Academic literature on the topic 'Contour Minkowski tensor'

Integration over connection type variables in the path integral for the discrete form of the first-order formulation of general relativity theory is studied. The result (a generalized function of the rest of variables of the type of tetrad or elementary areas) can be defined through its moments, i.e. integrals of it with the area tensor monomials. In our previous paper these moments have been defined by deforming integration contours in the complex plane as if we had passed to a Euclidean-like region. In this paper we define and evaluate the moments in the genuine Minkowski region. The distribution of interest resulting from these moments in this non-positively defined region contains the divergences. We prove that the latter contribute only to the singular (δ-function like) part of this distribution with support in the non-physical region of the complex plane of area tensors while in the physical region this distribution (usual function) confirms that defined in our previous paper which decays exponentially at large areas. Besides that, we evaluate the basic integrals over which the integral over connections in the general path integral can be expanded.

In this thesis we have introduced a real space morphological tool, Contour Minkowski tensor (CMT) to analyse the 21cm brightness temperature field from EoR. We showed that the size and shape information of structures encoded by the eigenvalues of CMT enable us to extract maximum information from minimum number of morphological descriptors. We devised a statistical framework which will help us answer a plethora of physical questions required to model EoR with upcoming 21cm observations. We showed that we can infer bubble size information, ionization history and astrophysical properties of first sources using CMT. We devised a pipeline for constraining model parameters by comparing theory with mock observation from future radio interferometers such as the SKA I low. We have set a starting stage to extend to the more generalized 3 dimensional Minkowski tensors in order to obtain conclusive comparisons with other methods in literature. We also plan to combine our technique with other real space topological descriptors. The full potential of real space descriptors for 21 cm observations of EoR can be realized if the design of future interferometers allows for cleaner images from the cosmic dawn and EoR with improved foreground cleaning and data handling