Related papers: A Cubic Matrix Action for the Standard Model and B…
We consider the matrix regularization of fields on a Riemann surface which couple to gauge fields with a nonvanishing magnetic flux. We show that such fields are described as rectangular matrices in the matrix regularization. We construct…
The four major asymptotic level density laws of random matrix theory may all be showcased though their Jacobi parameter representation as having a bordered Toeplitz form. We compare and contrast these laws, completing and exploring their…
We formulate the $c=1$ matrix model as a quantum fluid and discuss its classical limit in detail, emphasizing the $\hbar$ corrections. We view the fermi fluid profiles as elements of \winf-coadjoint orbit and write down a geometric action…
We study field theory models in the context of a gravitational theory based on the requirement that the measure of integration in the action is not necessarily \sqrt{-g} but it is determined dynamically through additional degrees of…
We study Toeplitz operators on Hilbert spaces of holomorphic functions on symmetric domains, and more generally on certain algebraic subvarieties, determined by integration over boundary orbits of the underlying domain. The main result…
The methods of quantum field theory are widely used in condensed matter physics. In particular, the concept of an effective action was proven useful when studying low temperature and long distance behavior of condensed matter systems. Often…
It is known that recently proposed model of mimetic gravity can be presented as general relativity with an additional mimetic matter. We discuss a possibility to analogously reformulate the embedding theory, which is the geometrical…
In this paper, we study different properties of the motion equations of interacting fields. In the second section, we prove that "Wightman's" fields (we use only a subset of Wightman's axioms) are unitarily equivalent to some operators on…
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…
The action principle is frequently used to derive the classical equations of motion. The action may also be used to associate group elements with curves in the space-time manifold, similar to the gauge transformations. The action principle…
We consider quantum gravity model with the squared curvature action. We construct lattice discretization of the model (both on hypercubic and simplicial lattices) starting from its teleparallel equivalent. The resulting lattice models have…
We perform renormalization group transformations to construct optimally local perfect lattice actions for free scalar fields of any mass. Their couplings decay exponentially. The spectrum is identical to the continuum spectrum, while…
We present an exact, unconstrained representation of the electron operators in terms of operators of opposite statistics. We propose a path--integral representation for the $t$-$J$ model and introduce a parameter controlling the…
It is shown that a covariant derivative on any d-dimensional manifold M can be mapped to a set of d operators acting on the space of functions on the principal Spin(d)-bundle over M. In other words, any d-dimensional manifold can be…
We show that given a finitely generated standard-graded algebra of dimension $d$ over an infinite field, its graded Noether normalizations obey a certain kind of `generic exchange', allowing one to pass between any two of them in at most…
Action integral for a matter system composed of 0- and 2-forms, $C$ and $B_{\mu\nu}$, topologically coupled to 3D spin-3 gravity is considered first in the frame-like formalism. The field $C$ satisfies an eq of motion, $\partial_{\mu} \,…
The transfer matrix in lattice field theory connects the covariant and the initial data frameworks; in spin foam models, it can be written as a composition of elementary cellular amplitudes/propagators. We present a framework for discrete…
The (heterotic) double field theories and the exceptional field theories are recently developed for manifestly duality covariant formulation of various supergravity theories, describing low-energy limit of various (heterotic) superstring…
In recent years more and more involved block structures appeared in the literature in the context of numerical approximations of complex infinite dimensional operators modeling real-world applications. In various settings, thanks the theory…
We derive new representations of the Einstein-Hilbert action in which graviton perturbation theory is immensely simplified. To accomplish this, we recast the Einstein-Hilbert action as a theory of purely cubic interactions among gravitons…