The idea of QFT on generically curved space times (Fulling 1989. He begins with a treatment of the ordinary one-dimensional quantum harmonic oscillator, progresses through the construction of quantum field theory in flat spacetime to possible constructions of quantum field theory in curved spacetime, and, ultimately, to an algebraic formulation of the theory.
LAMBDA CDM FROM QUANTUM FIELD THEORY IN CURVED SPACE TIME HOW TO
Ingredients of this approach are the formulation of quantum physics in terms of C*-algebras, the geometry of Lorentzian manifolds, in particular their causal structure, and linear hyperbolic differential equations where the well-posedness of the Cauchy problem plays a distinguished role, as well as more recently the insights from suitable concepts such as microlocal analysis. At the time of publication of this book, there was growing interest in how to formulate quantum field theory in spactimes with curved metrics with the intent of studying to what extent a non-flat curvature would change the properties and behavior of quantum fields as compared to the Minkowski case.The authors give an introduction to this. Quantum Field Theory on Curved Space Times. The RVMs are motivated from the renormalization group formalism of Quantum Field Theory in curved spacetime. Standard methods of classical and quantum eld theory on curved space time are. Surprisingly, this seemingly modest approach leads to far reaching conceptual and mathematical problems and to spectacular predictions, the most famous one being the Hawking radiation of black holes. In this thesis we present detailed analyses on various running vacuum models (RVMs), in which the vacuum energy density 'runs' with the cosmic expansion. It is postulated that dark matter-energy elds depend on the Ricci curvature R. There, to first approximation, one is left with the problem of quantum field theory on Lorentzian manifolds. After some decades of work a satisfactory theory of quantum gravity is still not available moreover, there are indications that the original field theoretical approach may be better suited than originally expected.
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