Prog. Theor. Phys. Vol. 33 No. 4 (1965) pp. 774-776

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On the New Theory of Gravitation of Hoyle and Narlikar

Research Institute for Theoretical Physics, Hiroshima University, Takehara, Hiroshima-ken

(Received January 18, 1965)

URL : http://ptp.ipap.jp/link?PTP/33/774/
DOI : 10.1143/PTP.33.774

F. Hoyle and J. V. Narlikar, Proc. R. Soc. A 282 (1964), 191.
T. Kimura, Prog. Theor. Phys. 33 (1965), 510[PTP].
The term λm²(-g)^1/4 φ² has the desired character but is not a scalar density.
Formally the conventional interpretation is possible provided that the indefinite metric is introduced in Hilbert space.
See, for instance, S. N. Gupta, Can. J. Phys. 35 (1957), 961.
In this case, the expecttion value of T_ik is also positive.
If we take <φφ>₀=(1/2)\displaystylelim _t'→t<{φ(x, t), φ(x, t')}>₀=(1/2)\displaystylelim _t'→tΔ⁽¹⁾(x, t; x, t') in place of Eq. (8), <φφ>₀ becomes negative and an attractive interaction is obtained.
However, such a definition is not satisfactory.