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We use the extension problem proposed by Caffarelli and Silvestre to study the quantization of a scalar nonlocal quantum field theory built out of the fractional Laplacian.
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2011
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C. Bjorland, L. Caffarelli and A. Figalli, Non-local gradient dependent operators , Advances in Mathematics 230
2012
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C. Bjorland, L. Caffarelli and A. Figalli, Nonlocal tug-of-war and the infinity fractional laplacian , Communications on Pure and Applied Mathematics 65
2012
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2012
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A. Sapora, P. Cornetti and A. Carpinteri, Wave propagation in nonlocal elastic continua modelled by a fractional calculus approach , Communications in Nonlinear Science and Numerical Simulation 18
2013
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2014
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N. Arkani-Hamed, S. Dimopoulos, G. Dvali and G. Gabadadze, Nonlocal modification of gravity and the cosmological constant problem , hep-th/0209227
Cited in the paper.
B. Barrios, A. Figalli and X. Ros-Oton, Global regularity for the free boundary in the obstacle problem for the fractional laplacian , American journal of mathematics 140
2018
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2018
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2018
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2019
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2019
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P. R. Stinga and J. L. Torrea, Extension problem and harnack’s inequality for some fractional operators , Communications in Partial Differential Equations 35
2092
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