Is equivalent to m tending to zero keeping e constant

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Unformatted text preview: t, it follows that one must send ÃQCD to zero. In this limit, the size of a resonance grows indefinitely, however, and it becomes undetectable to an observer of fixed size, since the observer lives within the resonance’s Compton wavelength.15 B. Asymptotic states and conserved charges The S-matrix theorems concern only particles that appear as asymptotic states. Moreover, within the perturbative approach, these asymptotic states are assumed to exist at all energy scales. Thus, an intriguing possibility is that there exists nonperturbatively defined higher-spin gauge theories in flat spacetime with mass gaps and confinement. We are not aware of any thorough investigations of such models and mechanisms so far, although Vasiliev’s higher-spin gravities in four-dimensional anti–de Sitter spacetime have been conjectured to possess a perturbatively defined mass gap, resulting from dynamical symmetry breaking induced via radiative corrections (Girardello, Porrati, and Zaffaroni, 2003), as we comment on below. As far as confinement is concerned,16 one may ask whether the higher-spin charges of asymptotic states might all vanish, such as for color charges in QCD. Incidentally, Weinberg pointed out in his book (Weinberg, 2000), p. 13, that some subtleties arise in the application of the Coleman-Mandula theorem in the presence of infrared divergences, but that there is no problem in non-Abelian gauge theories in which all massless particles are trapped—symmetries if unbroken would only govern S-matrix elements for gauge-neutral bound states. 14 Strictly speaking, one can arguably refer to the proton as stable while already the neutron is metastable while all other massive excitations are far more short lived. 15 We thank one of the referees for this comment. 16 This way out was briefly mentioned in the conclusions of Bekaert, Joung, and Mourad (2009). 994 Xavier Bekaert, Nicolas Boulanger, and Per A. Sundell: How higher-spin gravity surpasses the spin- . . . C. Lorentz minimal coupling To reiterate slightly, the S-matrix no-go theorems17 for ´ higher-spin interactions are engineered for Poincare-invariant relativistic quantum field theories aimed at describing physics at intermediate scales lying far in between the Planck and Hubble scales. In Lagrangian terms, the generalized Weinberg-Witten theorem can essentially be understood as resulting from demanding compatibility between linearized gauge symmetries and the Lorentz minimal coupling in the absence of a cosmological constant. This compatibility requires consistent cubic vertices with one and two derivatives for fermions and bosons, respectively. Vertices with these numbers of derivatives have the same dimension as the flatspace kinetic terms. If consistent, they therefore do not introduce any new mass parameter. Hence it is natural to extrapolate the Lorentz minimal coupling to all scales. In doing so, however, one needs to keep in mind not only the barrier for quantum fields in th...
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This document was uploaded on 09/28/2013.

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