Symmetry And Group

Download Automorphic forms on the metaplectic group by Gelbart S. PDF

By Gelbart S.

Show description

Read Online or Download Automorphic forms on the metaplectic group PDF

Best symmetry and group books

20th Fighter Group

The 20 th Fighter team joined the eighth Air strength Command in Dec of '43, flying the P-38 in lengthy diversity bomber escort position. the crowd later switched over to the P-51 in July of '44. the crowd destroyed a complete of 449 enemy airplane in the course of its strive against journey. Over one hundred fifty images, eight pages of colour, eighty pages.

Multiplizieren von Quantengruppen

Inhaltsangabe:Einleitung: Quantengruppen als quantisierte Universelle Einhüllende von Lie-Algebren sind Gegenstand der vorliegenden Arbeit. Sie bietet eine Einführung in die Thematik, setzt lediglich Grundkenntnisse der Darstellungstheorie Halbeinfacher Lie-Algebren voraus, wie sie etwa bei Humpfreys, Jacobsen, Serre oder Bourbaki vermittelt werden, und ordnet die Darstellungstheorie der Quantengruppen in die Physik konformer Feldtheorien ein.

Extra info for Automorphic forms on the metaplectic group

Sample text

G. Meissner, Phys. Lett. B309 (1993) 421. [15] S. Weinberg, Physica 96 A (1979) 327. [16] H. Leutwyler, Principles of chiral pertubation theory, In Proceedings of Hadron 94 Workshop, Gramado, Brazil 1994, hep-ph/9406283; World Scientific, 1995. F. Donoghue, E. R. , 1992. [18] H. , 1984. [19] H. M. R. Holstein, editors; Springer, 1995. [20] S. Weinberg, Phys. Rev. Lett. 17 (1966) 616. [21] S. Weinberg, Nucl. Phys. B363 (1991) 3. [22] E. Jenkins and A. Manohar, Nucl. Phys. B368 (1992) 190. [23] J.

Going to momentum space and introducing an effective mass, mef f (k, t), this equation can be approximately rewritten as ∂2 φ(k, t) = −(k 2 + m2ef f (t))φ(k, t) 2 ∂t (189) m2ef f (t) = λ( φ2 + σ 2 − v02 ) (190) with At zero temperature, in the ground state, σ 2 = fπ2 , Φ = 0, and we obtain the equation of motion for the pion with mass mπ . In the quench scenario (figure 10(b)), however, the expectation value of the sigma field vanishes and square of the effective mass becomes negative leading to an amplification of the modes with small mometum k!

Consider a given Feynman-diagram contributing to the scattering amplitude. It will have a certain number L of loops, a certain number Vi of vertices of type i involving di derivatives of the pion field an a certain number of internal lines Ip . The power D of the pion momentum q, this diagram will have at the end, can be determined as follows: • each loop involves an integral over the internal momenta d4 q ∼ q 4 • each internal pion line corresponds to a pion propagator, and thus contributes as 1 q2 • each vertex Vi involving di derivatives of the pion field, contributes like q di Consequently, the total power of q, q D is given by D = 4L − 2IP + Vi d i (158) i This can be simplified by using the general relation between the numbers of loops, internal lines and vertices of a given diagram L = Ip − Vi + 1 i 35 (159) to give D = 2 + 2L + i Vi (di − 2) (160) With this formula we can determine to which order of the Taylor expansion of the scattering amplitude a given diagram contributes.

Download PDF sample

Rated 4.02 of 5 – based on 16 votes