Related papers: Beyond Complex Langevin Equations: positive repres…
The homogeneous transform has many practical applications outside the realm of mathematics, for instance to represent the proportions of several chemical substances. We aim here to present results about the transformation of measures, which…
A new representation of Quantum Gravity is developed. This formulation is based on an extension of the group of loops. The enlarged group, that we call the Extended Loop Group, behaves locally as an infinite dimensional Lie group. Quantum…
Lorentz's group represented by the hypercomplex system of numbers, which is based on dirac matrices, is investigated. This representation is similar to the space rotation representation by quaternions. This representation has several…
We give a complete complexity classification for the problem of finding a solution to a given system of equations over a fixed finite monoid, given that a solution over a more restricted monoid exists. As a corollary, we obtain a complexity…
Module is effective representation of ring in Abelian group. Linear map of module over commutative ring is morphism of corresponding representation. This definition is the main subject of the book. To consider this definition from more…
We construct measure which determines a two-variable mean in a very natural way. Using that measure we can extend the mean to infinite sets as well. E.g. we can calculate the geometric mean of any set with positive Lebesgue measure. We also…
A flexible representation of uncertainty that remains within the standard framework of probabilistic measure theory is presented along with a study of its properties. This representation relies on a specific type of outer measure that is…
A new class of integrable mappings and chains is introduced. Corresponding $(1+2)$ integrable systems invariant with respect to such discrete transformations are presented in an explicit form. Their soliton-type solutions are constructed in…
The recently proposed Langevin equation, aimed to capture the relevant critical features of stochastic sandpiles, and other self-organizing systems is studied numerically. This equation is similar to the Reggeon field theory, describing…
We review the theory and applications of complex stochastic quantization to the quantum many-body problem. Along the way, we present a brief overview of a number of ideas that either ameliorate or in some cases altogether solve the sign…
In the case of nonabelian gauge theories with a complex weight, a controlled exploration of the complexified configuration space during a complex Langevin process requires the use of SL(N,C) gauge cooling, in order to minimize the distance…
The purpose of this paper is to articulate an observation that many interesting type of wavelets (or coherent states) arise from group representations which are not square integrable or vacuum vectors which are not admissible. This extends…
The reflection positivity property has played a central role in both mathematics and physics, as well as providing a crucial link between the two subjects. In a previous paper we gave a new geometric approach to understanding reflection…
We present a comparison of three different types of Langevin equation exhibiting absorbing states: the Langevin equation defining the Reggeon field theory, one with multiplicative noise, and a third type in which the noise is complex. Each…
We describe a construction of ordered algebraic structures (ordered abelian semigroups, ordered commutative semirings, etc.) and describe applications to codimension-1 laminations. For a suitable ordered semi- algebraic structure $\mathbb…
A measure of complexity based on a probabilistic description of physical systems is proposed. This measure incorporates the main features of the intuitive notion of such a magnitude. It can be applied to many physical situations and to…
Complex Langevin (CL) is a computational method to circumvent the numerical sign problem with applications in finite-density quantum chromodynamics and the real-time dynamics of quantum field theories. It has long been known that, depending…
The method of vector coherent states is generalized to study representations of the affine Lie algebra $\hat{sl}(2)$. A large class of highest weight irreps is explicitly constructed, which contains the integrable highest weight irreps as…
This work develops a procedure to find classes of Lagrangian densities that describe generalizations of the Abelian Maxwell-Higgs, the Chern-Simons-Higgs and the Maxwell-Chern-Simons-Higgs models. The investigation focuses on the…
We construct a class of negative spin irreducible representations of the su(2) Lie algebra. These representations are infinite-dimensional and have an indefinite inner product. We analyze the decomposition of arbitrary products of positive…