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Alexander O.E. Animalu
Dept. of Physics & Astronomy, Univ. of Nigeria, Nsukka
& Department of Physics, Tansian University, Oba, Nigeria
(e-mail: nascience@aol.com)
Some Implications of a Non-Unitary transformation of Planck's quantum hypothesis in Physics.
In this paper, I present a study of a group of (“isotopic” lifting) transformations of Planck’s hypothesis concerning the quantization of energy in black-body radiation in statistical mechanics, by expressing the hypothesis in terms of observables (i.e., statistical averages 
) as, 
, where 
characterizes a non-unitary transformation (
) of the Planck constant “unit” operator (
) in conventional quantum mechanics (CQM) to an “iso-unit” operator (
) of Santilli’s Hadronic Mechanics(SHM). For the purpose of eliminating all divergences (by selecting 
) and other mathematically inconsistencies in the current Feynman diagrammatic approach to the space-time evolution of quantum mechanical states, the study starts from the principles of classical statistical mechanics and uses Dirac’s bra-c-ket notation to relate averages in various (Schrodinger, Heisenberg and Interaction) pictures to Feynman’s space-time (r,t)-representation. In this way, two sources of divergences are identified as (i) the representation of the interacting particles by (space-time coordinates) “points” in the transformation from classical statistical mechanics to the Schrodinger and Heisenberg pictures of the 1st quantization formalism and (ii) the representation of long-range (action-at-distance) interaction between point-particles by straight lines (in “vacuum”) in Feynman’s path-integral formulation of the interaction picture in the 2nd quantization formalism. The mathematical inconsistency of CQM is identified at the algebraic level as arising from the use of the same “unit” of the conventional Lie algebra (CLA) of operators in both 1st and 2nd quantization levels of CQM rather than a unified Lie-isotopic algebra (LIA) of SHM for dealing with the intrinsically N-body (N>1) problem of interacting systems involving both fermions and bosons in number-space-time (Fock-Feynman) picture. The experimental consequences of the study will be discussed.
Refreshments will be served at 3:40pm