PELATIHAN PEMASARAN DIGITAL BAGI SANTRI PONDOK PASANTREN ABU DZAR DESA SUKAWANGI KABUPATEN BOGOR PAOPINSI JAWA BARAT

The PKM activity was carried out aiming to see the self-ability of the students of the Abu Dzar Islamic Boarding School through their self-concept, interest in particular in the entrepreneurship they pioneered. Therefore, it is necessary to make efforts to cultivate and develop skills in supporting these entrepreneurial activities. The problems raised were that they had never received briefing on how to market their products, especially online, and also the anxiety of the students to start a business. The method of implementing this service is carried out in several activities, namely (a). Preparation phase includes: (1). Initial survey (2) Consolidation and determination of target locations, (3). Preparation of training materials/materials. The results of this activity are very useful for the Abu Dzar Islamic Boarding School Santri in adding insight and knowledge about digital marketing. . Keywords: digital marketing, MSM

The Scalar Field Kernel in Cosmological Spaces

We construct the quantum mechanical evolution operator in the Functional Schrodinger picture - the kernel - for a scalar field in spatially homogeneous FLRW spacetimes when the field is a) free and b) coupled to a spacetime dependent source term. The essential element in the construction is the causal propagator, linked to the commutator of two Heisenberg picture scalar fields. We show that the kernels can be expressed solely in terms of the causal propagator and derivatives of the causal propagator. Furthermore, we show that our kernel reveals the standard light cone structure in FLRW spacetimes. We finally apply the result to Minkowski spacetime, to de Sitter spacetime and calculate the forward time evolution of the vacuum in a general FLRW spacetime.Comment: 13 pages, 1 figur

The Witt group of non-degenerate braided fusion categories

Contains fulltext : 83941.pdf (preprint version ) (Open Access)32 p

Multi-interval subfactors and modularity of representations in conformal field theory

We describe the structure of the inclusions of factors A (E) subset of A (E ')' associated with multi-intervals E subset of R for a local irreducible net A of von Neumann algebras on the real line satisfying the split property and Haag duality. In particular, if the net is conformal and the subfactor has finite index, the inclusion associated with two separated intervals is isomorphic to the Longo-Rehren inclusion, which provides a quantum double construction of the tenser category of superselection sectors of A. As a consequence, the index of A (E) subset of A(E ')' coincides with the global index associated with all irreducible sectors, the braiding symmetry associated with all sectors is non-degenerate, namely the representations of A form a modular tenser category, and every sector is a direct sum of sectors with finite dimension. The superselection structure is generated by local data. The same results hold true if conformal invariance is replaced by strong additivity and there exists a modular PCT symmetry

Multi-interval subfactors and modularity of representations in conformal field theory

We describe the structure of the inclusions of factors A (E) subset of A (E ')' associated with multi-intervals E subset of R for a local irreducible net A of von Neumann algebras on the real line satisfying the split property and Haag duality. In particular, if the net is conformal and the subfactor has finite index, the inclusion associated with two separated intervals is isomorphic to the Longo-Rehren inclusion, which provides a quantum double construction of the tenser category of superselection sectors of A. As a consequence, the index of A (E) subset of A(E ')' coincides with the global index associated with all irreducible sectors, the braiding symmetry associated with all sectors is non-degenerate, namely the representations of A form a modular tenser category, and every sector is a direct sum of sectors with finite dimension. The superselection structure is generated by local data. The same results hold true if conformal invariance is replaced by strong additivity and there exists a modular PCT symmetry