Related papers: Krawtchouk matrices from the Feynman path integral…
An abstract theory of ultradifferentiable sheafs is developed. Moreover, various applications to the theory of linear partial differential equations, differential geometry and, in particular, CR geometry are discussed.
Matrix integrals used in random matrix theory for the study of eigenvalues of matrix ensembles have been shown to provide $ \tau $-functions for several hierarchies of integrable equations. In this paper, we construct the matrix integral…
This work deals with two groups of spectral analysis results for matrices arising in fully implicit Runge-Kutta methods used for linear time-dependent partial differential equations. These were applied for different formulations of the same…
Efforts to give an improved mathematical meaning to Feynman's path integral formulation of quantum mechanics started soon after its introduction and continue to this day. In the present paper, one common thread of development is followed…
We propose a new framework to represent the perturbative S-matrix which is well-defined for all quantum field theories of massless particles, constructed from tree-level amplitudes and integrable term-by-term. This representation is derived…
We propose a new solvable class of multidimensional quantum harmonic oscillators for a linear diffusive particle and a quadratic energy absorbing well associated with a semi-definite positive matrix force. Under natural and easily checked…
This is a brief review on Brownian functionals in one dimension and their various applications, a contribution to the special issue ``The Legacy of Albert Einstein" of Current Science. After a brief description of Einstein's original…
The split property expresses a strong form of independence of spacelike separated regions in algebraic quantum field theory. In Minkowski spacetime, it can be proved under hypotheses of nuclearity. An expository account is given of…
Density matrices are powerful mathematical tools for the description of closed and open quantum systems. Recently, methods for the direct computation of density matrix elements in scalar quantum field theory were developed based on thermo…
We introduce the concept of regular quantum graphs and construct connected quantum graphs with discrete symmetries. The method is based on a decomposition of the quantum propagator in terms of permutation matrices which control the way…
We find in our quaternionic version of the electroweak theory an apparently hopeless problem: In going from complex to quaternions, the calculation of the real-valued parameters of the CKM matrix drastically changes. We aim to explain this…
Path integrals are a central tool when it comes to describing quantum or thermal fluctuations of particles or fields. Their success dates back to Feynman who showed how to use them within the framework of quantum mechanics. Since then, path…
This paper is devoted to the study of the separability problem in the field of Quantum information theory. We deal mainly with the bipartite finite dimensional case and with two types of matrices, one of them being the PPT matrices. We…
These lectures are intended for graduate students who want to acquire a working knowledge of path integral methods in a wide variety of fields in physics. In general the presentation is elementary and path integrals are developed in the…
The theory of matrix models is reviewed from the point of view of its relation to integrable hierarchies. Discrete 1-matrix, 2-matrix, ``conformal'' (multicomponent) and Kontsevich models are considered in some detail, together with the…
We develop techniques for computing and analyzing multiple unitarity cuts of Feynman integrals, and reconstructing the integral from these cuts. We study the relations among unitarity cuts of a Feynman integral computed via diagrammatic…
The theory of matrix models is reviewed from the point of view of its relation to integrable hierarchies. Determinantal formulas, relation to conformal field models and the theory of Generalized Kontsevich model are discussed in some…
This paper presents an experimental study on the application of quaternions in several machine learning algorithms. Quaternion is a mathematical representation of rotation in three-dimensional space, which can be used to represent complex…
While real Hamiltonian mechanics and Hermitian quantum mechanics can both be cast in the framework of complex canonical equations, their complex generalisations have hitherto been remained tangential. In this paper quaternionic and…
High precision calculations in perturbative QFT often require evaluation of big collection of Feynman integrals. Complexity of this task can be greatly reduced via the usage of linear identities among Feynman integrals. Based on…