Abstract
We revisit the computation of the phase of the Dirac fermion scattering operator in external gauge fields. The computation is through a parallel transport along the path of time evolution operators. The novelty of the present paper compared with the earlier geometric approach by Langmann and Mickelsson (J Math Phys 37(8):3933–3953, 1996) is that we can avoid the somewhat arbitrary choice in the regularization of the time evolution for intermediate times using a natural choice of the connection form on the space of appropriate unitary operators.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Deckert D.-A., Dürr D., Merkl F., Schottenloher M.: Time evolution of the external field problem in QED. J. Math. Phys. 51, 122–301 (2010)
Fierz H., Scharf G.: Particle interpretation for external field problems in QED. Helv. Phys. Acta 52(4), 37–453 (1980)
Gracia-Bondía J., Várilly J.V.: QED in external fields from the spin. J. Math. Phys. 35, 3340–3367 (1994)
Lamb W.E., Retherford R.C.: Fine structure of the hydrogen atom by a microwave method. Phys. Rev. 72(3), 241–243 (1947)
Langmann E., Mickelsson J.: Scattering matrix in external field problems. J. Math. Phys. 37(8), 3933–3953 (1996)
Lazarovici, D.: Time evolution in the external field problem of quantum electrodynamics. arXiv:1310.1778
Mickelsson J.: Wodzicki residue and anomalies of current algebras. Integrable models and strings (Espoo, 1993). Lecture Notes in Phys, vol. 436, pp. 123–135. Springer, Berlin (1994)
Mickelsson J.: Vacuum polarization and the geometric phase: gauge invariance. J. Math. Phys. 39(2), 831–837 (1998)
Paycha S.: Renormalized traces as a looking glass into infinite-dimensional geometry. Infin. Dimen. Anal. Quant. Probab. Relat. Top. 4(2), 221–266 (2001)
Palmer J.: Scattering automorphisms of the Dirac field. J. Math. Anal. Appl. 64(1), 189–215 (1978)
Pressley A., Segal G.: Loop Groups. Oxford Mathematical Monographs. Clarendon Press, Oxford University Press, Oxford (1986)
Ruijsenaars S.N.M.: Charged particles in external fields. II. The quantized Dirac and Klein–Gordon theories. Commun. Math. Phys. 52(3), 267–294 (1977)
Scharf G.: Finite Quantum Electrodynamics. The Causal Approach. 2nd ed. Texts and Monographs in Physics. Springer, Berlin (1995)
Shale D., Stinespring W.D.: Spinor representations of infinite orthogonal groups. J. Math. Mech. 14(2), 315–322 (1965)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Mickelsson, J. The Phase of the Scattering Operator from the Geometry of Certain Infinite-Dimensional Groups. Lett Math Phys 104, 1189–1199 (2014). https://doi.org/10.1007/s11005-014-0714-1
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11005-014-0714-1