IST Austria Library

Harmonic analysis on the n-dimensional Lorentz group and its application to conformal quantum field theory / V.K. Dobrev [and others].

Contributor(s): Dobrev, V. K
Material type: TextTextSeries: Lecture notes in physics: 63.Publisher: Berlin ; New York : Springer-Verlag, 1977Description: 1 online resource (x, 280 pages) : illustrationsContent type: text Media type: computer Carrier type: online resourceISBN: 9783540373810; 3540373810; 9783540081500; 354008150XSubject(s): Lorentz transformations | Quantum field theory | Harmonic analysis | Harmonic analysis | Lorentz transformations | Quantum field theoryGenre/Form: Electronic books. Additional physical formats: Print version:: Harmonic analysis on the n-dimensional Lorentz group and its application to conformal quantum field theory.DDC classification: 530 LOC classification: QC174.52.L6 | H37Online resources: Click here to access online
Contents:
1. Group structure. Preliminaries -- 2. Induced representations. Definition and various realizations -- 3. Further properties of the elementary representations -- 4. Intertwining operators: X-space realization -- 5. Momentum space expansion of the intertwining distribution and positivity -- 6. Nondecomposable representations and intertwining differential operators -- 7. Discrete and general properties of the discrete series -- 8. The Plancheral theorem. Concluding remarks -- 9. The Kronecker product of two elementary representations -- 10. Construction of the Clebsch Gordan expansion -- 11. Special cases and further properties of the expansion formula -- 12. Renormalizable models of self-interacting scalar fields. Dynamical equations for Green functions -- 13. Invariance and invariant solutions of the dynamical equations. Conformal partial wave expansion for the Euclidean Green functions -- 14. Implications of the dynamical equations. Pole structure of conformal partial waves -- 15. Another form of the conformal expansion, involving a Minkowski momentum space integral. The Q-kernels -- 16. The problem of crossing symmetry. Concluding remarks.
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Includes bibliographical references (pages 268-277).

1. Group structure. Preliminaries -- 2. Induced representations. Definition and various realizations -- 3. Further properties of the elementary representations -- 4. Intertwining operators: X-space realization -- 5. Momentum space expansion of the intertwining distribution and positivity -- 6. Nondecomposable representations and intertwining differential operators -- 7. Discrete and general properties of the discrete series -- 8. The Plancheral theorem. Concluding remarks -- 9. The Kronecker product of two elementary representations -- 10. Construction of the Clebsch Gordan expansion -- 11. Special cases and further properties of the expansion formula -- 12. Renormalizable models of self-interacting scalar fields. Dynamical equations for Green functions -- 13. Invariance and invariant solutions of the dynamical equations. Conformal partial wave expansion for the Euclidean Green functions -- 14. Implications of the dynamical equations. Pole structure of conformal partial waves -- 15. Another form of the conformal expansion, involving a Minkowski momentum space integral. The Q-kernels -- 16. The problem of crossing symmetry. Concluding remarks.

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