Partitioning Method and Van Vleck's Perturbation Theory

heating method with perturbation theory

The renormalization constants present in the lattice evaluation of the topolog-ical susceptibility can be non-perturbatively calculated by using the so-called heating method. We test this method for the O(3) non-linear σ-model in two dimensions. We work in a regime where perturbative calculations are exact and useful to check the values obtained from the heating method. The result of the test i...

Renormalization group method and canonical perturbation theory

Abstract. Renormalization group method is one of the most powerful tool to obtain approximate solutions to differential equations. We apply the renormalization group method to Hamiltonian systems whose integrable parts linearly depend on action variables. We show that the renormalization group method gives the same approximate solutions as canonical perturbation theory up to the second order of...

Testing the heating method with perturbation theory.

Perturbation Theory

1 Definition of the subject and its importance Perturbation Theory: Computation of a quantity depending on a parameter ε starting from the knowledge of is value for ε = 0 by deriving a power series expansion in ε, under the assumption of its existence, and if possible discussing the interpretation of the series. Perturbation theory is very often the only way to get a glimpse of the properties o...

Dimensional Perturbation Theory : An E cient Method forComputing Vibration - Rotation

Large-order perturbation theory in D ?1=2 , where D is the dimensionality of space, is shown to be an accurate and computationally eecient method for computing molecular vibration-rotation spectra. Results are presented for the ground vibrational state of CO 2 with J as high as 80. The rate of convergence of the perturbation expansion increases with J and the computational cost scales only as J...