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The propagation of the operator average is described in truncated space with some quantum number(s) being fixed. It is first shown that the propagation coefficient satisfies an analog of the Chapman–Kolmogorov equation. Next, particle‐hole symmetry is incorporated into the propagation of the...
We review and apply the method of Lagrangian dynamics to particle motion in higher‐dimensional spaces. We discuss in detail the case of a Kaluza–Klein theory with coset spaces as fiber. While the total metric we use in general need not allow for Killing vectors, we require that the...
Starting from an N ‐body quantum space, we consider the Lie‐algebraic framework where the Pöschl–Teller Hamiltonian, − 1/2 ∂ 2 χ + c sech 2 χ+ s csch 2 χ, is the single sp(2, R ) Casimir operator. The spectrum of this system is m i x e d : it contains a finite number of...
Exact solutions of Einstein’s equations are obtained for a superfluid flowing in a rigid solid.
The shift operator technique is used to give a complete analysis of all finite‐ and infinite‐dimensional irreducible representations of the exceptional Lie superalgebras D (2,1;α). For all cases, the star or grade star conditions for the algebra are investigated. Among the...
We have considered the excitation spectra for a three‐level atom interacting simultaneously with a strong pump field and a weak signal field. The atom consists of an upper excited state ‖2〉 and two lower states ‖1〉 and ‖3〉 where the transition ‖1〉↔‖3〉 is electric‐dipole...
A SU(3)‐gauge quantum field theory with a quark triplet, an antiquark triplet, and a self‐conjugate gluon octet as basic fields is investigated. In virtue of a nontrivial coupling between the representation of the translation group and the SU(3)‐color charge of the basic fields it is...
The decoupling theorem of quantum field theory is studied in Minkowski space for theories which on experimental grounds may contain particles with vanishingly small masses. Rules are set up to prove the distributional vanishing property of the renormalized amplitudes when any subset of the...
Chandrasekhar’s technique for separation of the Dirac equation in the Kerr background is applied to perfect fluid space‐times with local rotational symmetry. These space‐times fall into three distinct types. It is found that in case (1) the Dirac equation separates if the space‐time is at...
Several recent papers have dealt with the possibility of interpreting the Kerr–Newman metric as a viscous fluid as well as its usual interpretation of a rotating, charged black hole. In this paper we show that there is no possible viscous fluid with the Kerr–Newman metric.
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