Andrei Dolocan

A NEW HAMILTONIAN OF INTERACTION FOR FERMIONS

Using the Lagrangian formalism we attempt to introduce a new Hamiltonian for fermions. On this basis we have evaluated the expectation values for the interaction energy between fermions via bosons. The interaction energy between two fermions via phonons becomes attractive in a degenerate fermion-gas. The interaction energy between two fermions via photons appears to be attractive in certain conditions. The self-energy of the fermion + boson system, e.g. polaron and polariton, was evaluated.

QUANTUM MECHANICAL TREATMENT OF THE ELECTRON{BOSON INTERACTION VIEWED AS A COUPLING THROUGH FLUX LINES. POLARONS

By using a Hamiltonian based on the coupling through flux lines between electrons and bosons, we have calculated the electron–phonon interaction energy and the electron–electron interaction energy via bosons in an isotropic medium and in a lattice. We have calculated the correction energy to the electron energy due to the electron interaction with acoustic phonons and we have found that in covalent crystals it is of the order of 0.1 eV. Also, we have presented the results for the weak coupling and strong coupling polarons in ionic crystals. By applying this Hamiltonian to electron–electron interaction via mass less bosons we have found an equivalent expression for Coulombs law, αℏc/R, where α is the fine structure constant.

APPLICATIONS OF A NEW HAMILTONIAN OF INTERACTION TO ONE-DIMENSIONAL AND TWO-DIMENSIONAL STRUCTURES

We apply a new interaction Hamiltonian (Ref. 1) to two-dimensional and one-dimensional structures. We have found that, for small values of the wavevector, the interaction energy presents a logarithmic divergence and in a one-dimensional lattice, a cotangent divergence in addition. But, in a two-dimensional lattice the divergence terms may cancel, and from the point of view of the interactions the crystal structure is possible. The interaction energy has a polynomial dependence on the form 1/an where the maximum value of n is 7; a is the lattice constant.

RELATION OF INTER-ATOMIC FORCES IN SOLIDS TO BULK MODULUS, COHESIVE ENERGY AND THERMAL EXPANSION

We present theoretical expressions relating the cohesive energy to the bulk modulus, the force constant and the lattice constant applicable to solids with a variety of crystal structures. We have found that the cohesive energy is directly proportional to the ratio between the product of the bulk modulus through the atomic volume and the exponent of the repulsion term. We have defined a figure of merit for materials as the ratio between the product of the bulk modulus through the atomic volume and the cohesive energy. The reciprocal of this ratio is a measure of the hardness of materials. Likewise, we have found the expressions for anharmonicity and thermal expansion coefficients, which can explain, also, their possible negative values.

APPLICATION OF A NEW HAMILTONIAN OF INTERACTION TO VORTICES STRUCTURE IN SUPERCONDUCTORS

By using a new Hamiltonian,1 we have calculated the energy of one isolated vortex line and also the interaction energy between the vortices in superconductors. Also, we have calculated the elastic force constant in a vortex lattice. The interaction energy shows a minimum at a certain distance between the vortices. We analyze some aspects of this interaction. The obtained results are in good agreement with experimental data.

Quantum Mechanical Treatment of the Lamb Shift Without Taken into Account the Electric Charge

We present the calculus of the Lamb shift by using an equivalent expression for the Coulomb interaction energy, on the form αℏc ∕ R, where α is the fine structure constant. This expression was found by using a new Hamiltonian of interaction between fermions. The obtained results are in good agreement with experimental data. The calculus was fulfilled in both three-dimensional and two-dimensional spaces.

A HAMILTONIAN FOR THE BOSON–BOSON INTERACTION BASED ON ELASTIC COUPLING THROUGH FLUX LINES

We present a Hamiltonian for the boson–boson interaction, based on elastic coupling through flux lines. This Hamiltonian may be used to study polaritons and plasmons and likewise the cohesive energy in crystals of noble gases. The presented results for crystals of noble gases are in a good agreement with experimental data.

SOME ASPECTS OF THE ELECTRON-BOSON INTERACTION AND OF THE ELECTRON-ELECTRON INTERACTION VIA BOSONS

By using a Hamiltonian of interaction between fermions via bosons1 we derive some properties of the electro-phonon and electron-photon interaction and also of the electron-electron interaction. We have obtained that in a degenerate electron gas there is an attraction between two electrons via acoustical phonons. Also, in certain conditions, there may be an attraction between two electrons via longitudinal optical phonons. Although our expressions for the polaron energy in both cases of the acoustical and longitudinal optical phonons are different from that obtained in the standard theory, their magnitudes are the same with these and they are in good agreement with experimental data. The total emission rate of an electron against a phonon system at absolute zero is directly proportional to the electron momentum. Also, an attraction between two electrons may appear via photons.

A COMPARISON BETWEEN THE TWO-DIMENSIONAL AND THREE-DIMENSIONAL LATTICES

By using a new Hamiltonian of interaction we have calculated the interaction energy for two-dimensional and three-dimensional lattices. We present also, approximate analytical formulae and the analytical formulae for the constant of the elastic force. The obtained results show that in the three-dimensional space, the two-dimensional lattice has the lattice constant and the cohesive energy which are smaller than that of the three-dimensional lattice. For appropriate values of the coupling constants, the two-dimensional lattice in a two-dimensional space has both the lattice constant and the cohesive energy, larger than that of the two-dimensional lattice in a three-dimensional space; this means that if there is a two-dimensional space in the Universe, this should be thinner than the three-dimensional space, while the interaction forces should be stronger. On the other hand, if the coupling constant in the two-dimensional lattice in the two-dimensional space is close to zero, the cohesive energy should be comparable with the cohesive energy from three-dimensional space but this two-dimensional space does not emit but absorbs radiation.

ERRATA: QUANTUM MECHANICAL TREATMENT OF THE ELECTRICAL INTERACTION VIEWED AS AN ELASTIC COUPLING THROUGH FLUX LINES

Using the Lagrangian formalism we attempt to calculate the interaction energy between the two bodies, nonconnected and connected, in a linear lattice. The obtained results show that the interaction is dependent on the dispersion relation ω (q). On this basis we calculate the binding energy of an ionic lattice and we have found a good agreement with experimental data.