Abstract
We show that there is a unique C*-algebra for the transverse quantum electromagnetic field obeying the Maxwell equations with any classical charge-current. For nonzero charge, the representation of the C*-algebra differs from the representation with zero charge.
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References
L. Gross, “Norm Invariance of Mass Zero Equations under the Conformal Group,” J. Math. Phys. 5, 687–695 (1964).
S. Doplicher and J. E. Roberts, “Why there is a Field Algebra with a Compact Gauge Group Describing the Superselection Structure in Particle Physics,” Commun. Math. Phys. 131, 51–107 (1990).
D. Shale, “Linear Symmetries of Free Boson Fields,” Trans. Amer. Math. Soc. 103, 149–167 (1962).
R. Haag, and D. Kastler, “An Algebraic Approach to Quantum Field Theory,” J. Math. Phys. 5, 848–861 (1964).
G. Mackey, Induced Representations of Groups and Quantum Mechanics (W. A. Benjamin, 1968).
G. Mackey, “Quantum Mechanics from the Point of View of Group Representations,” Applications of Group Theory in Physics edited byM. Flato, P. Sally and G. Zuckerman, Amer. Math. Soc., 210–254 (1985).
J. Slawny, “On Factor Representations and the C*-algebra of the CCR,” Commun. in Mathematical Phys. 24, 151–170 (1972).
J. R. Klauder and B.-S. Skagerstam, Coherent States: Applications in Physics and Astrophysics (World Scientific, Singapore, 1985).
S. Adler, “Axial-Vector Vertex in Spinor Electrodynamics,” Phys. Rev. 177, 2426–2438 (1969).
J. S. Bell and R. Jackiw, “A PCAC puzzle: π0 → γ in the σ-model,” Nuovo Cimento, 51, pp. 47–61 (1969).
H. Araki, Mathematical Theory of Quantum Fields (Oxford University Press, 1999).
R. Haag, Local Quantum Physics (second edition, Springer-Verlag, Berlin, Heidelberg, New York, 1992).
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Dedicated to the memory of Slava Belavkin
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Streater, R.F. The C*-algebra of the electromagnetic field. Russ. J. Math. Phys. 21, 399–407 (2014). https://doi.org/10.1134/S1061920814030121
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DOI: https://doi.org/10.1134/S1061920814030121