Abstract
The Fourier transform of the (indefinite metric) Wightman two-point function \( - {\text{ }}(1/4\pi ){\text{ ln(}} - x^2 + i \in x^0 |_{{\text{c}} \downarrow {\text{0}}} \) of a free massless scalar quantum field in two-dimensional spacetime has been inconsistently reported by various authors. We compute the correct one from the definition of the Fourier transform of tempered distributions.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Wightman, A. S., Introduction to some aspects of the relativistic dynamics of quantized fields, in M.Lévy (ed.), High Energy Electromagnetic Interactions and Field Theory, Gordon and Breach, New York, 1967, p. 171.
Morchio, G., Pierotti, D., and Strocchi, F., J. Math. Phys. 31, 1467 (1990).
Dublin, D. A. and Tarski, J., J. Math. Phys. 7, 574 (1966).
Pierotti, D. Lett. Math. Phys. 15, 219 (1988).
Klaiber, B., Helv. Phys. Acta 37, 554, (1964).
Gradshteyn, I. S. and Ryzhik, I. M., Table of Integrals, Series, and Products, Academic Press, New York, 1980.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Embacher, H.G., Grübl, G. Fourier representation for the two-point function of the two-dimensional massless scalar field. Lett Math Phys 22, 235–238 (1991). https://doi.org/10.1007/BF00403550
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00403550