Isaac Scientific Publishing

New Horizons in Mathematical Physics

Some Theorems upon Negative Energy Density of a Quantum Free Scalar Field in an Inertial World Line of the Minkowski Space-Time

Download PDF (135.4 KB) PP. 33 - 36 Pub. Date: June 23, 2017

DOI: 10.22606/nhmp.2017.11005


  • M.A. Grado-Caffaro*
    M.A. Grado-Caffaro and M. Grado-Caffaro- Scientific Consultants, C/ Julio Palacios 11, 9-B, 28029-Madrid (Spain)
  • M. Grado-Caffaro
    M.A. Grado-Caffaro and M. Grado-Caffaro- Scientific Consultants, C/ Julio Palacios 11, 9-B, 28029-Madrid (Spain)


After presenting a lemma, two theorems on negative energy density associated with a quantum free scalar field are established. The first theorem provides a lower bound for a non-negative weight function whose existence is guaranteed by the lemma. The above energy density is evaluated over an inertial world line of the Minkowski space-time. The second theorem provides an upper bound for the averaged (with respect to the sampling function) absolute expectation value of the negative energy-density function. In particular, a complex-valued sampling function is introduced by the first time so a more generalized formulation is proposed.


Negative energy density, quantum field, inertial world line, Minkowski space-time.


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