Related papers: Co-algebraic methods for String Field Theory and Q…
Supersymmetric gauge theories in four dimensions have taught us many important physics lessons. These can both inform and be informed by future work on the lattice. I focus on three issues: the properties of supersymmetric Yang-Mills theory…
Quantum field theory provides the framework for the most fundamental physical theories to be confirmed experimentally and has enabled predictions of unprecedented precision. However, calculations of physical observables often require great…
Jet formalism provides the adequate mathematical formulation of classical field theory, reviewed in hep-th/0612182v1. A formulation of QFT compatible with this classical one is discussed. We are based on the fact that an algebra of…
We construct a class of quantum field theories depending on the data of a holomorphic Poisson structure on a piece of the underlying spacetime. The main technical tool relies on a characterization of deformations and anomalies of such…
Various aspects of the theory of quantum integrable systems are reviewed. Basic ideas behind the construction of integrable ultralocal and nonultralocal quantum models are explored by exploiting the underlying algebraic structures related…
We give another definition of two-dimensional extended homotopy field theories (E-HFTs) with aspherical targets and classify them. When the target of E-HFT is chosen to be a $K(G,1)$-space, we classify E-HFTs taking values in the symmetric…
The main objective consists in endowing the elementary particles with an algebraic space-time structure in the perspective of unifying quantum field theory and general relativity: this is realized in the frame of the Langlands global…
We look at the various aspects of treating general relativity as a quantum theory. It is briefly studied how to consistently quantize general relativity as an effective field theory. A key achievement here is the long-range low-energy…
We consider a superintegrable Hamiltonian system in a two-dimensional space with a scalar potential that allows one quadratic and one cubic integral of motion. We construct the most general associative cubic algebra and we present specific…
Aimed at complex geometers and representation theorists, this survey explores higher dimensional analogues of the rich interplay between Riemann surfaces, Virasoro and Kac-Moody Lie algebras, and conformal blocks. We introduce a panoply of…
In this paper we show how the rich algebraic formalism of Eliashberg-Givental-Hofer's symplectic field theory (SFT) can be used to define higher algebraic structures in Hamiltonian Floer theory. Using the SFT of Hamiltonian mapping tori we…
The monograph gives a general geometric background of the theory of field interactions, strings and diffusion processes on spaces, superspaces and isospaces with higher order anisotropy and inhomogenity. Our approach proceeds by developing…
Quantum matrix models in the large-N limit arise in many physical systems like Yang-Mills theory with or without supersymmetry, quantum gravity, string-bit models, various low energy effective models of string theory, M(atrix) theory,…
String diagrammatic calculi have become increasingly popular in fields such as quantum theory, circuit theory, probabilistic programming, and machine learning, where they enable resource-sensitive and compositional algebraic analysis.…
We discuss Hamiltonian learning in quantum field theories as a protocol for systematically extracting the operator content and coupling constants of effective field theory Hamiltonians from experimental data. Learning the Hamiltonian for…
The loop representation of quantum gravity has many formal resemblances to a background-free string theory. In fact, its origins lie in attempts to treat the string theory of hadrons as an approximation to QCD, in which the strings…
The virial expansion provides a non-perturbative view into the thermodynamics of quantum many-body systems in dilute regimes. While powerful, the expansion is challenging as calculating its coefficients at each order $n$ requires analyzing…
Previous work has shown that massless tree amplitudes of the type I and IIA/B superstrings can be dramatically simplified by expressing them as double copies between field-theory amplitudes and scalar disk/sphere integrals, the latter…
In this series of lectures directed towards a mainly mathematically oriented audience I try to motivate the use of operator algebra methods in quantum field theory. Therefore a title as ``why mathematicians are/should be interested in…
We investigate the possibility that the quantum theory of gravity could be constructed discretely using algebraic methods. The algebraic tools are similar to ones used in constructing topological quantum field theories.The algebraic tools…