Topological QFT
An earlier paper gave a means of calculating the Lamb shift via Feynman diagrams. Here we apply the same techniques to TQFT.
math.GM↗
arXiv subjects
Brian Jefferies
Publications and source records attributed to Brian Jefferies.
The Cotlar-Stein Lemma, Grothendiecks Inequality and All That
The purpose of this paper is point out connections between scattering theory, double operator integrals, Kreins spectral shift function, integration theory, bimeasures, Feynman path integrals, harmonic and functional analysis and many other applications to quantum physics made since the last 50 years or so. The starting point is Kluvaneks Integration Structures which he hoped to apply to quantum physics and is now bearing fruit from the contributions of many authors, especially former Soviet mathematical physicists in the intervening years. Soon, a practical quantum field theory in four space-time dimensions satisfying the Wightman axioms may be proved to exist. This is the aim of one of the Clay Prizes. At the moment, only toy models exist in fewer than four space-time dimensions.
math.FA↗
Holomorphic functions on the lie ball and their monogenic counterparts
The Cauchy integral formula in Clifford analysis allows us to associate a holomorphic function $\tilde f:L_n\to \C$ on the Lie ball $L_n$ in $\C^n$ with its monogenic counterpart $f:B_1(0)\to \C^{n+1}$ via the formula $\tilde f(z) = \int_{S^n}G_\om(z)\bs n(\om)f(\om)\,d\mu(\om)$, $z\in L_n.$ The inverse map $\tilde f\mapsto f$ is constructed here using the Cauchy-Hua formula for the Lie ball following the work of M. Morimoto \cite{Mori2}.
math.CV↗
Kippenhahn Varieties and the Weyl Calculus for Several Matrices I
The paper reviews properties of the Weyl functional calculus for several operators and its relation to the generalised numerical range of $n$ hermitian matrices. The support and singular support of the Weyl functional calculus for $n$ hermitian matrices are determined by Kippenhahn varieties in algebraic geometry.
math.FA↗