Searcharxiv⌕ Search

arXiv subjects

John P. Cullerne

Publications and source records attributed to John P. Cullerne.

7 recordsLinked to original sources
arXiv2002

Classical behaviour of the Dirac bispinor

It is usually supposed that the Dirac and radiation equations predict that the phase of a fermion will rotate through half the angle through which the fermion is rotated, which means, via the measured dynamical and geometrical phase factors, that the fermion must have a half-integral spin. We demonstrate that this is not the case and that the identical relativistic quantum mechanics can also be derived with the phase of the fermion rotating through the same angle as does the fermion itself. Under spatial rotation and Lorentz transformation the bispinor transforms as a four-vector like the potential and Dirac current. Previous attempts to provide this form of transformational behaviour have foundered because a satisfactory current could not be derived.(14)

quant-ph↗
arXiv2002

A new approach to quantum gravity: a summary

Quantum Electrodynamics (QED) has been so successful a theory that it is taken as a model for the production of further quantum theories. However, when the prescription for quantising electromagnetic interactions that so successfully resulted in QED is applied to General Relativity the theory obtained is not renormalizable. We derive a different method of quantising classical electromagnetism which also results in QED. We call the method the versatile method. We then apply the versatile method to General Relativity, in particular the Einstein equation which equates a geometrical description derivable from the metric to the energy-momentum-stress tensor, or as we shall call it the matter tensor of the matter field. The method can be applied provided that there is always a reference frame, which may differ with location and time, where the matter tensor can be reduced to a mass density with the other elements zero. We call such matter tensors simple. This restriction means that the tensor can be put into one to one correspondence with the Dirac current. When the versatile method of quantising a classical theory is applied to General Relativity the theory that results is renormalizable. It is in fact isomorphic to QED, provided that the temporal and a spatial co-ordinate are exchanged.

gr-qc↗
arXiv2002

QED derived from the two-body interaction (1) Mapping to M-space

We have shown in a previous paper that the Dirac bispinor can vary like a four-vector and that Quantum Electrodynamics (QED) can be reproduced with this form of behaviour.(1) Here, in part I of this paper, we show that QED with the same transformational behaviour also holds in an alternative space we call M-space. We use the four-vector behaviour to model the two-body interaction in M and show that this has similar physical properties to the usual model which it predicts. In part (2) of this paper(4) we use M-space to show that QED can be reduced to two simple rules for a two-body interaction.

quant-ph↗
arXiv2002

QED derived from the two-body interaction (2) The derivation

We have shown in a previous paper that the Dirac bispinor can vary like a four-vector and that Quantum Electrodynamics (QED) can be reproduced with this form of behaviour.(2) We have also shown in part I (3) of this paper, that QED with the same transformational behaviour also holds in a second space which we called M-space. Here we use M-space to show that QED can be reduced to two simple rules for a two-body interaction.

quant-ph↗
arXiv2002

The two-body interaction with a circle in time

We complete our previous(1, 2) demonstration that there is a family of new solutions to the photon and Dirac equations using spatial and temporal circles and four-vector behaviour of the Dirac bispinor. We analyse one solution for a bound state, which is equivalent to the attractive two-body interaction between a charged point particle and a second, which remains at rest. We show this yields energy and angular momentum eigenvalues that are identical to those found by the usual method of solving of the Dirac equation,(4) including fine structure. We complete our previous derivation(3) of QED from a set of rules for the two-body interaction and generalise these. We show that QED may be decomposed into a two-body interaction at every point in spacetime.

quant-ph↗
arXiv2000

The Dirac algebra and its physical interpretation

A version of the Dirac equation is derived from first principles using a combination of quaternions and multivariate 4-vectors. The nilpotent form of the operators used allows us to derive explicit expressions for the wavefunctions of free fermions, vector bosons, scalar bosons; Bose-Einstein condensates, and baryons;annihilation, creation and vacuum operators; the quantum field integrals; and C, P and T transformations; and to suggest new insights into the meaning of supersymmetry and renormalization.

quant-ph↗