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Quantum Fields in Curved Space N. D. Birrell, P. C. W. Davies
Publisher: Cambridge University Press

The noise kernel is the vacuum expectation value of the (operator-valued) stress-energy bitensor, which describes the fluctuations of quantum-matter fields in curved spacetimes. Matthews, and Nobel laureate Frank Wilczek, who have created scientific models where the Big Bang and thus the entire universe could arise from nothing but a random quantum vacuum fluctuation in the quantum field -- via natural processes. Michio Kaku, Alan Guth, Alex Vilenkin, Robert A.J. This has been extended further by taking into account polynomials of the scalar curvature \(R\) (so-called \(f(R)\)-truncations) (Codello et. Al., 2009), and the square of the Weyl curvature tensor (Benedetti et. There is an entire field of study dedicated to the development of quantum field theories in general relativistic -- including time dependent -- backgrounds, called Quantum Field Theory in Curved Spacetime. As explained in the discussion of the stress-energy curvature in the previous post, in addition to the gravity mediators (gravitons) presumably being quantized rather than a continuous or continuum curved spacetime, there is the Quantum field theory is suggestive that the correct Feynman diagram for any interaction is not a continuous, smooth curve, but instead a number of steps due to discrete interactions of the field quanta with the charge (i.e., gravitational mass). This book introduces the quantum mechanics of particles that move in curved space by employing path integrals and then using them to compute anomalies in quantum field theories. Quantum field theory in curved spacetime predicts that event horizons emit radiation like a black body with a finite temperature. 'Sketchy', in my own sense that some approximations have to be made in the classical solutions of the field equations in the background of a curved space-time and bring these over to the context of a quantum field theory. All objects move without additional external force along a straight line in curved spacetime and the geometry of the spacetime is dictated by the present mass/energy" . Professor Winstanley's research interests lie in general relativity, quantum gravity and quantum field theory in curved space-time. The second input is to take some spacetime manifold (like flat Minkowski space or something more curved) and attach a C*-algebra to each open subset in a compatible way. The Field Equations control the curvature of space-time and represent our theory of gravity, while the Yang-Mills and Dirac equations represent the theory of particle interactions on a quantum level. As a postdoctoral fellow at Cambridge University, he worked with Stephen Hawking in cosmology, quantum field theory in curved space time and quantum theories of gravitation. Quantum field theory on curved spacetime , Lecture notes in physics, Springer (2009). While quantum mechanics may be formulated for a wide range of physical systems, interpreted as particles, extended particles and fields, the quantum mechanics of fields is often called the quantum field theory and the quantum mechanics of systems of a fixed finite number of particles is often view as the quantum mechanics in a narrow sense. A new improved criterion for the validity of First, we consider metric perturbations in a Minkowski spacetime, compute the two-point correlation functions of these perturbations and prove that Minkowski spacetime is a stable solution of semiclassical gravity. Quantum Einstein Gravity (QEG) is the generic name for any quantum field theory of gravity that (regardless of its bare action) takes the spacetime metric as the dynamical field variable and whose symmetry is given by diffeomorphism invariance. Later Einstein postulated that the gravitational field was not a property of matter at all, but the result of space-time curving in response to matter.