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On the physical interpretation of effective actions using Schwinger’s formula. (English) Zbl 0833.47057

Summary: We show explicitly that Schwinger’s formula for one-loop effective actions corresponds to the summation of energies associated with the zero-point oscillations of the fields. We begin with a formal proof and after that we confirm it using a regularization prescription.

MSC:

47N50 Applications of operator theory in the physical sciences
81V10 Electromagnetic interaction; quantum electrodynamics
33D10 Basic theta functions (MSC1991)

References:

[1] Casimir, H. G. B.:Proc. K. Ned. Akad. Wet 51, 793 (1948).
[2] Dittrich, W. and Reuter, M.:Effective Lagrangians in Quantum Electrodynamics, Lecture Notes In Physics 220, Springer, Berlin, 1985.
[3] Bernard, C.:Phys. Rev. D 9, 3312 (1974). · doi:10.1103/PhysRevD.9.3312
[4] Myers, E.:Phys. Rev. Lett. 59, 165 (1987). · doi:10.1103/PhysRevLett.59.165
[5] Schwinger, J.:Phys. Rev. 82, 664 (1951). · Zbl 0043.42201 · doi:10.1103/PhysRev.82.664
[6] Schwinger, J.:Lett. Math. Phys. 24, 59 (1992). · Zbl 0900.33015 · doi:10.1007/BF00430003
[7] Birrel, N. D. and Davies, P. C. W.:Quantum Fields in Curved Space, Cambridge University Press, Cambridge, 1982.
[8] Cougo-Pinto, M. V., Farina, C., and Seguí-Santonja, A. J.:Lett. Math. Phys. 30, 169 (1994). · Zbl 0860.58037 · doi:10.1007/BF00939704
[9] Cougo-Pinto, M. V., Farina, C., and Seguí-Santonja, A. J.: to appear inLett. Math. Phys.
[10] Plunien, G., Muller, B., and Greiner, W.:Phys. Rep. 134, 87 (1986). · doi:10.1016/0370-1573(86)90020-7
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