On Noether's theorem for the invariant of the time-dependent harmonic oscillator

2009 ◽  
Vol 30 (6) ◽  
pp. 1337-1343 ◽  
Author(s):  
Sumiyoshi Abe ◽  
Yuichi Itto ◽  
Mamoru Matsunaga
Keyword(s):  
Harmonic Oscillator ◽  
Time Dependent ◽  
Noether’S Theorem ◽  
Noether's Theorem

scholarly journals LINEAR TIME-DEPENDENT INVARIANTS FOR SCALAR FIELDS AND NOETHER’S THEOREM

1994 ◽  
Vol 09 (19) ◽  
pp. 1785-1790 ◽  
Author(s):  
O. CASTAÑOS ◽  
R. LÓPEZ-PEÑA ◽  
V.I. MAN’KO
Keyword(s):  
Scalar Field ◽  
Infinite Number ◽  
Linear Time ◽  
Scalar Fields ◽  
Time Dependent ◽  
Noether’S Theorem ◽  
Noether's Theorem

The infinite number of time-dependent linear in field and conjugated momenta invariants is derived for the scalar field using the Noether’s theorem procedure.

scholarly journals Noether's theorem and time-dependent quantum invariants

1994 ◽  
Vol 27 (5) ◽  
pp. 1751-1770 ◽  
Author(s):  
O Castanos ◽  
R Lopez-Pena ◽  
V I Man'ko
Keyword(s):  
Time Dependent ◽  
Noether’S Theorem ◽  
Quantum Invariants ◽  
Noether's Theorem

Noether's theorem in time-dependent lagrangian mechanics

1992 ◽  
Vol 31 (2) ◽  
pp. 189-203 ◽  
Author(s):  
JoséF. Cariñena ◽  
Eduardo Martínez ◽  
José Fernández-Núẽz
Keyword(s):  
Time Dependent ◽  
Lagrangian Mechanics ◽  
Noether’S Theorem ◽  
Noether's Theorem

scholarly journals ON SECOND NOETHER'S THEOREM AND GAUGE SYMMETRIES IN MECHANICS

2006 ◽  
Vol 03 (03) ◽  
pp. 471-487 ◽  
Author(s):  
JOSÉ F. CARIÑENA ◽  
JOAN-ANDREU LÁZARO-CAMÍ ◽  
EDUARDO MARTÍNEZ
Keyword(s):  
Infinitesimal Generator ◽  
Evolution Operator ◽  
Time Dependent ◽  
Noether’S Theorem ◽  
Time Evolution Operator ◽  
Noether's Theorem ◽  
Constraint Manifold ◽  
Gauge Symmetries ◽  
Lagrangian And Hamiltonian Formalisms ◽  
Geometric Formulation

We review the geometric formulation of the second Noether's theorem in time-dependent mechanics. The commutation relations between the dynamics on the final constraint manifold and the infinitesimal generator of a symmetry are studied. We show an algorithm for determining a gauge symmetry which is closely related to the process of stabilization of constraints, both in Lagrangian and Hamiltonian formalisms. The connections between both formalisms are established by means of the time-evolution operator.

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