Related papers: Fock space methods and large N
We use geometric ideas coming from certain classic algebraic constructions to associate, to every classical field theory, a symmetric monoidal double functor from the double category of cobordisms with corners to a certain symmetric…
We propose a supersymmetric quantum field theory with exotic symmetry related to fracton phases. We use superfield formalism and write down the action of a supersymmetric version of the $\varphi$ theory in 3+1 dimensions. It contains a…
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…
Symmetry plays a central role in quantum field theory. Recent developments include symmetries that act on defects and other subsystems, and symmetries that are categorical rather than group-like. These generalized notions of symmetry allow…
We show that a dynamical spacetime generates entanglement between modes of a quantum field. Conversely, the entanglement encodes information concerning the underlying spacetime structure, which hints at the prospect of applications of this…
This talk surveys a broad range of applications of quantum field theory, as well as some recent developments. The stress is on the notion of effective field theories. Topics include implications of neutrino mass and a possible small value…
The purpose of this paper is to present the mathematical techniques of a new quantum scheme using a dual pair of reflexive topological vector spaces in terms of the non-Hermitian form. The scheme is shown to be a generalization of the…
Many complex systems are characterized by intriguing spatio-temporal structures. Their mathematical description relies on the analysis of appropriate correlation functions. Functional integral techniques provide a unifying formalism that…
The paper presents a Fock space model suitable for constructions of c-free algebras. Immediate applications are direct proofs for the properties of the c-free R- and S-transforms.
The construction of the known interacting quantum field theory models is mostly based on euclidean techniques. The expectation values of interesting quantities are usually given in terms of euclidean correlation functions from which one…
Concepts of quantum open systems and ideas of correlation dynamics in nonequilibrium statistical mechanics, as well as methods of closed-time-path effective action and influence functional in quantum field theory can be usefully applied for…
Application of the so-called refined algebraic quantization scheme for constrained systems to the relativistic particle provides an inner product that defines a unique Fock representation for a scalar field in curved space-time. The…
In this letter we outline some reasons for considering a quantum field theory symmetric under quantum groups and we sketch some results obtained with collaborators in the k-Poincare framework. We deal with this latter as a toy model towards…
We review recent progress in operator algebraic approach to conformal quantum field theory. Our emphasis is on use of representation theory in classification theory. This is based on a series of joint works with R. Longo.
After a review of how Boson Fock space (of arbitrary multiplicity) may be approximated by a countable Hilbert-space tensor product (known as toy Fock space) it is shown that vacuum-adapted multiple quantum Wiener integrals of bounded…
Relational particle models are employed as toy models for the study of the Problem of Time in quantum geometrodynamics. These models' analogue of the thin sandwich is resolved. It is argued that the relative configuration space and shape…
We map Spekkens' toy model to a quantum mechanics defined over the finite field $\mathbb{F}_5$. This allows us to define arbitrary linear combinations of the epistemic states in the model. For Spekkens' elementary system with only $2^2=4$…
We discuss a formulation of harmonic superspace approach for noncommuative N=2 supersymmetric field theories paying main attention on new features arising because of noncommutativity. We begin with the known notions of the harmonic…
Much of our intuition about Effective Field Theories (EFTs) stems from their formulation in flat spacetime, yet EFTs have become indispensable tools in cosmology, where time-dependent backgrounds are the norm. In this work, we demonstrate…
We study function spaces that are related to square-integrable, irreducible, unitary representations of several low-dimensional nilpotent Lie groups. These are new examples of coorbit theory and yield new families of function spaces on…