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Quantum Massless Field in 1+1 Dimensions

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Mathematical Physics of Quantum Mechanics

Part of the book series: Lecture Notes in Physics ((LNP,volume 690))

Abstract

We present a construction of the algebra of operators and the Hilbert space for a quantum massless field in 1+1 dimensions.

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References

  1. Acerbi, F., Morchio, G., Strocchi, F.: Infrared singular fields and nonregular representations of canonical commutation relation algebras, Journ. Math. Phys. 34 (1993) 899–914.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  2. Acerbi, F., Morchio, G., Strocchi, F.: Theta vacua, charge confinement and charged sectors from nonregular representations of CCR algebras, Lett. Math. Phys. 27 (1993) 1–11.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  3. Brattelli, O., Robinson D. W.: Operator Algebras and Quantum Statistical Mechanics, Volume 2, Springer-Verlag, Berlin, second edition 1996.

    Google Scholar 

  4. S. De Biùvre and J. Renaud: A conformally covariant quantum field in 1+1 dimension, J. Phys. A34 (2001) 10901–10919.

    Article  MATH  MathSciNet  Google Scholar 

  5. Buchholz, D.: Quarks, gluons, colour: facts or fiction?, Nucl. Phys. B 469 (1996) 333–356.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  6. D. Buchholz and R. Verch, Scaling algebras and renormalization group in algebraic quantum field theory. II. Instructive examples, Rev. Math. Phys. 10 (1998) 775–800.

    Article  MATH  MathSciNet  Google Scholar 

  7. J. DereziƄski: Van Hove Hamiltonians – exactly solvable models of the infrared and ultraviolet problem, Ann. H. PoincarĂ© 4 (2003) 713–738.

    Article  MATH  Google Scholar 

  8. M.B. Green, J.H. Schwarz and E. Witten: Superstring theory, Cambridge Univ. Press, Cambridge 1987.

    MATH  Google Scholar 

  9. G.W. Greenberg, J.K. Kang and C.H. Woo: Infrared regularization of the massless scalar free field in two-dimensional space-time via Lorentz expansion, Phys. Lett. 71B (1977) 363–366.

    MathSciNet  ADS  Google Scholar 

  10. C. Itzykson and J.B. Zuber: Quantum Field Theory, McGraw-Hill, 1980, Chap. 11.

    Google Scholar 

  11. G. Morchio, D. Pierotti and F. Strocchi: Infrared and vacuum structure in two-dimensional local quantum field theory models. The massless scalar field, Journ. Math. Phys. 31 (1990) 1467–1477.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  12. N. Nakanishi: Free massless scalar field in two-dimensional space-time, Prog. Theor. Phys. 57 (1977) 269–278.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  13. N. Nakanishi: Free massless scalar field in two-dimensional space-time: revisited, Z. Physik C. Particles and Fields 4 (1980) 17–25.

    Article  MathSciNet  ADS  Google Scholar 

  14. R.F. Streater and A.S. Wightman: PCT, spin and statistics and all that, W.A. Benjamin, New York-Amsterdam 1964.

    MATH  Google Scholar 

  15. R.F. Streater and I.F. Wilde: Fermion states of a boson field, Nucl. Phys. B24 (1970) 561–575.

    Article  ADS  Google Scholar 

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DereziƄski, J., Meissner, K.A. (2006). Quantum Massless Field in 1+1 Dimensions. In: Asch, J., Joye, A. (eds) Mathematical Physics of Quantum Mechanics. Lecture Notes in Physics, vol 690. Springer, Berlin, Heidelberg . https://doi.org/10.1007/3-540-34273-7_11

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