Abstract
Solutions to many problems in physics often invoke the use of integral transforms which are associated with certain invariance or transformation groups of the particular physical system under consideration. The most well-known example is the use of the Fourier transform in problems of non-relativistic and relativistic physics. There are other integral transforms which are also very useful. Fock’s solution to the bound state hydrogen atom problem1 uses an integral transform which is related, thru stereographic projection from S3 onto R3, to a Knapp-Stein intertwining operator2 of the associated SO0(1,4) transformation group of the problem.3 The Wightman function for a masseless scalar field is a kernel of an intertwining operator between two elementary representations (ERs) of the conformal group.4 We also wish to note the use of the Radon transform in problems of radiography.5
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References
V. Fock, Z.Physik 98 (1935), 145
J. Schwinger, J. Math.Phy., 5, (1964), 1606.
P. Moylan, Fortsch d. Phys., 28, (1980), 269–284.
M. Bander, C. Itzykson, Rev. Mod. Phys., 38, (1966), 330.
G. Mack, Comm. Math. Phys., 55, (1977), 1–28.
S. Helgason, Groups and Geometric Analysis…, (Academic Press, New York, 1984), 130.
G. W. Mackey, in Lie Groups and their Representations, Summer School of the Bolyai Janos Mathematical Society, Proceedings, Budapest, 1971, ed. I. M. Gel’fand, (Wiley, London, 1975), 361.
I. E. Segal, Proc. Math. Acad. Sci. USA, 79, (1982), 7961.
S. M. Paneitz, I. E. Segal, Journ. Funct. Anal., 47, (1982), 78–142.
P. Moylan, Fortsch. d. Phys., 11, (1986) (in press).
G. Mack, I. T. Todorov, Phys. Rev. D., 86, (1972), 1764–1787.
Gregg Zuckermann, in Lecture Note in Mathematics 1077, Lie Group Representations III, Proceedings, University of Maryland (1982–1983, Eds. R. Herb. et.al., (Springer-Verlag, New York, 1984), P. 437.
S. W. Hawking, G.F.R. Ellis, The Large Scale Structure of Space-Time, (Cambridge, New York, 1973).
R. Penrose, Proc. Roy. Soc. London, A284, (1965), 163.
D. R. Brill, J. A. Wheeler, Rev. Mod. Phys. 29, #3, (1957), 467.
G. Warner, Harmonic Analysis on Semisimple Lie Groups I, Springer-Verlag, (New York, 1972).
K. C. Hannabuss, Proc. Camb. Phil. Soc., 70 (1971), 283.
J. Hebda, P. Moylan, Homogeneous Spaces and Associated Group Decompositions, St. Louis University, (1986).
J. E. Gilbert, R. A. Kunze, P. A. Tomas, Intertwining Kernels and Invariant Operators in Analysis, Univ. of Texas at Austin, (1984).
P.A.M. Dirac, Ann. Math, 36, (1935), 657.
P. Moylan, Dissertation, U.T. Austin (1982).
R. Strichartz, Jour. Funct. Anal., 12, (1973), 341–383.
W. Rossmann, Jour. Funct. Anal., 30, (1978), 448–447.
A. W. Knapp, B. Speh, Jour. Funct. Anal., 45, (1982), 41.
V. K. Dobrev, Jour. Math. Phys., 26 (2), (1985), 235–251.
V. K. Dobrev, P. Moylan, MPI Preprint, MPI-PAE/PTh 49/85, (to appear in Jour. Math. Phys.).
A. W. Knapp, E. M. Stein, Ann. Math., 93, (1971) 489.
S. Helgason, Differential Geometry and Symmetric Spaces, Adacemic Press, (New York, 1962).
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Moylan, P. (1986). Integral Transforms on Homogeneous Spaces of the de Sitter and Conformal Groups. In: Gruber, B., Lenczewski, R. (eds) Symmetries in Science II. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-1472-2_32
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DOI: https://doi.org/10.1007/978-1-4757-1472-2_32
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