scholarly journals The Schwinger Action Principle and Its Applications to Quantum Mechanics

10.5772/53472 ◽  
2013 ◽  
Author(s):  
Paul Bracken
Keyword(s):  
Quantum Mechanics ◽  
Action Principle ◽  
Schwinger Action Principle

Schwinger action principle, eikonal theory and two-time rotation-translation of coordinates

1990 ◽  
Vol 42 (1) ◽  
pp. 9-13 ◽  
Author(s):  
Antônio B Nassar ◽  
Luis C L Botelho ◽  
J M F Bassalo ◽  
P T S Alencar
Keyword(s):  
Action Principle ◽  
Schwinger Action Principle

Parastatistics from the Schwinger action principle

1972 ◽  
Vol 49 ◽  
pp. 392-404 ◽  
Author(s):  
F.J. Bloore ◽  
Ruth M. Lovely
Keyword(s):  
Action Principle ◽  
Schwinger Action Principle

Schwinger Action Principle and Variational Calculus

2018 ◽  
Author(s):  
Norman J. Morgenstern Horing
Keyword(s):  
Particle Physics ◽  
Relativistic Quantum ◽  
Equations Of Motion ◽  
Variational Calculus ◽  
Action Principle ◽  
Full Detail ◽  
Heisenberg Equation ◽  
Field Equations ◽  
Potential Sources ◽  
Schwinger Action Principle

Chapter 4 introduces the Schwinger Action Principle, along with associated particle and potential sources. While the methods described here originally arose in the relativistic quantum field theory of elementary particle physics, they have also profoundly advanced our understanding of non-relativistic many-particle physics. The Schwinger Action Principle is a quantum-mechanical variational principle that closely parallels the Hamilton Principle of Least Action of classical mechanics, generalizing it to include the role of quantum operators as generalized coordinates and momenta. As such, it unifies all aspects of quantum theory, incorporating Hamilton equations of motion for those operators and the Heisenberg equation, as well as producing the canonical equal-time commutation/anticommutation relations. It yields dynamical coupled field equations for the creation and annihilation operators of the interacting many-body system by variational differentiation of the Hamiltonian with respect to the field operators. Also, equations for the development of matrix elements (underlying Green’s functions) are derived using variations with respect to particle and potential “sources” (and coupling strength). Variational calculus, involving impressed potentials, c-number coordinates and fields, also quantum operator coordinates and fields, is discussed in full detail. Attention is given to the introduction of fermion and boson particle sources and their use in variational calculus.

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.

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