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- W2949754194 abstract "Let S(x) be a massless scalar quantum field which lives on the three-dimensional hyperboloid $xx= (x^0)^2-(x^1)^2-(x^2)^2-(x^3)^2=-1.$ The classical action is assumed to be $(hbar=1=c)(8pi e^2)^{-1}int dx g^{ik}partial_i Spartial_k S$, where $e^2$ is the coupling constant, $dx$ is the invariant measure on the de Sitter hyperboloid $xx=-1$ and $g_{ik}, i,k=1,2,3$, is the internal metric on this hyperboloid. Let $u$ be a fixed four-velocity. The field $S(u)=(1/4 pi)int dxdelta(ux)S(x)$is smooth enough to be exponentiated. We prove that if $0 =exp(-iS(u))mid 0>$, where $mid 0>$ is the Lorentz invariant vacuum state, contains a normalizable eigenstate of the Casimir operator $C_1=-(1/2)M_{munu}M^{munu}$; $M_{munu}$ are generators of the proper orthochronous Lorentz group. This theorem was first proven by the Author in 1992 in his contribution to the Czyz Festschrift, see Erratum {it Acta Phys. Pol. B} {bf 23}, 959 (1992). In this paper a completely different proof is given: we derive the partial, differential equation satisfied by the matrix element $ , sigma > 0$, and show that the function $exp (z)cdot (1-z)cdot exp[-sigma z (2-z)], z= e^2/ pi$, is an exact solution of this differential equation, recovering thus both the eigenvalue and the probability of occurrence of the bound state." @default.
- W2949754194 created "2019-06-27" @default.
- W2949754194 creator A5028942655 @default.
- W2949754194 date "2004-06-30" @default.
- W2949754194 modified "2023-09-27" @default.
- W2949754194 title "A New Proof of Existence of a Bound State in the Quantum Coulomb Field" @default.
- W2949754194 hasPublicationYear "2004" @default.
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