2008/01/25 by W. H. Klink, Klink, W. H. · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #Noncommutative and Quantum Gravity Theories #Nuclear Theory (nucl-th) #Quantum Electrodynamics and Casimir Effect #nucl-th
paper · pdf · doi:10.48550/arxiv.0801.4039
arxiv created 2008/01/25 · openalex publication_date 2008/01/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In constrast to discretized space-time approximations to continuum quantum field theories, discretized velocity space approximations to continuum quantum field theories are investigated. A four-momentum operator is given in terms of bare fermion-antifermion-boson creation and annihilation operators with discrete indices. In continuum quantum field theories the fermion-antifermion creation and annihilation operators appear as bilinears in the four-momentum operator and generate a unitary algebra. When the number of modes range over only a finite number of values, the algebra is that associated with the Lie algebra of U(2N). By keeping N finite (but arbitrary) problems due to an infinite Lorentz volume and to the creation of infinite numbers of bare fermion-antifermion pairs are avoided. But even with a finite number of modes, it is still possible to create an infinite number of bare bosons. We show how the full boson algebra arises as the contraction limit of another unitary algebra that restricts the number of bare bosons in any mode to be finite. Generic properties of finite mode Hamiltonians are investigated, as are several simple models to see the rate of convergence of the boson contraction; the possibility of fine tuning the bare strong coupling constant is also briefly discussed.