By E.S. Fradkin, Mark Ya. Palchik
Our best problem during this e-book is to debate a few best prosppcts that experience happened lately in conformally invariant quantum box thought in a D-diuwnsional area. essentially the most promising developments is developing an pxact answer for a cprtain type of types. This job seems relatively possible within the mild of contemporary resllits. the location this is to a point just like what was once occurring some time past ypars with the two-dimensional quantum box thought. Our research of conformal Ward identities in a D-dimensional house, performed as a ways hack because the overdue H. J7Gs, confirmed that during the D-dimensional quantum box thought, regardless of the kind of interartion, there exists a different set of states of the sphere with the subsequent estate: if we rpqllire that this sort of states should still vanish, this determines an actual resolution of three. sure box version. those states are analogous to null-vectors which ensure the minimum types within the two-dimensional box concept. however, the new resparches provided us with a couple of symptoms at the existencp of an intinite-parampter algebra analogous to the Virasoro algebra in areas of upper dimensions D 2: :~. It has additionally been proven that this algebra admits an operator rentral growth. it sort of feels to us that the above-mentioned versions are box theoretical realizations of the representations of those new symmetries for D 2: ;3.
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Extra resources for Conformal Quantum Field Theory in D-dimensions
12) on the conformal field algebra. 6) is the main goal of the second Chapter. In Chapter III these results are formulated in terms of Euclidean conformal fields. At the next step the second statement, that is, the existence of the energymomentum tensor and the current, is studied. 4) together with the conditions of conformal symmetry makes possible to find the states of the type ... 6). This result is justified rigorously under the following additional constraint: a current and energymomentum tensor in Euclidean space transform by irreducible representations of the conformal group.
6) is the main goal of the second Chapter. In Chapter III these results are formulated in terms of Euclidean conformal fields. At the next step the second statement, that is, the existence of the energymomentum tensor and the current, is studied. 4) together with the conditions of conformal symmetry makes possible to find the states of the type ... 6). This result is justified rigorously under the following additional constraint: a current and energymomentum tensor in Euclidean space transform by irreducible representations of the conformal group.
20). 12) belong. The dynamical principle which governs the effective interaction, is formulated in this subspace, called below the dynamical sector of a Hilbert space. The states also belong to this sector. Since the dynamical sector is generated by energy-momentum tensor and the current, an introduction of any consistent model-fixing condition on the states of this sector may be regarded as a means of specification of an effective Hamiltonian. For a number of simplest models (see sections 4,5 of the Chapter VIII), the constraint on the states of the dynamical sector can be obtained directly from the initial Lagrangian.
Conformal Quantum Field Theory in D-dimensions by E.S. Fradkin, Mark Ya. Palchik