اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدAn algebraic approach to laying a ghost to rest
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In the recent literature there has been a resurgence of interest in the fourth-order field-theoretic model of Pais-Uhlenbeck cite {Pais-Uhlenbeck 50 a}, which has not had a good reception over the last half century due to the existence of {em ghosts} in the properties of the quantum mechanical solution. Bender and Mannheim cite{Bender 08 a} were successful in persuading the corresponding quantum operator to `give up the ghost. Their success had the advantage of making the model of Pais-Uhlenbeck acceptable to the physical community and in the process added further credit to the cause of advancement of the use of ${cal PT} $ symmetry. We present a case for the acceptance of the Pais-Uhlenbeck model in the context of Diracs theory by providing an Hamiltonian which is not quantum mechanically haunted. The essential point is the manner in which a fourth-order equation is rendered into a system of second-order equations. We show by means of the method of reduction of order cite {Nucci} that it is possible to construct an Hamiltonian which gives rise to a satisfactory quantal description without having to abandon Dirac.
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