Renormalization of Hamiltonians

Journal Article · Wed Dec 15 00:00:00 EST 1993 · Physical Review, D (Particles Fields); (United States)

DOI:https://doi.org/10.1103/PhysRevD.48.5863· OSTI ID:5586612

Glazek, S D ^[1]; Wilson, K G ^[2]

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1. Institute of Theoretical Physics, Warsaw University, ul. Hoza 69, 00-681 Warsaw (Poland)
2. Department of Physics, The Ohio State University, 174 West 18th Avenue, Columbus, Ohio 43210-1106 (United States)

This paper presents a new renormalization procedure for Hamiltonians such as those of light-front field theory. The bare Hamiltonian with an arbitrarily large, but finite cutoff, is transformed by a specially chosen similarity transformation. The similarity transformation has two desirable features. First, the transformed Hamiltonian is band diagonal: in particular, all matrix elements vanish which would otherwise have caused transitions with big energy jumps, such as from a state of bounded energy to a state with an energy of the order of the cutoff. At the same time, neither the similarity transformation nor the transformed Hamiltonian, computed in perturbation theory, contain vanishing or near-vanishing energy denominators. Instead, energy differences in denominators can be replaced by energy sums for purposes of order of magnitude estimates needed to determine cutoff dependences. These two properties make it possible to determine relatively easily the list of counterterms needed to obtain finite low energy results (such as for eigenvalues). A simple model Hamiltonian is discussed to illustrate the method.

• OSTI ID: 5586612
• Journal Information: Physical Review, D (Particles Fields); (United States), Journal Name: Physical Review, D (Particles Fields); (United States) Vol. 48:12; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

662110* -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-)
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
FIELD THEORIES
HAMILTONIANS
LIGHT CONE
MATHEMATICAL OPERATORS
MATRIX ELEMENTS
PERTURBATION THEORY
QUANTUM FIELD THEORY
QUANTUM OPERATORS
RENORMALIZATION
SPACE-TIME
ULTRAVIOLET DIVERGENCES