the cosmological constant and vacuum energy in the emergent quantum field theory. However, since the scale invariance condition does not require the operator Tμμ to vanish, the spontaneous breakdown of scale invariance is still permitted.