Related papers: Coloring Operads for Algebraic Field Theory
We analyze some consequences of two possible interpretations of the action of the ladder operators emerging from generalized Heisenberg algebras in the framework of the second quantized formalism. Within the first interpretation we…
A framework allowing for perturbative calculations to be carried out for quantum field theories with arbitrary smoothly curved boundaries is described. It is based on an expansion of the heat kernel derived earlier for arbitrary mixed…
It is clarified how cohomologies and Gerstenhaber algebras can be associated with linear pre-operads (comp algebras). Their relation to mechanics and operadic physics is concisely discussed.
Factorization algebras are local-to-global objects living on manifolds, and they arise naturally in mathematics and physics. Their local structure encompasses examples like associative algebras and vertex algebras; in these examples, their…
We provide a very general approach to placing model structures and semi-model structures on algebras over symmetric colored operads. Our results require minimal hypotheses on the underlying model category $\mathcal{M}$, and these hypotheses…
In this paper we relate two mathematical frameworks that make perturbative quantum field theory rigorous: perturbative algebraic quantum field theory (pAQFT) and the factorization algebras framework developed by Costello and Gwilliam. To…
We study the correlation functions of logarithmic conformal field theories. First, assuming conformal invariance, we explicitly calculate two-- and three-- point functions. This calculation is done for the general case of more than one…
Quantum mechanical operators and quantum fields are interpreted as realizations of timespace manifolds. Such causal manifolds are parametrized by the classes of the positive unitary operations in all complex operations, i.e. by the…
Motivated by the sharp contrast between classical and quantum physics as probability theories, in these lecture notes I introduce the basic notions of operator algebras that are relevant for the algebraic approach to quantum physics.…
We apply the theory of operadic Koszul duality to provide a cofibrant resolution of the colored operad whose algebras are prefactorization algebras on a fixed space M. his allows us to describe a notion of prefactorization algebra up to…
We construct a generalization of the operadic nerve, providing a translation between the equivariant simplicially enriched operadic world to the parametrized $\infty$-categorical perspective. This naturally factors through genuine…
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,…
The deformation equation and its integrability condition (Bianchi identity) of a non-associative deformation in operad algebra are found. Their relation to the theory of gravity is discussed.
A random field that is empirically equivalent to the quantized electromagnetic field is constructed. A mapping between the creation and annihilation operator algebras of a random field and of the quantized electromagnetic field provides a…
Defining complexity in quantum field theory is a difficult task, and the main challenge concerns going beyond free models and associated Gaussian states and operations. One take on this issue is to consider conformal field theories in 1+1…
It is shown that the linearized fields of causal variational principles give rise to linear bosonic quantum field theories. The properties of these field theories are studied and compared with the axioms of local quantum physics.…
In the worldline approach to non-Abelian field theory the colour degrees of freedom of the coupling to the gauge potential can be incorporated using worldline "colour" fields. The colour fields generate Wilson loop interactions whilst…
The reductions of conformal field theories which lead to generalized abelian cosets are studied. Primary fields and correlation functions of arbitrary abelian coset conformal field theory are explicitly expressed in terms of those of the…
Applied category theory provides powerful mathematical tools for modelling processes and their composition. Symmetric monoidal categories, which involve series and parallel composition, are particularly well-suited for describing the…
This paper describes a higher-categorical version of the theory of colored operads, giving applications to the study of commutative ring spectra.