- Access by Xinjiang University
Physical Interpretation of Complex-Energy Negative-Metric Theories
Phys. Rev. D 1, 474 – Published 15 January, 1970
DOI: https://doi.org/10.1103/PhysRevD.1.474
Abstract
It has long been held that the divergences of field theory could be removed if the theory was formulated on a Hilbert space with an indefinite metric. The difficulty of this approach was that the theory then possessed channels with negative probability and therefore violated unitarity. In a recent paper, Lee and Wick have observed that this difficulty could be eliminated if negative-metric states had complex energy. In this paper, we produce a model which shows several of the difficulties associated with the Lee-Wick proposal. The existence of complex energies leads to interpretation difficulties and, in higher sectors, does not completely solve the unitarity problem. We use the model to show how the Lee-Wick conjecture can be extended to overcome the difficulties that are produced. We describe the physical meaning of "good" theories with an indefinite metric.
References (13)
- R. E. Peierls and H. McManus, Proc. Roy. Soc. (London) A195, 323 (1948) H. Yukawa, Phys. Rev. 76, 300 (1949) ibid.76, 1731 (1949) ibid.77, 219 (1950) C. Bloch, Kgl. Danske Videnskab. Selskab, Mat.-Fys. Medd. 27, No. 8 (1952) M. Auretieu and R. E. Peierls, Proc. Roy. Soc. (London) A223, 968 (1954) T. Takabayash, in Proceedings of the International Theoretical Physics Conference on Particles and Fields, Rochester, New York, 1967, edited by C. R. Hagen (Wiley-Interscience, Inc., New York, 1968), p. 413
- W. Pauli and F. Villars, Rev. Mod. Phys. 21, 434 (1949) R. P. Feynman, Phys. Rev. 76, 749 (1949)
- P. A. M. Dirac, Proc. Roy. Soc. (London) A180, 1 (1942) W. Heisenberg, Nucl. Phys. 1, 532 (1951)
- S. N. Gupta, Proc. Phys. Soc. (London) A63, 681 (1950) ibid.A64, 850 (1951) K. Bleuler, Helv. Phys. Acta 23, 567 (1951)
- K. L. Nagy, Nuovo Cimento Suppl. 17, 92 (1960) L. K. Pandit, ibid. 10, 157 (1959) S. Schleider, Z. Naturforsch. 15a, 448 (1960) ibid.15a, 460 (1960) ibid.15a, 555 (1960) E. Scheibe, Ann. Acad. Sci. Fennicae Ser. AI, 294, 1 (1960) J. G. Taylor (unpublished report)
- M. E. Arons, M. Y. Han, and E. C. G. Sudarshan, Phys. Rev. 137, B1085 (1965)
- E. C. G. Sudarshan, Fundamental Problems in Elementary Particle Physics (Wiley-Interscience, Inc., New York, 1968)
- T. D. Lee and G. C. Wick, Nucl. Phys. B9, 209 (1969) ibid.B10, 1 (1969) T. D. Lee, CERN Report No. Th. 914 (unpublished)
- T. D. Lee and R. Serber (unpublished) C. J. Goebel, Phys. Rev. 109, 1946 (1958)
- E. C. G. Sudarshan, in Lectures in Theoretical Physics, Brandeis Summer Institute, 1961 (W. A. Benjamin, Inc., New York, 1962)
- P. A. M. Dirac, Principles of Quantum Mechanics (Oxford University Press, London, 1958), 4th ed., pp. 195-198
- E. C. G. Sudarshan, Phys. Rev. 123, 2183 (1961) H. J. Schnitzer and E. C. G. Sudarshan, ibid. 123, 2193 (1961)
- [12], [6] [7]