Conformal Quantum Field Theory in D-dimensions

1. Front Matter

   Pages i-2

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2. Goals and Perspectives

   • Efim S. Fradkin, Mark Ya. Palchik

   Pages 3-43

3. Global Conformal Symmetry and Hilbert Space

   • Efim S. Fradkin, Mark Ya. Palchik

   Pages 45-97

4. Euclidean Formulation of the Conformal Theory

   • Efim S. Fradkin, Mark Ya. Palchik

   Pages 99-142

5. Approximate Methods of Calculating Critical Indices

   • Efim S. Fradkin, Mark Ya. Palchik

   Pages 143-162

6. Spontaneous Breakdown of Conformal Symmetry

   • Efim S. Fradkin, Mark Ya. Palchik

   Pages 163-169

7. Ward Identities

   • Efim S. Fradkin, Mark Ya. Palchik

   Pages 171-204

8. Contribution of Electromagnetic and Gravitational Interactions into the General Solution of Ward Identities

   • Efim S. Fradkin, Mark Ya. Palchik

   Pages 205-240

9. Dynamical Sector of the Hilbert Space

   • Efim S. Fradkin, Mark Ya. Palchik

   Pages 241-316

10. Conformal Invariance in Gauge Theories

    • Efim S. Fradkin, Mark Ya. Palchik

    Pages 317-346

11. Special Features of Conformal Transformation of Current, Energy-Momentum Tensor and Gauge Fields

    • Efim S. Fradkin, Mark Ya. Palchik

    Pages 347-372

12. Back Matter

    Pages 373-465

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Our prime concern in this book is to discuss some most interesting prosppcts that have occurred recently in conformally invariant quantum field theory in a D-diuwnsional space. One of the most promising trends is constructing an pxact solution for a cprtain class of models. This task seems to be quite feasible in the light of recent resllits. The situation here is to some extent similar to what was going on in the past ypars with the two-dimensional quantum field theory. Our investigation of conformal Ward identities in a D-dimensional space, carried out as far hack as the late H. J7Gs, showed that in the D-dimensional quantum field theory, irrespective of the type of interartion, there exists a special set of states of the field with the following property: if we rpqllire that one of these states should vanish, this determines an exact solution of 3. certain field model. These states are analogous to null-vectors which determine the minimal models in the two-dimensional field theory. On the other hand, the recent resparches supplied us with a number of indications on the existencp of an intinite-parampter algebra analogous to the Virasoro algebra in spaces of higher dimensions D 2: :~. It has also been shown that this algebra admits an operator rentral expansion. It seems to us that the above-mentioned models are field theoretical realizations of the representations of these new symmetries for D 2: ;3.

• Minkowski space
• Minkowski spacetime
• algebra
• differential equation
• field
• field theory
• gauge theories
• gravity
• quantum field
• quantum field theory
• transformation

• Nuclear Physics Section, Russian Academy of Sciences; and P.N. Lebedev Physical Institute, Moscow, Russia

  Efim S. Fradkin

• Institute of Automation and Electrometry, Novosibirsk, Russia

  Mark Ya. Palchik

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