Physical Particle Representation and Generalized Transformation Theory

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Abstract
The investigation of the recently described generalized transformation theory which leads to a non-Hamiltonian description of dynamics is pursued. The concept of generalized unitary transformations of superoperators is introduced and a specific class of transformations studied. For nondissipative systems it is equivalent to the usual unitary transformations that diagonalize the Hamiltonian. The important point is that this class of transformations remains meaningful for dissipative systems, hence a new representation of dynamics that we shall call the „physical particle” representation. It has the following properties: ( a ) The energy (or an arbitrary function of the energy) is represented by a diagonal matrix. ( b ) In the (0) II space (see these Proceedings , 65 , 789 (1970)) corresponding to the coherent processes, the evolution can be described in terms of the changes in population of the physical particles. ( c ) At thermodynamic equilibrium, the physical particles are uncorrelated and behave as independent entities; the entropy has a purely combinatorial meaning. A full description of dynamics in this representation will be given in a forth-coming paper.

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