Quantum inequalities in two-dimensional Minkowski spacetime

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 56, Issue 8, 1997, Pages 4922-4926

  Flanagan, Éanna É ^a  

^a Department of Population Medicine and Diagnostic Sciences   (United States)

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EID: 0000843028     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.56.4922     Document Type: Article

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22. Note that we are using a notation where the argument of (Formula presented) is always the (Formula presented) coordinate of the spacetime point, never the (Formula presented) coordinate; in other words we shall not use the notation (Formula presented) to denote the field operator at the spacetime point with (Formula presented)-coordinate value (Formula presented) and (Formula presented) coordinate value (Formula presented)
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25. Roman has recently derived constraints on averages over both space and time of energy density [T. A. Roman (unpublished)]. Similar constraints can also be obtained by an application of our result (2.6): we can obtain lower bounds on very general space-time smearings of the stress-energy tensor using the fact that for any smooth tensor (Formula presented) (Formula presented) where (Formula presented) and (Formula presented) The expected value of two terms on the right-hand side can be bounded below using Eq. (2.6).