The Representation Theory of Decoherence Functionals in History Quantum Theories

摘要: In the first part of this paper general perspective history quantum theoriesis reviewed. History theories provide a conceptual and mathematicalframework for formulating without globally definedHamiltonian time evolution introducing concept space-time eventinto theory. On mathematical level theory ischaracterized by space histories, which represent events, andby decoherence functionals, mechanicalstates in approach. The second is devoted to thestudy structure functionals some physicallyreasonable spaces histories detail. temporal reformulation ofstandard Hamiltonian suggests consider case that thespace given (i) lattice projection operators on someHilbert or, slightly more generally, (ii) set insome von Neumann algebra. conditions are identified underwhich can be represented by, respectively, trace classoperators, bounded operators, or families class tensorproduct underlying Hilbert itself. Moreover, we discuss thenaturally arising representations as sesquilinear forms.The ends with discussion consequences results thegeneral axiomatic framework theories.