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We extend the Hopf algebra description of a simple quantum system given previously, to a more elaborate Hopf algebra, which is rich enough to encompass that related to a description of perturbative quantum field theory (pQFT). This provides…

Algebraic quantum field theory provides a general, mathematically precise description of the structure of quantum field theories, and then draws out consequences of this structure by means of various mathematical tools -- the theory of…

This is the author's PhD-thesis, which was written in 2006. The version posted here is identical to the printed one. Instead of an abstract, the short list of contents: Preface 5 1 Introduction 9 2 K-theory and cyclic type homology theories…

Long ago, in math.AG/0112004, we pledged more details on the algebraic version of Chen-Ruan's math.AG/0103156. This is it.

This paper is now part of the new paper "Series with Hermite polynomials and applications" arXiv:1710.00687.

There has been some recent interest in applying the techniques of Algebraic Quantum Field Theory (AQFT) to entanglement problems in perturbative QFT. In particular, the Hilbert space independence of this formulation makes it particularly…

The review of modern study of algebraic, geometric and differential properties of quaternionic (Q) numbers with their applications. Traditional and "tensor" formulation of Q-units with their possible representations are discussed and groups…

An earlier paper gave a means of calculating the Lamb shift via Feynman diagrams. Here we apply the same techniques to TQFT.

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 prove part of the conjectures in [Li10a] (arXiv:1007.5384). We also relate the construction of quantum modified algebras in [Li10a] with the functorial construction in [ZH08](arXiv:0803.3668).

A non-commutative, planar, Hopf algebra of rooted trees was proposed in L. Foissy, Bull. Sci. Math. 126 (2002) 193-239. In this paper we propose such a non-commutative Hopf algebra for graphs. In order to define a non-commutative product we…

This paper is removed from the network permanently. The content in this paper has now been put together with hep-th/9310183. See the recently replaced and widely revised version of the latter.

It is discussed to which extent the AdS-CFT correspondence is compatible with fundamental requirements in quantum field theory.

We propose a categorification of the cyclotomic Hecke algebra in terms of the equivariant K-theory of the framed matrix factorizations. The construction generalizes the earlier construction of the authors for a categorification of the…

An associative $*$-algebra is introduced (containing a $TTR$-algebra as a subalgebra) that implements the form factor axioms, and hence indirectly the Wightman axioms, in the following sense: Each $T$-invariant linear functional over the…

The quaternion Fourier transform (QFT) satisfies some uncertainty principles similar to the Euclidean Fourier transform. In this paper, we establish Miyachi's theorem for this transform.

We show that reasonably well behaved 3d and 4D TQFts must contain certain algebraic structures. In 4D, we find both Hopf categories and trialgebras.

In this paper, we pursue the discussion of the connections between rational conformal field theories (CFT) and graphs. We generalize our recent work on the relations of operator product algebra (OPA) structure constants of $sl(2)\,$…

There are essentially two different approaches to the axiomatization of quantum field theory (QFT): algebraic QFT, going back to Haag and Kastler, and functorial QFT, going back to Atiyah and Segal. More recently, based on ideas by Baez and…

In this paper an exponential multiplicative formula for the R-matrix is provided for the twisted affine quantum algebras.