Isaac Scientific Publishing

New Horizons in Mathematical Physics

NHMP > Volume 1, Issue 1, June 2017

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

Author(s)

  • 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)

Abstract

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.

Keywords

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

References

[1] M. Bordag, U. Mohideen, V.M. Mostepanenko, Phys. Rep. 353 (2001) 1.

[2] C.J. Fewster, S.P. Eveson, Phys. Rev. D 58 (1998) 084010.

[3] C.J. Fewster, E. Teo, Phys. Rev. D 59 (1999) 104016.

[4] S.P. Eveson, Ch.J. Fewster, R. Verch, Ann. Henri Poincaré 6 (2005) 1-30.

[5] M.A. Grado-Caffaro, M. Grado-Caffaro, Nonlin. Opt. Quant. Opt. 42 (2011) 103-108.

[6] M.A. Grado-Caffaro, M. Grado-Caffaro, Int. J. Theor. Phys. Group Theory Nonlin. Opt. 17 (2013) 91-100.

[7] M.A. Grado-Caffaro, M. Grado-Caffaro, Adv. Studies Theor. Phys. 7 (2013) 549-554.

[8] M.A. Grado-Caffaro, M. Grado-Caffaro, Optik 122 (2011) 1216-1217.

[9] M.A. Grado-Caffaro, M. Grado-Caffaro, Optik 124 (2013) 4095-4096.

[10] M.S. Morris, K.S. Thorne, U. Yurtsever, Phys. Rev. Lett. 61 (1988) 1446.

[11] M.S. Morris, K.S. Thorne, Amer. J. Phys. 56 (1988) 395.

[12] H. Bostelmann, D. Cadamuro, Phys. Rev. D 93 (2016) 065001.

[13] L.M. Butcher, Phys. Rev. D 90 (2014) 024019.

[14] S. Kruchinin, Rev. Theor. Sci. 4 (2016) 117-144.

[15] S. Kruchinin, H. Nagao, S. Aono: Modern aspects of superconductivity: theory of superconductivity, World Scientific Pub. (2010) p.220.