INVESTIGADORES
CIRILO Diego Julio
artículos
Título:
Non-compact Groups, Coherent States, Relativistic Wave Equations and the Harmonic Oscillator
Autor/es:
DIEGO JULIO CIRILO-LOMBARDO
Revista:
FOUNDATIONS OF PHYSICS
Editorial:
SPRINGER
Referencias:
Año: 2007 p. 919 - 950
ISSN:
0015-9018
Resumen:
Relativistic geometrical action for a quantum particle in the superspace is
analyzed from theoretical group point of view. To this end an alternative technique
of quantization outlined by the authors in a previous work and that is
based in the correct interpretation of the square root Hamiltonian, is used.
The obtained spectrum of physical states and the Fock construction consist of
Squeezed States which correspond to the representations with the lowest weights
ë = 1/4 and ë = 3/4 with four possible (non-trivial) fractional representations for
the group decomposition of the spin structure. From the theory of semigroups
the analytical representation of the radical operator in the superspace is constructed,
the conserved currents are computed and a new relativistic wave equation
is proposed and explicitly solved for the time-dependent case. The relation
with the Relativistic Schr¨odinger equation and the Time-dependent Harmonic
Oscillator is analyzed and discussed.= 1/4 and ë = 3/4 with four possible (non-trivial) fractional representations for
the group decomposition of the spin structure. From the theory of semigroups
the analytical representation of the radical operator in the superspace is constructed,
the conserved currents are computed and a new relativistic wave equation
is proposed and explicitly solved for the time-dependent case. The relation
with the Relativistic Schr¨odinger equation and the Time-dependent Harmonic
Oscillator is analyzed and discussed.