On the Semi-classical Approach to the Physical Axiomatic of Quantum Mechanics and the New Wave-Particle Interpretation of Light

The Dirac Hamiltonian with an external Coulomb field is considered in Fock space; it contains an even part that conserves the number of fermion–antifeimion pairs and an odd part that permits pair annihilation and creation. By successive unitary transformations the nondiagonal terms connecting subspaces with different numbers of pairs can be removed order by order in an (1/m) expansion and the effective no-pair Hamiltonian can be explicitly constructed. If all disconnected graphs are excluded the result is then identical to the result obtained by a similar procedure applied to the Dirac–Coulomb one particle problem in relativistic quantum mechanics.

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Reflection symmetric Erdélyi-Kober type operators — A quasi-particle interpretation

Fractional Calculus and Applied Analysis ◽

10.2478/s13540-014-0221-1 ◽

2014 ◽

Vol 17 (4) ◽

Cited By ~ 1

Author(s):

Richard Herrmann

Keyword(s):

Fractional Integral ◽

Integral Operators ◽

Particle Systems ◽

Quantum Model ◽

Classical Approach ◽

Fractional Quantum ◽

Quasi Particle ◽

Fractional Integral Operators ◽

Creation And Annihilation Operators ◽

Particle Interpretation

AbstractThe reflection symmetric Erdélyi-Kober type fractional integral operators are used to construct fractional quasi-particle generators. The eigenfunctions and eigenvalues of these operators are given analytically. A set of fractional creation- and annihilation-operators is defined and the properties of the corresponding free Hamiltonian are investigated. Analogously to the classical approach for interacting multi-particle systems, the results are interpreted as a fractional quantum model for a description of residual interactions of pairing type.

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An Entropic Dynamics Approach to Geometrodynamics

Proceedings ◽

10.3390/proceedings2019033013 ◽

2019 ◽

Vol 33 (1) ◽

pp. 13

Author(s):

Selman Ipek ◽

Ariel Caticha

Keyword(s):

General Relativity ◽

Quantum Mechanics ◽

Quantum Theory ◽

First Principles ◽

Scalar Fields ◽

Poisson Brackets ◽

Classical Approach ◽

Quantum Domain ◽

Physical Information ◽

Entropic Dynamics

In the Entropic Dynamics (ED) framework quantum theory is derived as an application of entropic methods of inference. The physics is introduced through appropriate choices of variables and of constraints that codify the relevant physical information. In previous work, a manifestly covariant ED of quantum scalar fields in a fixed background spacetime was developed. Manifest relativistic covariance was achieved by imposing constraints in the form of Poisson brackets and of intial conditions to be satisfied by a set of local Hamiltonian generators. Our approach succeeded in extending to the quantum domain the classical framework that originated with Dirac and was later developed by Teitelboim and Kuchar. In the present work the ED of quantum fields is extended further by allowing the geometry of spacetime to fully partake in the dynamics. The result is a first-principles ED model that in one limit reproduces quantum mechanics and in another limit reproduces classical general relativity. Our model shares some formal features with the so-called “semi-classical” approach to gravity.

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