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  3. The Pinch Technique and its Applications to Non-Abelian Gauge Theories
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    • Publisher:
      Cambridge University Press
      Publication date:
      February 2011
      December 2010
      ISBN:
      9780511763038
      DOI:
      https://doi.org/10.1017/CBO9780511763038
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      • Subjects:
      Particle Physics and Nuclear Physics, Physics and Astronomy, Theoretical Physics and Mathematical Physics
      Series:
      Cambridge Monographs on Particle Physics, Nuclear Physics and Cosmology (31)
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    Subjects:
    Particle Physics and Nuclear Physics, Physics and Astronomy, Theoretical Physics and Mathematical Physics
    Series:
    Cambridge Monographs on Particle Physics, Nuclear Physics and Cosmology (31)
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    Book description

    Non-Abelian gauge theories, such as quantum chromodynamics (QCD) or electroweak theory, are best studied with the aid of Green's functions that are gauge-invariant off-shell, but unlike for the photon in quantum electrodynamics, conventional graphical constructions fail. The Pinch Technique provides a systematic framework for constructing such Green's functions, and has many useful applications. Beginning with elementary one-loop examples, this book goes on to extend the method to all orders, showing that the Pinch Technique is equivalent to calculations in the background field Feynman gauge. The Pinch Technique Schwinger-Dyson equations are derived, and used to show how a dynamical gluon mass arises in QCD. Applications are given to the center vortex picture of confinement, the gauge-invariant treatment of resonant amplitudes, the definition of non-Abelian effective charges, high-temperature effects, and even supersymmetry. This book is ideal for elementary particle theorists and graduate students.

    Reviews

    "The authors are authorities in the field. Cornwall is the person who introduced the pinch techniques in the late 1970's; Papavassiliou and Binosi did most of their research in this field. Nobody knows this matter better than the authors."
    Giuseppe Nardelli, Mathematical Reviews

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