By Antonio Dobado, Angel Gomez-Nicola, Antonio L. Maroto, Jose R. Pelaez

This booklet offers a close and pedagogical exposition of the powerful Lagrangian strategies and their functions to high-energy physics. It covers the most theoretical rules and describes comprehensively tips on how to use them in numerous fields, resembling chiral perturbation conception and the symmetry breaking zone of the normal version or even low-energy quantum gravity. The publication is written within the language of contemporary quantum box conception. a few of the theoretical subject matters taken care of are: decoupling, the Goldstone theorem, the non-linear sigma version, anomalies, the Wess--Zumino--Witten time period, and the equivalence theorem.

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B104 (1976) 445 W. Heisenberg and H. Euler, Z. Phys. 98 (1936) 714 J. Schwinger, Phys. Rev. H. Furry, Phys. Rev. 51 (1937) 125 F. Feruglio, L. Maiani and A. Masiero, Nucl. Phys. B387 (1992) 523 E. D'Hoker and E. Farhi, Nucl. Phys. R. M. Fraser, Phys. Rev. D31 (1985) 2605 2. Global Symmetries in Quantum Field Theory Symmetries play an important role in the determination of the structure of the different terms appearing in an effective Lagrangian. For this reason we briefly review in this chapter the basic notions related with global symmetries in quantum field theories (QFT).

51 (1937) 125 F. Feruglio, L. Maiani and A. Masiero, Nucl. Phys. B387 (1992) 523 E. D'Hoker and E. Farhi, Nucl. Phys. R. M. Fraser, Phys. Rev. D31 (1985) 2605 2. Global Symmetries in Quantum Field Theory Symmetries play an important role in the determination of the structure of the different terms appearing in an effective Lagrangian. For this reason we briefly review in this chapter the basic notions related with global symmetries in quantum field theories (QFT). Starting from the Noether theorem for classical systems we derive the Ward identities for the Green functions.

The precise definition of the action also requires knowing the functional space in which it is defined, or in other words, the field boundary conditions on 8n. 3). The equations of motion are obtained from the variational principle 85[P] = o. 2). 6) Il Now we will assume 5[P] to be invariant under the G group. Therefore we have 5[P] = 5[P'] = 5[P + 8P] . e. not affecting the space-time coordinates) and then the above equation is equivalent to 8£ = o. 8) In this case, and using the equation of motion, it is not difficult to find 81l (8(~~P/P) =0.

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