Pascual Jordan, his contributions to quantum mechanics and his legacy in contemporary local quantum physics

After recalling episodes from Pascual Jordan's biography including his pivotal role in the shaping of quantum field theory and his much criticized conduct during the NS regime, I draw attention to his presentation of the first phase of development of quantum field theory in a talk presented at the 1929 Kharkov conference. He starts by giving a comprehensive account of the beginnings of quantum theory, emphasising that particle-like properties arise as a consequence of treating wave-motions quantum-mechanically. He then goes on to his recent discovery of quantization of ``wave fields'' and problems of gauge invariance. The most surprising aspect of Jordan's presentation is however his strong belief that his field quantization is a transitory not yet optimal formulation of the principles underlying causal, local quantum physics. The expectation of a future more radical change coming from the main architect of field quantization already shortly after his discovery is certainly quite startling. I try to answer the question to what extent Jordan's 1929 expectations have been vindicated. The larger part of the present essay consists in arguing that Jordan's plea for a formulation without ``classical correspondence crutches'', i.e. for an intrinsic approach (which avoids classical fields altogether), is successfully addressed in past and recent publications on local quantum physics.Comment: More biographical detail, expansion of the part referring to Jordan's legacy in quantum field theory, 37 pages late

Practices of Using Blockchain Technology in ICT under the Digitalization of the World Economy

Abstract. Pursuing the purpose of effective functioning in today's conditions, the business is forced to transform rapidly, to modernize at all levels. The world is changing, erasing the limits of its certainty. Companies need quality transformations and strategies that are effective in the face of rapid change towards "deep" digitization. Massive corporate management systems increasingly need the flexibility to keep pace with change. And companies with an innovative culture are more in need of creative tasks than implementing detailed regulations. In the post-industrial time of digital economy, issues related to the development of the information sphere, the media and communications, the usage of modern information systems to develop the economy and stabilize social development as a whole, come first. The basic principles of practical application of Blockchain are investigated in the work. The stages of development of Blockchain technology, the stages of development of Blockchain technologies by time, the application of distributed registry technology in Blockchain applications, the principles of construction and operation of Blockchain have been specified. The benefits of using NEM for business are substantiated and the components of Proxima X technology, protocols and service layers, on-line and off-line protocols, decentralized applications are exposed

Quantum-secured blockchain

Blockchain is a distributed database which is cryptographically protected against malicious modifications. While promising for a wide range of applications, current blockchain platforms rely on digital signatures, which are vulnerable to attacks by means of quantum computers. The same, albeit to a lesser extent, applies to cryptographic hash functions that are used in preparing new blocks, so parties with access to quantum computation would have unfair advantage in procuring mining rewards. Here we propose a possible solution to the quantum era blockchain challenge and report an experimental realization of a quantum-safe blockchain platform that utilizes quantum key distribution across an urban fiber network for information-theoretically secure authentication. These results address important questions about realizability and scalability of quantum-safe blockchains for commercial and governmental applications.Comment: 7 pages, 2 figures; published versio

"Quantization is a mystery"

Expository notes which combine a historical survey of the development of quantum physics with a review of selected mathematical topics in quantization theory (addressed to students that are not complete novices in quantum mechanics). After recalling in the introduction the early stages of the quantum revolution, and recapitulating in Sect. 2.1 some basic notions of symplectic geometry, we survey in Sect. 2.2 the so called prequantization thus preparing the ground for an outline of geometric quantization (Sect. 2.3). In Sect. 3 we apply the general theory to the study of basic examples of quantization of Kaehler manifolds. In Sect. 4 we review the Weyl and Wigner maps and the work of Groenewold and Moyal that laid the foundations of quantum mechanics in phase space, ending with a brief survey of the modern development of deformation quantization. Sect. 5 provides a review of second quantization and its mathematical interpretation. We point out that the treatment of (nonrelativistic) bound states requires going beyond the neat mathematical formalization of the concept of second quantization. An appendix is devoted to Pascual Jordan, the least known among the creators of quantum mechanics and the chief architect of the "theory of quantized matter waves".Comment: lecture notes, 51 page