Narrow Results

We examine and implement the concept of non-additive composition laws in the quantum theory of closed bosonic strings moving in (3+1)-dimensional Minkowski space. Such laws supply exact selection rules for the merging and splitting of closed strings.

Yang's theorem forbids the process Z⁰ →2γ in any Poincaré invariant theory if photons are bosons and their two-particle states transform under the Poincaré group in the standard way (under the standard coproduct of the Poincaré group). This is an important result as it does not depend on the assumptions of quantum field theory. Recent work on noncommutative geometry requires deforming the above coproduct by the Drinfel'd twist. We prove that Z⁰ →2γ is forbidden for the twisted coproduct as well. This result is also independent of the assumptions of quantum field theory. As an illustration of the use of our general formulae, we further show that Z⁰ →ν+ ν is forbidden for the standard or twisted coproduct of the Poincaré group if the neutrino is massless, even if lepton number is violated. This is a special case of our general result that a massive particle of spin j cannot decay into two identical massless particles of the same helicity if j is odd, regardless of the coproduct used.

The existing methods for calculating the energy of stationary states relate it to the energy of the electron, considering it negative in the atom. Formally, choosing a point that corresponds to zero potential energy you can assign a negative value to the electron energy. However, this approach does not answer many other questions, for example, the actual value of the energy of stationary states is unknown, but only the difference in energies between stationary states is known; the concept of “minimum energy of the system” loses its meaning (choosing the origin of the energy reference, we replace the minimum with the maximum, or vice versa); the physical reason for the stability of stationary states is not clear; it is impossible to reveal the physical reason for the introduction of selection rules, since the Heisenberg uncertainty relations exclude the analysis of the transition mechanism, replacing it with the concept of a “quantum leap”. Let us show that the energy of stationary states is the energy of a spherical capacitor, the covers of which are spheres whose radii are equal to the radius of the nuclear and corresponding stationary state. The energy of the ground state in the hydrogen atom is 0.8563997 MeV. The presence of charges and a magnetic field presupposes the circulation of energy in the volume of the atom (the Poynting vector is not zero). Revealed quantization of the angular momentum of the electromagnetic field in stationary states is $Ln=n\hslash$. The change in the angular momentum of the electromagnetic field during transitions between stationary states in atoms removes the physical grounds for introducing selection rules. The analysis shows that the Heisenberg uncertainty relations are not universal, and their application in each specific case must be justified.

Direct optical absorption of light in cylindrical quantum dot was theoretically investigated. Analytical expressions for light absorption coefficients were found for two regimes of size quantization: strong and weak. The corresponding selection rules for optical transitions are defined. The expressions for absorption threshold frequencies are found. The obtained results are compared with the case of light direct optical absorption in spherical quantum dot.

An application of Holstein-Primakoff boson expansion to both single-particle and total angular momenta provides an algebraic solution for the particle-rotor model with one high-j nucleon coupled to a triaxially deformed core, and leads two kinds of quantum numbers to classify the rotational bands. The selection rules for the intraband and interband transitions are derived referring to these quantum numbers. The variable moments of inertia are preferable to fit the experimental data both for the positive and negative parity bands in Lu isotopes.