Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1997-06-12
Gen.Rel.Grav. 29 (1997) 1357-1362
Physics
High Energy Physics
High Energy Physics - Theory
Second award in the Gravity Research Foundation Essay Competition for 1997; to appear in General Relativity and Gravitation. P
Scientific paper
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 $0=Re Tr T_{\mu}^{\mu}$, with $T_{\mu \nu}$ 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 $T_{\mu}^{\mu}$ to vanish, the spontaneous breakdown of scale invariance is still permitted.
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