Related papers: Markov loops, determinants and Gaussian fields
A formula expressing the fermionic determinant (a large order polynomial) as an infinite product of smaller determinants is derived and discussed. These smaller determinants are of a fixed size, independent of the size of the lattice and…
An attempt is made to give a heuristic explanation of the distinguished role of measurement in the quantum theory. We question the notion of "naive" reductionism by stressing the difference between an isolated quantum and classical object.…
A typical introductory treatment of electromagnetism culminates with the investigation of Maxwell's equations, showing the beautiful connection between the concepts covered in the many prior weeks. The lab described here is an experimental…
Mechanical quantum systems, such as resonators and levitated particles, offer unique opportunities for quantum metrology. Particularly, their significant mass and quantum-level control enable applications in measuring gravitational effects.…
In this contribution we discuss the role disordered (or random) systems have played in the study of non-Gibbsian measures. This role has two main aspects, the distinction between which has not always been fully clear: 1) {\em From}…
These notes are dedicated to whom may be interested in algorithms, Markov chain, coupling, and graph theory etc. I present some preliminaries on coupling and explanations of the important formulas or phrases, which may be helpful for us to…
The physically interesting gravitational analogue of magnetic monopole in electrodynamics is considered in the present paper. The author investigates the field equation of gravitomagnetic matter, and the exact static cylindrically symmetric…
We study Wilson loops as a necessary tool for unambiguous identification of non-Abelian synthetic gauge fields, with attention to certain crucial but often overlooked features, such as the requirement of at least three distinct loops. We…
We give a new combinatorial explanation for well-known relations between determinants and traces of matrix powers. Such relations can be used to obtain polynomial-time and poly-logarithmic space algorithms for the determinant. Our new…
Arguments are made in favor of broadening the scope of the various approaches to splitting spacetime into a single common framework in which measured quantities, derivative operations, and adapted coordinate systems are clearly understood…
This short note describes a connection between algorithmic dimensions of individual points and classical pointwise dimensions of measures.
A simple relation between the Maxwell system and the Dirac equation based on their quaternionic reformulation is discussed. We establish a close connection between solutions of both systems as well as a relation between the wave parameters…
We present correspondences induced by some classical mappings between measures on an interval and measures on the unit circle. More precisely, we link their sequences of orthogonal polynomial and their recursion coefficients. We also deduce…
The aim of this work is to compare the distinct notions of Mal'tsev object in the sense of Weighill and in the sense of Montoli-Rodelo-Van der Linden.
These are lecture notes on the subject defined in the title. As such, they do not pretend to be really new, probably except for the only section about Poisson equations with potentials. Yet, the hope of the author is that they may serve as…
The integral formulation of Maxwell's equations expressed in terms of an arbitrary observer family in a curved spacetime is developed and used to clarify the meaning of the lines of force associated with observer-dependent electric and…
The role of the gauge invariance in noncommutative field theory is discussed. A basic introduction to noncommutative geometry and noncommutative field theory is given. Background invariant formulation of Wilson lines is proposed. Duality…
Gaussian double Markovian models consist of covariance matrices constrained by a pair of graphs specifying zeros simultaneously in the covariance matrix and its inverse. We study the semi-algebraic geometry of these models, in particular…
The main motivations and challenges related with the physics of large-scale magnetic fields are briefly analyzed. The interplay between large-scale magnetic fields and scalar CMB anisotropies is addressed with specific attention on recent…
A simple theory of the covariant derivatives, deformed derivatives and relative covariant derivatives of extensor fields is present using algebraic and analytical tools developed in previous papers. Several important formulas are derived.