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Physics Letters B

Quantum action principle and base operators for bosons and fermions

L.D. Swift, Z. E. Musielak, John L. Fry

Published Sep 16, 2005• 0 citations
Publisher
DOI
10.1016/j.physletb.2005.08.118

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Fundamental issues of quantum electrodynamics of nanophotonic systems essential for further progress of nanotechnology are considered. Hypothesis of natural oscillatory systems with distributed parameters (NOSs) as bases for “real”, not “probabilistic”, de Broglie matter waves underlies the theory of natural oscillatory systems (TNOS). TNOS is a 4D theory in essence; the action, not momentum-energy, is regarded as a primary conservative and quantized physical value of Universe causing excitation of NOSs. Conservation laws individually for the positive and the negative parts of action are supposed. The spatial localization of fermion NOS wave packets (“particles”) and Heisenberg's uncertainty principle both are supposed to be results of a stochastic “spread” of fermion NOS action over multiple degrees of freedom of boson NOSs (according to the general laws of statistical physics). The physical origin of both Coulomb potential and own (spin) magnetic moment of fermions is considered to be also the action spread over boson NOS. A 4D spatio-temporal structure of fermion wave packet conjointly with estimation of actions of respective “forced” eigenmodes of boson NOS (virtual photons) is the subject of this paper.
We provide a Hilbert space approach to quantum mechanics where space and time are treated on an equal footing. Our approach replaces the standard dependence on an external classical time parameter with a spacetime-symmetric algebraic structure, thereby unifying the axioms that traditionally distinguish the treatment of spacelike and timelike separations. Standard quantum evolution can be recovered from timelike correlators, defined by means of a quantum action operator, a quantum version of the action of classical mechanics. The corresponding map also provides an alternative perspective on the path integral formulation that, in the case of fermions, does not require the use of Grassmann variables. In addition, the formalism can be interpreted in terms of generalized quantum states, codifying both the conventional information of a quantum system at a given time and its evolution. We show that these states are solutions to a quantum principle of stationary action grounded in timelike correlations and pseudo-entropies.
Abstract A Grassmann functional phase space is formulated for the definition of fermionic Wigner functionals by identifying suitable fermionic operators that are analogues to boson quadrature operators. Instead of the Majorana operators, we use operators that are defined with relative spin transformations between the ladder operators. The eigenstates of these operators are shown to provide orthogonal bases, provided that the dual space is defined with the incorporation of a spin transformation. These bases then serve as quadrature bases in terms of which Wigner functionals are defined in a way equivalent to the bosonic case. As an application, we consider a two-level fermion system.