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Prog. Theor. Phys. Vol. 57 No. 1 (1977) pp. 269-278

[ Full Text PDF : FREE ACCESS (546K) ]

Free Massless Scalar Field in Two-Dimensional Space-Time

Noboru Nakanishi

Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606

(Received June 23, 1976)

Abstract:

It is known that because of infrared divergence a free massless scalar field in two-dimensional space-time cannot be consistently quantized in a positive-difinite Hilbert space. It is shown that this difficulty can be overcome in the framework of the indefinite-metric quantum field theory. The positivity condition is recovered in a relativistically invariant physical subspace. Various properties of the free massless scalar field are studied in detail as the preliminaries for the investigation of the Thirring and Schwinger models.


URL : http://ptp.ipap.jp/link?PTP/57/269/
DOI : 10.1143/PTP.57.269

[ Full Text PDF : FREE ACCESS (546K) ] Citation:

References:

  1. A. S. Wightman, 1964 Cargèse Lectures in Theoretical Physics, edited by M. Lévy (Gordon and Breach, 1967), p. 171.
    See also, J. Tarski, J. Math. Phys. 5 (1964), 1713[CrossRef].
  2. S. Coleman, Commun. Math. Phys. 31 (1973), 259[CrossRef].
  3. N. Nakanishi, Prog. Theor. Phys. to be published.
  4. B. Klaiber, 1967 Boulder Lectures in Theoretical Physics, (Gordon and Breach, 1968) Vol. XA, p. 141.

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 57 No. 2 (1977) pp. 580-592 :
    Operator Solutions in Terms of Asymptotic Fields in the Thirring and Schwinger Models
    Noboru Nakanishi
  2. Progress of Theoretical Physics Vol. 57 No. 3 (1977) pp. 1025-1037 :
    Operator Solutions in Terms of Asymptotic Fields in the Thirring and Schwinger Models. II
    Noboru Nakanishi
  3. Progress of Theoretical Physics Vol. 57 No. 3 (1977) pp. 1079-1081 :
    Operator Solution in Terms of Asymptotic Fields in the Schroer Model
    Noboru Nakanishi
  4. Progress of Theoretical Physics Vol. 58 No. 3 (1977) pp. 1007-1013 :
    Lorentz Transformation Properties in the Thirring and Schwinger Models
    Noboru Nakanishi
  5. Progress of Theoretical Physics Vol. 58 No. 5 (1977) pp. 1580-1584 :
    Operator Solution in Terms of Asymptotic Fields in the Pre-Schwinger Model
    Noboru Nakanishi
  6. Progress of Theoretical Physics Vol. 58 No. 6 (1977) pp. 1927-1934 :
    Reconstruction of the Lowenstein-Swieca Solution from the Asymptotic-Field One in the Schwinger Model
    Noboru Nakanishi
  7. Progress of Theoretical Physics Vol. 59 No. 2 (1978) pp. 607-618 :
    Asymptotic Completeness and Confinement in the Massive Schwinger Model
    Noboru Nakanishi
  8. Progress of Theoretical Physics Vol. 59 No. 4 (1978) pp. 1403-1404 :
    Dipole-Ghost Gauge Theory as a Possible Model of the Gluon
    Noboru Nakanishi
  9. Progress of Theoretical Physics Vol. 60 No. 3 (1978) pp. 892-907 :
    Boson-Representation of U(n)-Symmetric Thirring Model in Indefinite Metric Space
    P. Mitra
  10. Progress of Theoretical Physics Vol. 62 No. 6 (1979) pp. 1718-1741 :
    On the Lorentz Transformations of Operator Solutions of the Pre-Schwinger Model
    Yuji Nakawaki
  11. Progress of Theoretical Physics Vol. 62 No. 6 (1979) pp. 1742-1755 :
    On the Bosonization of Fermi Field in 1+1 Dimensions
    Kiusau Tesima
  12. Progress of Theoretical Physics Vol. 63 No. 5 (1980) pp. 1823-1826 :
    Possible Resolution of the Goto-Imamura Difficulty without Introducing the Schwinger Term
    Noboru Nakanishi
  13. Progress of Theoretical Physics Vol. 64 No. 5 (1980) pp. 1828-1851 :
    On the Confinement and the Vacuum Degeneracy in the Schwinger Model
    Yuji Nakawaki
  14. Progress of Theoretical Physics Vol. 66 No. 4 (1981) pp. 1458-1465 :
    Restoration of Well-Defined Charge and Chiral Charge and Correct Lorentz-Transformation Property in the Thirring and Pre-Schwinger Models
    Yuji Nakawaki
  15. Progress of Theoretical Physics Vol. 66 No. 5 (1981) pp. 1910-1913 :
    Fermion Confinement and Non-Existence of Physical Multiple Vacua in the Schwinger Model
    Yuji Nakawaki
  16. Progress of Theoretical Physics Vol. 67 No. 3 (1982) pp. 935-950 :
    Theory of a Fusion Field Composed of Free Massless Spinor Fields in Two Dimensions
    Tsuneo Suzuki and Seiichi Tameike
  17. Progress of Theoretical Physics Vol. 67 No. 3 (1982) pp. 965-976 :
    Singularity-Free Canonical Theory of Gauge Fields in the Axial Gauge
    Noboru Nakanishi
  18. Progress of Theoretical Physics Vol. 68 No. 1 (1982) pp. 287-293 :
    Comments on the Bosonization in Massless Two-Dimensional Models
    Noboru Nakanishi
  19. Progress of Theoretical Physics Vol. 70 No. 4 (1983) pp. 1105-1123 :
    Fermion Structures of State Vectors of the Schwinger Model with Multi-Fermions
    Yuji Nakawaki
  20. Progress of Theoretical Physics Vol. 86 No. 2 (1991) pp. 517-545 :
    Zweibein Operator Formalism of Two-Dimensional Quantum Gravity
    Mitsuo Abe and Noboru Nakanishi
  21. Progress of Theoretical Physics Vol. 102 No. 6 (1999) pp. 1187-1200 :
    Perturbative or Path-Integral Approach versus Operator-Formalism Approach
    Mitsuo Abe and Noboru Nakanishi
  22. Progress of Theoretical Physics Vol. 111 No. 3 (2004) pp. 301-337 :
    Method for Solving Quantum Field Theory in the Heisenberg Picture
    Noboru Nakanishi

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