Abstract Analytic continuation from (3, 1) signature Minkowski to (2, 2) signature Klein space has emerged as a useful tool for the understanding of scattering amplitudes and flat space holography. Under this continuation, past and future null infinity merge into a single boundary ( ) which is the product of a null line with a (1, 1) signature torus. The Minkowskian -matrix continues to a Kleinian -vector which in turn may be represented by a Poincaré-invariant vacuum state in the Hilbert space built on . contains all information about in a novel, repackaged form. We give an explicit construction of in a Lorentz/conformal basis for a free massless scalar. separates into two halves which are the asymptotic null boundaries of the regions timelike and spacelike separated from the origin. is shown to be a maximally entangled state in the product of the Hilbert spaces.
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The linearization of the boundary rigidity problem for MP-systems and generic local boundary rigidity
Abstract We consider an -system, that is, a compact Riemannian manifold with boundary, endowed with a magnetic field and a potential. On simple -systems, we study the -ray transform in order to obtain new boundary rigidity results for -systems. We show that there is an explicit relation between the -ray transform and the magnetic one, which allows us to apply results from Dairbekovet al(2007Adv. Math.216535–609) to our case. Regarding rigidity, we show that there exists a generic set of simple -systems, which is open and dense, such that any two -systems close to an element in it and having the same boundary action function, must bek-gauge equivalent.
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- Award ID(s):
- 2154489
- PAR ID:
- 10554847
- Publisher / Repository:
- IOP Publishing
- Date Published:
- Journal Name:
- Inverse Problems
- Volume:
- 40
- Issue:
- 12
- ISSN:
- 0266-5611
- Format(s):
- Medium: X Size: Article No. 125008
- Size(s):
- Article No. 125008
- Sponsoring Org:
- National Science Foundation
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