Search

It is conjectured that Stark states of excited hydrogen atom posses magnetic charge for which the quantum mechanical operator is $${\cal G}_{op} = {e\over \hbar} (\vec\sigma\cdot\vec A)$$ where $\vec A$ is the Runge-Lenz vector. The expectation value $g$ of this operator for Stark states is found to be $$ g = e(n_1-n_2)$$ which obeys a Dirac-Saha type quantization formula $${eg\over c} = (n_1-n_2)\alpha$$ where $\alpha$ is the fine structure constant and $n_1$ and $n_2$ are parabolic quantum numbers. An experimental arrangement is outlined to test this conjecture.

The electron would decay into a photon and neutrino if the law of electric charge conservation is not respected. Such a decay would cause vacancy in closed shells of atoms giving rise to emission of x-rays and Auger electrons. Experimental searches for such very rare decay have given an estimate for the life time to be greater than $2.7 \times 10^{23}$ years. The simplest theoretical model which would give rise to such a decay is one where the electron is regarded as the first excited state and neutrino as the ground state of a fundamental spin 1/2 particle bound to a scalar particle by a super strong force and the photon is considered as a bound state of a fundamental spin 1/2 fermion-antifermion pair. The fine structure constant of the super strong coupling is found to be unity from the masslessness of the neutrino and the lower bound of the mass of the fundamental particles is estimated by using quantum mechanical formula for photon emission by atoms and found to be $10^{22}$ GeV from the bound for electron decay time indicating thereby that the composite nature of electron, neutrino and the photon would be revealed in the Planckian energy regime. A model based on extension of $SU(2)\otimes SU(2)$ symmetry of Dirac equation to $SU(3)\otimes SU(3)$ gives a lower bound for the mass of the gauge boson mediating the decay to be $10^9 GeV$ which is the geometric mean of the masses of the electron and the fundamental particles., Comment: 6 pages, 1 figure

It is shown that both the electric and magnetic dipole moment vectors of hydrogen atom in the excited states with wave function $$ u_n^{(\pm)} = {1\over\sqrt 2} [R_{n,n-1}(r) Y_{n-1,\pm (n-2)}(\theta\phi) \pm R_{n,n-2}(r) Y_{n-2,\pm (n-2)}(\theta\phi)]$$ align themselves in the direction of an external uniform electric field which is characteristic of magneto-electric effect. These states are found to have magnetic charge $g={3n\over (n-2)e}$ on account of this effect. This result is confirmed by an independent method. An experiment is suggested to fabricate these states and detect the magnetic charge. It ma be worth noting that inspite of many experimental searchs, magnetic charge, whose existence has been theorized both in electrodynamics and non-abelian gauge theories, none have been found so far, nor there exist any suggstion as to where these are to be found.

It is shown that electrons and photons can be considered as composities of particles representating the fundamental representation of the extended Lorentz group $SU(3)\otimes SU(3)$ in (8+1) dimensional space-time which are held together by force mediated by gauge particles belonging to the regular representation. In this theory, spin states of electron, positron and photon belong to the $8\otimes 8$ representation of the group. The fine structure constant of the fundamental gauge interaction is found to be unity from the fact that the photon is massless. The mass of the fundamental particles constituting the electron and the photon is estimated to be $\geq 10^{21}$ GeV from the experimental limit for the life-time of electron decay into neutrino and photon which is a consequence of the model. This corresponds to distances of less than $10^{-35}$ cm which is smaller than the Planck length indicating thereby that the composite nature of electrons and photons will be revealed when we go to Planckian energies., Comment: 10 Pages, 3 figures

In continuation of our model of composite electron, its companion neutrinos, photon and electro-weak gauge bosons as well as their super-partners based on extended Lorentz group $SU(3)\otimes SU(3)$ in (8+1) dimensional space-time, we show that the remaining leptons, quarks, lepto-quarks and gluons as well as their respective super-partners can be considered as composites of fundamental particles belonging to the $5\otimes 5$ dimensional representation of the further extended Lorentz group $SU(5)\otimes SU(5)$ in (24+1) dimensional space-time. The fundamental particles constituting the composite ones do not posses quantum numbers of the latter such as charge, hypercharge etc. Since according to our estimate based on experimental limit on the electron life-time, the mass of the fundamental particles is in the Planckian regime, the composite particles would break up into their constituents at these energies and lose their quantum numbers., Comment: 7 pages, no figures

It is shown that the excited states of hydrogen atom in a uniform electric field (Stark States) posess magnetic charge whose magnitude is given by a Dirac-Saha type relation: $$ {eg\over \hbar c} = \sqrt 3 n $$ An experiment is proposed to fabricate such states and to detect their magnetic charge., Comment: 8 pages, revised substantially