scholarly journals Quadratic canonical transformation theory and higher order density matrices

2009 ◽  
Vol 130 (12) ◽  
pp. 124102 ◽  
Author(s):  
Eric Neuscamman ◽  
Takeshi Yanai ◽  
Garnet Kin-Lic Chan
Keyword(s):  
Canonical Transformation ◽  
Higher Order ◽  
Transformation Theory ◽  
Density Matrices

scholarly journals Theory of Generalized Canonical Transformations for Birkhoff Systems

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Yi Zhang
Keyword(s):  
Canonical Transformation ◽  
Natural Generalization ◽  
Analytical Mechanics ◽  
Hamiltonian Mechanics ◽  
Canonical Transformations ◽  
Transformation Theory ◽  
Special Cases ◽  
Criterion Equation ◽  
Important Means ◽  
Transformation Formulas

Transformation is an important means to study problems in analytical mechanics. It is often difficult to solve dynamic equations, and the use of variable transformation can make the equations easier to solve. The theory of canonical transformations plays an important role in solving Hamilton’s canonical equations. Birkhoffian mechanics is a natural generalization of Hamiltonian mechanics. This paper attempts to extend the canonical transformation theory of Hamilton systems to Birkhoff systems and establish the generalized canonical transformation of Birkhoff systems. First, the definition and criterion of the generalized canonical transformation for the Birkhoff system are established. Secondly, based on the criterion equation and considering the generating functions of different forms, six generalized canonical transformation formulas are derived. As special cases, the canonical transformation formulas of classical Hamilton’s equations are given. At the end of the paper, two examples are given to illustrate the application of the results.

Canonical formulation of Pais–Uhlenbeck action and resolving the issue of branched Hamiltonian

2017 ◽  
Vol 14 (03) ◽  
pp. 1750038 ◽  
Author(s):  
Kaushik Sarkar ◽  
Nayem Sk ◽  
Ranajit Mandal ◽  
Abhik Kumar Sanyal
Keyword(s):  
Scalar Curvature ◽  
Canonical Transformation ◽  
Auxiliary Variable ◽  
Order Theory ◽  
Higher Order ◽  
End Points ◽  
Canonical Formulation ◽  
Higher Order Terms ◽  
Theory Of Gravity ◽  
Higher Order Theory

Canonical formulation of higher order theory of gravity requires to fix (in addition to the metric), the scalar curvature, which is acceleration in disguise, at the boundary. On the contrary, for the same purpose, Ostrogradski's or Dirac's technique of constrained analysis, and Horowit'z formalism, tacitly assume velocity (in addition to the co-ordinate) to be fixed at the end points. In the process when applied to gravity, Gibbons–Hawking–York term disappears. To remove such contradiction and to set different higher order theories on the same footing, we propose to fix acceleration at the endpoints/boundary. However, such proposition is not compatible to Ostrogradski's or Dirac's technique. Here, we have modified Horowitz's technique of using an auxiliary variable, to establish a one-to-one correspondence between different higher order theories. Although, the resulting Hamiltonian is related to the others under canonical transformation, we have proved that this is not true in general. We have also demonstrated how higher order terms can regulate the issue of branched Hamiltonian.

scholarly journals Canonical transformation theory from extended normal ordering

2007 ◽  
Vol 127 (10) ◽  
pp. 104107 ◽  
Author(s):  
Takeshi Yanai ◽  
Garnet Kin-Lic Chan
Keyword(s):  
Canonical Transformation ◽  
Transformation Theory ◽  
Normal Ordering

scholarly journals Canonical transformation theory for multireference problems

2006 ◽  
Vol 124 (19) ◽  
pp. 194106 ◽  
Author(s):  
Takeshi Yanai ◽  
Garnet Kin-Lic Chan
Keyword(s):  
Canonical Transformation ◽  
Transformation Theory
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