Renormalized semiclassical quantization for rescalable Hamiltonians (10 pages)

Satoshi Takahashi, Kazuo Takatsuka

A renormalized semiclassical quantization method for rescalable Hamiltonians is proposed. A classical Hamilton system having a potential function that consists of homogeneous polynomials like the Coulombic potential can have a scale invariance in its extended phase space (phase space plus time). Consequently, infinitely many copies of a single trajectory constitute a one-parameter family that is characterized in terms of a scaling factor. This scaling invariance in classical dynamics is lost in quantum mechanics due to the presence of the Planck constant. It is shown that in a system whose classical motions have a self-similarity in the above sense, classical trajectories adopted in the semiclassical scheme interact with infinitely many copies of their own that are reproduced by the relevant scaling procedure, thereby undergoing quantum interference among themselves to produce a quantized spectrum.

Hiroshi Kuratsuji, Shinji Iida

Takanori Sugihara, Masanobu Yahiro

We propose a non-perturbative renormalization procedure for light-front Hamiltonian. Wilson's renormalization group prescription is applied to ..1<,64-model within a light-front Fock space truncated up to three-body state. Renormalized Hamiltonian which preserves lowenergy physics for arbitrary renormalization transformations is presented. Renormalization group equations for mass parameter tl and coupling constant A are derived by integrating high invariant mass space and rescaling transverse momenta and fields.

E. Doron, Uzy Smilansky

T. Sugihara, Masanobu Yahiro

We propose a non-perturbative renormalization procedure for light-front Hamiltonian. Wilson's renormalization group prescription is applied to λΦ4-model within a light-front Fock space truncated up to three-body state. Renormalized Hamiltonian which preserves low-energy physics for arbitrary renormalization transformations is presented. Renormalization group equations for mass parameter μ2 and coupling constant λ are derived by integrating high invariant mass space and rescaling transverse momenta and fields.

Jonathan M. Robbins