TY - JOUR

T1 - On the electromagnetic interaction in relativistic quantum mechanics

AU - Horwitz, L. P.

PY - 1984/10

Y1 - 1984/10

N2 - A fundamental problem in the construction of local electromagnetic interactions in the framework of relativistic wave equations of Klein-Gordon or Dirac type is discussed, and shown to be resolved in a relativistic quantum theory of events described by functions in a Hilbert space on the manifold of space-time. The relation, abstracted from the structure of the electromagnetic current, between sequences of events, parametrized by an evolution parameter τ ("historical time"), and the commonly accepted notion of particles is reviewed. As an illustration of these ideas, a perturbative calculation is made for photon emission from a charged two-body system in which the electromagnetic field is quantized in the usual way. The result is in essential agreement with calculations in which the charged particles are treated in the framework of nonrelativistic quantum mechanics, and provides them with a relativistic interpretation. In particular, we obtain a relativistically invariant form of the Bohr radiation condition.

AB - A fundamental problem in the construction of local electromagnetic interactions in the framework of relativistic wave equations of Klein-Gordon or Dirac type is discussed, and shown to be resolved in a relativistic quantum theory of events described by functions in a Hilbert space on the manifold of space-time. The relation, abstracted from the structure of the electromagnetic current, between sequences of events, parametrized by an evolution parameter τ ("historical time"), and the commonly accepted notion of particles is reviewed. As an illustration of these ideas, a perturbative calculation is made for photon emission from a charged two-body system in which the electromagnetic field is quantized in the usual way. The result is in essential agreement with calculations in which the charged particles are treated in the framework of nonrelativistic quantum mechanics, and provides them with a relativistic interpretation. In particular, we obtain a relativistically invariant form of the Bohr radiation condition.

UR - http://www.scopus.com/inward/record.url?scp=0038880313&partnerID=8YFLogxK

U2 - 10.1007/BF01889252

DO - 10.1007/BF01889252

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AN - SCOPUS:0038880313

SN - 0015-9018

VL - 14

SP - 1027

EP - 1046

JO - Foundations of Physics

JF - Foundations of Physics

IS - 10

ER -