Related papers: Light-ray Operators and the BMS Algebra
In this paper, we introduce the notions of relative Rota-Baxter operators of weight $1$ on Lie-Yamaguti algebras, and post-\LYA s, which is an underlying algebraic structure of relative Rota-Baxter operators of weight $1$. We give the…
We consider the quantum state seen by an observer in the diamond-shaped region, which is a globally hyperbolic open submanifold of the Minkowski space-time. It is known from the operator-algebraic argument that the vacuum state of the…
We study the type IIB superstring in the plane-wave background with Ramond-Ramond flux and formulate it as an exact conformal field theory in operator formalism. One of the characteristic features of the superstring in a consistent…
This is my PhD thesis. In this thesis we study the gauge theories on noncommutative Moyal space. We find new static solitons and instantons in terms of the so called generalized Bose operators. Generalized Bose operators are constructed to…
In constrast to discretized space-time approximations to continuum quantum field theories, discretized velocity space approximations to continuum quantum field theories are investigated. A four-momentum operator is given in terms of bare…
We discuss the appearance of the GL(1) charged physical operators in the twistor string theory. These operators are shown to be BRST-invariant and non-trivial, and some of their correlators and conformal beta-functions are computed.…
A canonical realization of the BMS (Bondi-Metzner-Sachs) algebra is given on the phase space of the classical real Klein-Gordon field . By assuming the finiteness of the generators of the Poincar\'e group, it is shown that a countable set…
Weighted Rota-Baxter operators on associative algebras are closely related to modified Yang-Baxter equations, splitting of algebras, weighted infinitesimal bialgebras, and play an important role in mathematical physics. For any $\lambda \in…
In this short note, we study the infinite-dimensional symmetry algebras which appear in holomorphic twists of 4d $\mathcal{N}=1$ supersymmetric quantum field theories. In particular, we investigate whether their representation theory helps…
We suppose that $G$ is a locally compact abelian group, $Y$ is a measure space, and $H$ is a reproducing kernel Hilbert space on $G\times Y$ such that $H$ is naturally embedded into $L^2(G\times Y)$ and it is invariant under the…
We construct a new gauge theory on a pair of d-dimensional noncommutative tori. The latter comes from an intimate relationship between the noncommutative geometry associated with a lattice vertex operator algebra A and the noncommutative…
Metals approaching the Mott insulator generate a new hierarchy in the electronic structure accompanied by a momentum dependent electron differentiation, beyond the Mott-Hubbard, Brinkman-Rice and Slater pictures of the Mott transition. To…
In this paper, we construct Laplace-Beltrami operators associated with arbitrary Riemannian metrics on noncommutative tori of any dimension. These operators enjoy the main properties of the Laplace-Beltrami operators on ordinary Riemannian…
Given a renormalizable theory we construct the dilatation operator, in the sense of generator of RG flow of composite operators. The generator is found as a differential operator acting on the space of normal symbols of composite operators…
Using ideas from Jones, lattice gauge theory and loop quantum gravity, we construct 1+1-dimensional gauge theories on a spacetime cylinder. Given a separable compact group $G$, we construct localized time-zero fields on the spatial torus as…
We discuss the discrete as well as the continuous symmetry transformations for a three $(2+1)$-dimensional $(3D)$ combined system of the free Abelian 1-form and 2-form gauge theories within the framework of Becchi-Rouet-Stora-Tyutin (BRST)…
We classify the Lagrangians and anomalies of an extended BMS field theory using BRST methods. To do so, we establish an intrinsic gauge-fixing procedure for the geometric data, which allows us to derive the extended BMS symmetries and the…
In Quantum Mechanics operators must be hermitian and, in a direct product space, symmetric. These properties are saved by Lie algebra operators but not by those of quantum algebras. A possible correspondence between observables and quantum…
We define a supersymmetric quantum mechanics of fermions that take values in a simple Lie algebra. We summarize what is known about the spectrum and eigenspaces of the Laplacian which corresponds to the Koszul differential d. Firstly, we…
The Bol operators are unary differential operators between spaces of weighted densities on the 1-dimensional manifold invariant under projective transformations of the manifold. On the $1|n$-dimensional supermanifold (superstring)…