![]() However, at these scales relativistic effects become observable. There are advanced plans to use satellites to distribute entanglement for quantum cryptography and teleportation (e.g., the Space-QUEST project 5) and to install quantum clocks in space (e.g., the Space Optical Clock project 6). Partly motivated by this success, major space agencies, e.g., in Europe and Canada, have invested resources for the implementation of space-based quantum technologies 2, 3, 4. For instance, in 2012 a teleportation protocol was successfully performed across a distance of 143 km by the group led by A. Experiments in quantum communication are rapidly progressing from table-top to space-based setups. Quantum technologies are widely expected to bring about many key technological advances this century. As an example, we present a high precision device which in principle improves the state-of-the-art in quantum accelerometers by exploiting relativistic effects. Indeed, the techniques can be applied to develop a novel generation of relativistic quantum technologies for gravimeters, clocks and sensors. This framework allows for high precision estimation of parameters that appear in quantum field theory including proper times and accelerations. Quantum field theory properly incorporates quantum theory and relativity, in particular, at regimes where space-based experiments take place. To include and exploit these effects, we introduce techniques for the application of metrology to quantum field theory. ![]() However, typical setups do not take into account the effects of relativity on quantum properties. There are advanced plans to implement these and other quantum technologies in space, for instance Space-QUEST and Space Optical Clock projects intend to implement quantum communications and quantum clocks at regimes where relativity starts to kick in. ![]() Quantum metrology has been so far successfully applied to design precision instruments such as clocks and sensors which outperform classical devices by exploiting quantum properties. D 11, 1404 (1975).We present a framework for relativistic quantum metrology that is useful for both Earth-based and space-based technologies. Parker, “Aspects of Quantum Field Theory in Curved Sapcetime, Effective Action and Energy‐Momentum Tensor,” in Proceedings of the NATO Advanced Study Institute on Gravitation: Recent Developments,” edited by M. ![]() Kreyszig, Introduction to differential geometry and Riemannian Geometry (University of Toronto, 1968), Sec. Caianello, “Combinatorics and Renormalization in Quantum Field Theory,” Frontiers in Physics (Benjamin, New York, 1973). These is a similar error in his equation for V ij. It is clear from examination of his (161) that this is in fact an error. 11, except that the indices on α −1 in his Eq. This is the same notation as used by DeWitt in Ref. For a more extensive discussion of the important question of being able to choose a time parametrization see B. Ellis, The Large Scale Structure of Space‐Time (Cambridge University, Cambridge, Mass., 1973). Wheeler, Gravitation (Freeman, San Francisco, 1973). We use units in which ℏ = c = 1, and sign conventions for the metric and curvature tensors which are (‐ ‐ ‐) in the terminology of C. Parker, “The production of elementary particles by strong gravitationsl fields,” in Asymptotic Structure of Space‐Time, F. Drell, Relativistic Quantum Fields (McGraw‐Hill, New York, 1965). Scarf, “A soluble quantum field theory in curved space,” in Let Theóries Relativistes de la Gravitation (Centre National De Recherche Scientifique, 1962). We shed some light on the nonlocalizability of the production process and on the definition of the S matrix for such processes. Finally particle production from the vacuum by the gravitational field is discussed with particular reference to Schwarzschild spacetime. It is shown that the possibility of field theories becoming nonrenormalizable there cannot be ruled out, although, allowing certain modifications to the theory, φ 3 (4) is proven renormalizable in a large class of spacetimes. The extension of these techniques to curved spacetimes is considered. Coordinate space techniques for showing renormalizability are developed in Minkowski space, for λφ 3 (4,6) field theories. Green’s functions equations are obtained and a diagrammatic representation for them given, allowing a formal, diagrammatic renormalization to be effected. Reduction formulas for S‐matrix elements in terms of vacuum Green’s functions are derived, special attention being paid to the possibility that the ’’in’’ and ’’out’’ vacuum states may not be equivalent. A detailed analysis of interacting quantized fields propagating in a curved background spacetime is given.
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