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Unification of Quantum Statistics ? It`s possible with quaternions to
Unification of Quantum Statistics ? It`s possible with quaternions to

... the cosine of  is equal to - 1 and the sine of  is equal to zero, modulo 2. So we see the possibility of an extension of dependence of the Statistics also on momentum could make possible that Fermi-Dirac and Bose-Einstein statistics were special case of two quaternionic ones for p=> 0 o for pc/K ...
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Igor Herbut (Simon Fraser University, Vancouver) Lukas Janssen

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Unitarity and Effective Field Theory Results in Quantum Gravity

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leading quantum correction to the newtonian potential
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Explicit solution of the continuous Baker-Campbell
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Why quantum gravity? - University of Oxford
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Physics 120 Homework Set #1 (due Sunday
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Asymptotic safety in quantum gravity

Asymptotic safety (sometimes also referred to as nonperturbative renormalizability) is a concept in quantum field theory which aims at finding a consistent and predictive quantum theory of the gravitational field. Its key ingredient is a nontrivial fixed point of the theory's renormalization group flow which controls the behavior of the coupling constants in the ultraviolet (UV) regime and renders physical quantities safe from divergences. Although originally proposed by Steven Weinberg to find a theory of quantum gravity, the idea of a nontrivial fixed point providing a possible UV completion can be applied also to other field theories, in particular to perturbatively nonrenormalizable ones. In this respect, it is similar to Quantum triviality.The essence of asymptotic safety is the observation that nontrivial renormalization group fixed points can be used to generalize the procedure of perturbative renormalization. In an asymptotically safe theory the couplings do not need to be small or tend to zero in the high energy limit but rather tend to finite values: they approach a nontrivial UV fixed point. The running of the coupling constants, i.e. their scale dependence described by the renormalization group (RG), is thus special in its UV limit in the sense that all their dimensionless combinations remain finite. This suffices to avoid unphysical divergences, e.g. in scattering amplitudes. The requirement of a UV fixed point restricts the form of the bare action and the values of the bare coupling constants, which become predictions of the asymptotic safety program rather than inputs.As for gravity, the standard procedure of perturbative renormalization fails since Newton's constant, the relevant expansion parameter, has negative mass dimension rendering general relativity perturbatively nonrenormalizable. This has driven the search for nonperturbative frameworks describing quantum gravity, including asymptotic safety which — in contrast to other approaches—is characterized by its use of quantum field theory methods, without depending on perturbative techniques, however. At the present time, there is accumulating evidence for a fixed point suitable for asymptotic safety, while a rigorous proof of its existence is still lacking.
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