Related papers: Logarithmic operators and logarithmic conformal fi…
The operator algebras of a new family of relativistic geometric models of the relativistic oscillator are studied. It is shown that, generally, the operator of number of quanta and the pair of the shift operators of each model are the…
We mostly survey results concerning the $L^2$ boundedness of oscillatory and Fourier integral operators. This article does not intend to give a broad overview; it mainly focusses on a few topics directly related to the work of the authors.
We review the basic features of a logarithmic conformal field theory that arise in the context of the scaling limit of lattice models. The theory of interest is the symplectic fermions, whose central charge is $-2$. We provide an explicit…
With the present trend in experimental particle physics of probing yet shorter distances and with the requirement on the theoretical side of renormalizability, conformal invariance becomes an attractive symmetry for particle interactions.…
We examine the correspondence between the conformal field theory of boundary operators and two-dimensional hyperbolic geometry. By consideration of domain boundaries in two-dimensional critical systems, and the invariance of the hyperbolic…
Multivariate random fields whose distributions are invariant under operator-scalings in both time-domain and state space are studied. Such random fields are called operator-self-similar random fields and their scaling operators are…
It is discussed how a limiting procedure of conformal field theories may result in logarithmic conformal field theories with Jordan cells of arbitrary rank. This extends our work on rank-two Jordan cells. We also consider the limits of…
Based on any chiral vertex operator algebra satisfying a suitable finiteness condition, the semisimplicity of the zero-mode algebra as well as a regularity for induced modules, we construct conformal field theory over the projective line…
We study non-relativistic conformal field theory on a flat space in the presence of a planar boundary. We compute correlation functions of primary operators and obtain the expression for the boundary conformal block. We also discuss the…
We explore a well-known integral representation of the logarithmic function, and demonstrate its usefulness in obtaining compact, easily-computable exact formulas for quantities that involve expectations and higher moments of the logarithm…
In this paper we review our previous isoperimetric results for the logarithmic potential and Newton potential operators. The main reason why the results are useful, beyond the intrinsic interest of geometric extremum problems, is that they…
We study subleading corrections to the corner free energy in classical two-dimensional critical systems, focusing on a generic boundary perturbation by the stress-tensor of the underlying conformal field theory (CFT). In the particular case…
We discuss the structure of 2D conformal field theories (CFT) at central charge c=0 describing critical disordered systems, polymers and percolation. We construct a novel extension of the c=0 Virasoro algebra, characterized by a number b…
It is generally taken for granted that two-dimensional critical phenomena can be fully classified by the well known two-dimensional (rational) conformal quantum field theories (CQFTs). In particular it is believed that in models with a…
Spatio-temporally chaotic dynamics of a classical field can be described by means of an infinite hierarchy of its unstable spatio-temporally periodic solutions. The periodic orbit theory yields the global averages characterizing the chaotic…
Representations of polynomial covariance commutation relations by pairs of linear integral and differential operators are constructed in the space of infinitely continuously differentiable functions. Representations of polynomial covariance…
Effective Field Theory calculations used in countless phenomenological analyses employ dimensional regularization, and at intermediate stages of computations, the operator bases extend beyond the four-dimensional ones. The extra pieces --…
Lattice scalar field theories encounter a sign problem when the coupling constant is complex. This is a close cousin of the real-time sign problems that afflict the lattice Schwinger-Keldysh formalism, and a more distant relative of the…
Field theory is an area in physics with a deceptively compact notation. Although general purpose computer algebra systems, built around generic list-based data structures, can be used to represent and manipulate field-theory expressions,…
Trivially-acting symmetries in two-dimensional conformal field theory include twist fields of dimension zero which are local topological operators. We investigate the consequences of regarding these operators as part of the global symmetry…