Quick Search:
Prog. Theor. Phys. Vol. 11 No. 3 (1954) pp. 291-308
On the Construction of S-matrix in Lagrangian Formalism
Tsutomu Imamura,
Sigenobu Sunakawa and
Ryôyû Utiyama
Department of Physics, Osaka University
(Received December 31, 1953)
Abstract:
Some differential equations with respect to a coupling constant g are written down in Lagrangian formalism. By integrating these equations S-matrix can be derived in two different forms; one is expressed in terms of the chronological symbol T* (or P*); the other in terms of T (or P). This way of consideration is applied to the system of local fields with non-local interactions. According to the result thus obtained, it seems necessary to make a further investigation on a new condition which ensures the existence of S-matrix.
URL :
http://ptp.ipap.jp/link?PTP/11/291/
DOI : 10.1143/PTP.11.291
References:
-
H. Yukawa, Phys. Rev. 77 (1950), 219[APS];
ibid. 80 (1950), 1047[APS].
-
M. Fierz, Phys. Rev. 78 (1950), 184[APS].
- P. Kristensen and C. Møller, Danske Vidensk. Selsk. Mat. -fys. Medd. 27 (1952), No. 7.
C. Bloch, Danske Vidensk. Selsk. Mat. -fys. Medd. 27 (1952), No. 8.
M. Chrétien and R. E. Peierls, Nuovo Cim. 10 (1953), 669.
Y. Takahashi and H. Umezawa, Prog. Theor. Phys. 9 (1953), 14[PTP].
Y. Katayama, Prog. Theor. Phys. 10 (1953), 31[PTP].
- W. Pauli, Nuovo Cim. 10 (1953), 648.
-
J. Schwinger, Phys. Rev. 82 (1951), 914[APS].
- In the International Congress in Kyoto Bloch proposed to determine S-matrix in every order of g by adding some terms to the original Lagrangian density in such a way as to be able to get the S-matrix in that order of g.
However, it seems that this procedure results in substituting another problem for the given one, and further it is quite doubtful if this procedure will converge.
- In order to prove the relation (II) in case of F=π, it is necessary to know the expression of Δπ as a functional of φ, π and Δφ.
Δπ is determined as follows:
Let it be supposed that π is transformed into π=π+Δπ according to the variation of φ→φ=φ+Δφ.
Since π must be canonically conjugate to φ, we have the relation; [π(\vecx, τ), φ(\vecx',τ)]=[π(\vecx, τ), φ(\vecx',τ)]=1/i·δ(\vecx-\vecx').
If Δφ is assumed to be commutative with φ, we can get an equation [Δπ, φ]+[π, Δφ]=((δΔπ)/(δπ)+(δΔφ)/(δφ))[π,φ]=0 from the above relation, By integrating this with respect to, π, Δπ is given as follows, Δπ=-½ {π((δΔφ)/(δφ))+((δΔφ)/(δφ))π}.
-
W. K. Burton, Phys. Rev. 84 (1951), 159[APS].
- A similar work was done by C. Levinson, the preprint of which was shown us by Professor H. Yukawa.
Citing Article(s) :
-
Progress of Theoretical Physics Vol. 24 No. 4 (1960) pp. 689-720
:
-
Energy Spectrum and Scattering Problem in Quantized Field Theory
-
Shûkô Azuma
-
Progress of Theoretical Physics Vol. 25 No. 3 (1961) pp. 381-403
:
-
Phase Shift and Identities in Quantized Field Theory
-
Shûkô Azuma
-
Progress of Theoretical Physics Vol. 59 No. 4 (1978) pp. 1376-1390
:
-
S-Matrix for Interacting Extended Boson Fields. II
-
A. Z. Capri and C. C. Chiang
