We show that the Stark and Kerr Hamiltonians are deeply connected in the framework of dynamical algebras. We found that the algebras for both Hamiltonians are the same when physically relevant magnitudes, such as the population inversion and the $n$ th order coherence function are considered as elements of a Lie algebra under commutation with the Hamiltonians. By analyzing the equations of motion we were able to find a set of conditions for the characteristic magnitudes of both Hamiltonians that leads to the same dynamical behavior for all the elements of the group. Finally, we conclude that the results of this paper can be generalized to any extension of the Jaynes-Cummings model, where any of the different elements of the group are present.We show that the Stark and Kerr Hamiltonians are deeply connected in the framework of dynamical algebras. We found that the algebras for both Hamiltonians are the same when physically relevant magnitudes, such as the population inversion and the $n$th order coherence function are considered as elements of a Lie algebra under commutation with the Hamiltonians. By analyzing the equations of motion we were able to find a set of conditions for the characteristic magnitudes of both Hamiltonians that leads to the same dynamical behavior for all the elements of the group. Finally, we conclude that the results of this paper can be generalized to any extension of the Jaynes-Cummings model, where any of the different elements of the group are present.

Physical Review ASep 1, 19974 citations

Algebra of physical observables

Susumo Okubo

Cambridge University Press eBooksAug 3, 19950 citations

Mathematical Physics and Matrix Representations

R. Aldrovandi

WORLD SCIENTIFIC eBooksMar 28, 20250 citations

Action as an algebraic vector magnitude

А. А. Кецарис

The article shows that quantum phenomena can be explained by the algebraic structure of space of the fundamental physical value of action. The eigenvalue operator problem is obtained as a consequence of an algebraic action vector multiplication law, existence of which we conceded. Thus we come to the explanation of quantum phenomena by the algebraic structure of the space of action vectors. Also the authors planned the path for explanations of types of quantum operators in relation to classical differentiation operators: multipliers included into the structure constants can be transferred to the operators of differentiation. Such multipliers include imaginary unit. In addition, it was established understanding of wave function as a partial differential of an action vector.The article shows that quantum phenomena can be explained by the algebraic structure of space of the fundamental physical value of action. The eigenvalue operator problem is obtained as a consequence of an algebraic action vector multiplication law, existence of which we conceded. Thus we come to the explanation of quantum phenomena by the algebraic structure of the space of action vectors. Also the authors planned the path for explanations of types of quantum operators in relation to classical differentiation operators: multipliers included into the structure constants can be transferred to the operators of differentiation. Such multipliers include imaginary unit. In addition, it was established understanding of wave function as a partial differential of an action vector.

Izvestiya MGTU MAMIFeb 10, 20130 citations

Measurement Algebra

Julian Schwinger

Springer eBooksJan 1, 200113 citations

n

th order coherence function are considered as elements of a Lie algebra under commutation with the Hamiltonians. By analyzing the equations of motion we were able to find a set of conditions for the characteristic magnitudes of both Hamiltonians that leads to the same dynamical behavior for all the elements of the group. Finally, we conclude that the results of this paper can be generalized to any extension of the Jaynes-Cummings model, where any of the different elements of the group are present.