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Prog. Theor. Phys. Vol. 11 No. 1 (1954) pp. 1-10

Invariant Delta Functions in the Sense of Distributions

Takehito Takahashi

Seizyo University, Setagaya, Tokyo

(Received November 16, 1953)

Abstract:

Invariant delta functions are most adequately interpreted in the sense of distributions of L. Schwartz. They are expressed as the sum of proper distributions and mass-dependent point functions. First terms are interpreted as the logarithmic or finite parts of the divergent integrals corresponding to the inverse square of the four-dimensional distance. Point function term of Δ⁽¹⁾ exhibits logarithmic singularities on the surface of the light cone, defining a finite value as a distribution.

URL : http://ptp.ipap.jp/link?PTP/11/1/
DOI : 10.1143/PTP.11.1

[ Full Text PDF : FREE ACCESS (554K) ] Citation: Plain Text BiBTeX EndNote(RIS) RSS

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References:

1. L. Schwartz, Théorie des distributions, I, II, Paris, Hermann (1950-51).
2. L. Schwartz, Ann. Inst. Fourier 2 (1950), 19.
3. R. Courant und D. Hilbert, Methoden der mathematischen Physik, II, Berlin, Springer (1937), 159, 165, 402, 448.
4. W. Güttinger, Phys. Rev. 89 (1953), 1004[APS].

Citing Article(s) :

1. Progress of Theoretical Physics Vol. 13 No. 6 (1955) pp. 612-626 :

   Products of Improper Operators and the Renormalization Problem of Quantum Field Theory

   Werner Güttinger

2. Progress of Theoretical Physics Vol. 14 No. 3 (1955) pp. 260-261 :

   Some Remarks on the Applicability of the Field Theory from the Standpoint of the Distribution Analysis

   Hitoshi Wakita

3. Progress of Theoretical Physics Vol. 15 No. 2 (1956) pp. 167-177 :

   On a Regular Formulation of Quantum Field Theory, I

   Ken-iti Gotô

4. Progress of Theoretical Physics Vol. 16 No. 2 (1956) pp. 149-150 :

   An Attempt of Generalizing the Hypothesis of Charge Independence

   Osamu Hara and Yasunori Fujii

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