相关论文: New features of FORM
The rise of quantum information science has opened up a new venue for applications of the geometric phase (GP), as well as triggered new insights into its physical, mathematical, and conceptual nature. Here, we review this development by…
In a series of papers, a many-minds interpretation of quantum theory has been developed. The aim in these papers is to present an explicit mathematical formalism which constitutes a complete theory compatible with relativistic quantum field…
Harmonic sums and their generalizations are extremely useful in the evaluation of higher-order perturbative corrections in quantum field theory. Of particular interest have been the so-called nested sums,where the harmonic sums and their…
We introduce a new "positive formalism" for encoding quantum theories in the general boundary formulation, somewhat analogous to the mixed state formalism of the standard formulation. This makes the probability interpretation more natural…
We give a very concise review of the group field theory formalism for non-perturbative quantum gravity, a higher dimensional generalisation of matrix models. We motivate it as a simplicial and local realisation of the idea of 3rd…
The new axiomatic system for the quantum field theory is proposed. The new axioms are the description of the distributions. For the finite series these distributions satisfy the linear Wightman axioms.
In this article, we describe various aspects of categorification of the structures appearing in information theory. These aspects include probabilistic models both of classical and quantum physics, emergence of F-manifolds, and motivic…
Although quantum circuits have been ubiquitous for decades in quantum computing, the first complete equational theory for quantum circuits has only recently been introduced. Completeness guarantees that any true equation on quantum circuits…
Different relativistic quantum mechanics approaches have recently been used to calculate properties of various systems, form factors in particular. It is known that predictions, which most often rely on a single-particle current…
The emerging field of quantum computing has shown it might change how we process information by using the unique principles of quantum mechanics. As researchers continue to push the boundaries of quantum technologies to unprecedented…
A geometric framework for describing quantum particles on a possibly curved background is proposed. Natural constructions on certain distributional bundles (`quantum bundles') over the spacetime manifold yield a quantum ``formalism'' along…
We give a basic overview of computational complexity, query complexity, and communication complexity, with quantum information incorporated into each of these scenarios. The aim is to provide simple but clear definitions, and to highlight…
This note, in a rather expository manner, serves as a conceptional introduction to the certain underlying mathematical structures encoding the geometric quantization formalism and the construction of Witten's quantum invariants, which is in…
In this paper we propose a new perspective on the evolution and history of the idea of mathematical proof. Proofs will be studied at three levels: syntactical, semantical and pragmatical. Computer-assisted proofs will be give a special…
Quantum computing is a rapidly developing field in the second wave of quantum development, with the potential to revolutionize a wide range of industries and fields of study. As the capabilities of quantum computers continue to advance,…
Recent theoretical results confirm that quantum theory provides the possibility of new ways of performing efficient calculations. The most striking example is the factoring problem. It has recently been shown that computers that exploit…
We present FORM 5, a major release of the symbolic-manipulation system FORM. Version 5 introduces an integrated diagram generator, based on the GRACE graph-generator, to produce Feynman diagrams directly from FORM scripts. This release also…
We describe a simple experimental apparatus which allows one to observe the wave properties of light in a new way. This apparatus also makes possible to introduce and illustrate, in a very suggestive way, some fundamental principles of…
We proposed a third quantization scheme to derive the quantum dynamics of the functional phase space distribution in quantum field theory (QFT). The derivation is straightforward and algorithmic. This readily yields the ballistic quantum…
A new approach is suggested which allows to describe phenomenologically arbitrary topologies of the Universe. It consists in a generalizaton of third quantization. This quantization is carried out for the case of asymptotic closeness to a…