Calculation of the propagator for a time-dependent damped, forced harmonic oscillator using the Schwinger action principle

1984 ◽  
Vol 23 (12) ◽  
pp. 1105-1127 ◽  
Author(s):  
Luis F. Urrutia ◽  
Eduardo Hernández
Keyword(s):  
Harmonic Oscillator ◽  
Action Principle ◽  
Time Dependent ◽  
Schwinger Action Principle

RENORMALIZATION AND THE ACTION PRINCIPLE

1996 ◽  
Vol 11 (19) ◽  
pp. 3549-3585
Author(s):  
MARK BURGESS
Keyword(s):  
Renormalization Group ◽  
Gauge Field Theories ◽  
Action Principle ◽  
Time Dependent ◽  
Field Theories ◽  
Gauge Sector ◽  
Yang Mills ◽  
Nonlocal Sources ◽  
Schwinger Action Principle ◽  
Infrared Problem

An action principle technique provides an unusual perspective on the infrared problem in the effective action for gauge field theories. It is shown by means of a dynamical analogy that the renormalization group and the ansatz of nonlocal sources can be simultaneously presented through generalized variations of an action supplemented by sources in the manner of the Schwinger action principle. Indiscriminate resummations of the effective potential often lead to erroneous conclusions about phase transitions in a gauge theory if they resum matter self-energies at the expense of the gauge sector. The action principle method illuminates the reason for this and shows a way of proceeding, without having to go to nonzero momentum. Some examples are computed to the lowest order, reproducing results previously obtained through the renormalization group, and a new example is computed in Yang–Mills theory. The dynamical analogy leads to a comparison with a class of phenomenological nonequilibrium Lagrangians in which time-dependent couplings are used to model the influence of an external system. These models and some of their implications are discussed in terms of the action principle.

On the Quantization Problem of a Driven Harmonic Oscillator with Time Dependent Mass and Frequency

2003 ◽  
Vol 17 (18) ◽  
pp. 983-990 ◽  
Author(s):  
Swapan Mandal
Keyword(s):  
Harmonic Oscillator ◽  
Time Dependent ◽  
Present Solution ◽  
Quadratic Hamiltonian ◽  
Dependent Mass ◽  
Quantization Problem

The quantization of a driven harmonic oscillator with time dependent mass and frequency (DHTDMF) is considered. We observe that the driven term has no influence on the quantization of the oscillator. It is found that the DHTDMF corresponds the general quadratic Hamiltonian. The present solution is critically compared with existing solutions of DHTDMF.

scholarly journals Time-dependent propagator for an-harmonic oscillator with quartic term in potential

2021 ◽  
Vol 62 (2) ◽  
pp. 023501
Author(s):  
J. Boháčik ◽  
P. Prešnajder ◽  
P. Augustín
Keyword(s):  
Harmonic Oscillator ◽  
Time Dependent ◽  
Quartic Term

GENERALIZED HANNAY ANGLE FOR THE MOST GENERAL TIME-DEPENDENT HARMONIC OSCILLATOR

1993 ◽  
Vol 07 (28) ◽  
pp. 4827-4840 ◽  
Author(s):  
DONALD H. KOBE ◽  
JIONGMING ZHU
Keyword(s):  
Harmonic Oscillator ◽  
Berry Phase ◽  
Time Dependent ◽  
Canonical Momentum ◽  
Gauge Invariant ◽  
Classical Counterpart ◽  
Mass Spring ◽  
Adiabatic Case ◽  
General Time ◽  
Total Angle

The most general time-dependent Hamiltonian for a harmonic oscillator is both linear and quadratic in the coordinate and the canonical momentum. It describes in general a harmonic oscillator with mass, spring “constant,” and friction (or antifriction) “constant,” all of which are time dependent, that is acted on by a time-dependent force. A generalized Hannay angle, which is gauge invariant, is defined by making a distinction between the Hamiltonian and the energy. The generalized Hannay angle is the classical counterpart of the generalized Berry phase in quantum theory. When friction is present the generalized Hannay angle is nonzero. If the Hamiltonian is (incorrectly) chosen to be the energy, the generalized Hannay angle is different. Nevertheless, in the adiabatic case the same total angle is obtained.

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