Related papers: A product formula and combinatorial field theory

We present an algebraic theory of orthogonal polynomials in several variables that includes classical orthogonal polynomials as a special case. Our bottom line is a straightforward connection between apolarity of binary forms and the inner…

We study the sum-product problem for the planar hypercomplex numbers: the dual numbers and double numbers. These number systems are similar to the complex numbers, but it turns out that they have a very different combinatorial behavior. We…

We propose a suitable formulation of the Hamiltonian formalism for Field Theory in terms of Hamiltonian connections and multisymplectic forms where a composite fibered bundle, involving a line bundle, plays the role of an extended…

In [8] a notion of generalized Hadamard product was introduced. We show that when certain kinds of tensors interact with the eigenvalues of symmetric matrices the resulting formulae can be nicely expressed using the generalized Hadamard…

We describe the most general local, Lorentz-invariant, effective field theory of scalars, fermions and gauge bosons up to mass dimension 6. We first obtain both a Green and a physical basis for such an effective theory, together with the…

We propose a formally exact statistical field theory for describing classical fluids with ingredients similar to those introduced in quantum field theory. We consider the following essential and related problems : i) how to find the correct…

The Hamiltonian describing fermion pair production from an arbitrarily time-varying electric field in two dimensions is studied using a group-theoretic approach. We show that this Hamiltonian can be encompassed by two, commuting SU(2)…

This paper generalizes the normally ordered tensor product from Tate vector spaces to Tate objects over arbitrary exact categories. We show how to lift bi-right exact monoidal structures, duality functors, and construct external Homs. We…

We develop a formalism for particle production in a field theory coupled to a strong time-dependent external source. An example of such a theory is the Color Glass Condensate. We derive a formula, in terms of cut vacuum-vacuum Feynman…

Motivated by the mixing of UV and IR effects, we test the OPE formula in noncommutative field theory. First we look at the renormalization of local composite operators, identifying some of their characteristic IR/UV singularities. Then we…

The aim of this paper is to establish various factorization results and then to derive estimates for linear functionals through the use of a generalized Taylor theorem. Additionally, several error bounds are established including…

We consider properties of the operators D(r,M)=a^r(a^\dag a)^M (which we call generalized Laguerre-type derivatives), with r=1,2,..., M=0,1,..., where a and a^\dag are boson annihilation and creation operators respectively, satisfying…

Complicated mathematical equations involving products of tensors with permutation symmetries, frequently encountered in fields such as general relativity and quantum chemistry (e.g., equations in high-order coupled cluster theories),…

We provide a recursive method for constructing product formula approximations to exponentials of commutators, giving the first approximations that are accurate to arbitrarily high order. Using these formulas, we show how to approximate…

We derive a formula expanding the bracket with respect to a natural deformation parameter. The expansion is in terms of a two-variable polynomial algebra of diagram resolutions generated by basic operations involving the Goldman bracket. A…

Using functional equations, we define functors that generalize standard examples from calculus of one variable. Examples of such functors are discussed and their Taylor towers are computed. We also show that these functors factor through…

We generalize the tensor product theory for modules for a vertex operator algebra previously developed in a series of papers by the first two authors to suitable module categories for a ``conformal vertex algebra'' or even more generally,…

We describe a general framework for notions of commutativity based on enriched category theory. We extend Eilenberg and Kelly's tensor product for categories enriched over a symmetric monoidal base to a tensor product for categories…

The union of a collection of $n$ sets is generally expressed in terms of a characteristic (indicator) function that contains $2^{n}-1$ terms. In this article, a much simpler expression is found that requires the evaluation of $n$ terms…

This is the first of a pair of papers where we construct and investigate a closed monoidal structure on the category of generalized algebraic theories (in the sense of Cartmell). In the present text, as a starting point, we define the…