By S. Ketov
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Half I provides an in depth, self-contained and mathematically rigorous exposition of classical conformal symmetry in n dimensions and its quantization in dimensions. The conformal teams are decided and the appearence of the Virasoro algebra within the context of the quantization of two-dimensional conformal symmetry is defined through the category of valuable extensions of Lie algebras and teams.
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Extra resources for Advances in Quantum Field Theory
5 and 6 is to suggest the richness, ﬂexibility and economy of texture available for solutions in a basis function approach. Next, we introduce the total invariant mass-squared M2 for the low-lying physical states in terms of a Hamiltonian H times a dimensionless integer for the total light-front momentum K M2 + P⊥ P⊥ → M2 + const = P+ P− = KH (4) where we absorb the constant into M2 . For simplicity, the transverse functions for both the electron and the photon were taken as eigenmodes of the external trap in our initial application (7) which we discuss here (below, we present results with the external trap removed).
The light-front Hamiltonian quantized within a basis function approach as described here offers a promising avenue that capitalizes on theoretical and computational achievements in quantum many-body theory over the past decade. By way of background, one notes that Hamiltonian light-front ﬁeld theory in a discretized momentum basis (1) and in transverse lattice approaches (2; 3) have shown signiﬁcant promise. I outline here a Hamiltonian basis function approach following Refs. (4–10) that exploits recent advances in solving the non-relativistic strongly interacting nuclear many-body problem (11; 12).
1997). Effective interactions for mesons and baryons in nuclei, Progr. Theor. , 98, 927-941. V. (2004). Clothed particle representation in quantum ﬁeld theory: Mass renormalization, Phys. Rev. D 70, 085011. V. (2007). Relativistic interactions for the meson-two-nucleon system in the clothed-particle unitary representation, Ann. , 322, 736-768. ; Glöckle, W. (1999). Approach towards N-nucleon effective generators of the Poincaré group derived from a ﬁeld theory, Phys. Rev. C 59, 31919-1929. V. (1993).
Advances in Quantum Field Theory by S. Ketov