Related papers: Generalized Wavefunctions for Correlated Quantum O…

Finite quantum field theories may be constructed from the most general renormalizable quantum field theory by forbidding, order by order in the perturbative loop expansion, all ultraviolet-divergent renormalizations of the physical…

We present a manifestly covariant quantization procedure based on the de Donder--Weyl Hamiltonian formulation of classical field theory. This procedure agrees with conventional canonical quantization only if the parameter space is $d=1$…

We extend constructions of classical Clifford analysis to the case of indefinite non-degenerate quadratic forms. Clifford analogues of complex holomorphic functions - called monogenic functions - are defined by means of the Dirac operators…

We present the fully general time-dependent multiconfiguration self-consistent-field method to describe the dynamics of a system consisting of arbitrary different kinds and numbers of interacting fermions and bosons. The total wave function…

We develop the method of averaging in Clifford (geometric) algebras suggested by the author in previous papers. We consider operators constructed using two different sets of anticommuting elements of real or complexified Clifford algebras.…

This paper is to serve as a key to the projective (homogeneous) model developed by Charles Gunn (arXiv:1101.4542 [math.MG]). The goal is to explain the underlying concepts in a simple language and give plenty of examples. It is targeted to…

In the framework of the canonical quantization of the electromagnetic field, we impose as primary condition on the dynamics the positive definiteness of the energy spectrum. This implies that (Glauber) coherent states have to be considered…

General dynamic properties like controllability and simulability of spin systems, fermionic and bosonic systems are investigated in terms of symmetry. Symmetries may be due to the interaction topology or due to the structure and…

We consider a four dimensional space-time symmetry which is a non trivial extension of the Poincar\'e algebra, different from supersymmetry and not contradicting {\sl a priori} the well-known no-go theorems. We investigate some field…

We develop a general theory of Clifford algebras for finite morphisms of schemes and describe applications to the theory of Ulrich bundles and connections to period-index problems for curves of genus 1.

In this article we present a new and not fully employed geometric algebra model. With this model a generalization of the conformal model is achieved. We discuss the geometric objects that can be represented. Furthermore, we show that the…

This paper develops a geometric model for coupled two-state quantum systems (qubits), which is formulated using geometric (aka Clifford) algebra. It begins by showing how Euclidean spinors can be interpreted as entities in the geometric…

This article presents the description of the internal spaces of fermion and boson fields in $d$-dimensional spaces, with the odd and even "basis vectors" which are the superposition of odd and even products of operators $\gamma^a$. While…

We introduce the Non-commutative Subset Convolution - a convolution of functions useful when working with determinant-based algorithms. In order to compute it efficiently, we take advantage of Clifford algebras, a generalization of…

The Standard Models contain chiral fermions coupled to gauge theories. It has been a long-standing problem to give such gauged chiral fermion theories a quantum non-perturbative definition. By classification of quantum anomalies and…

I show how to associate a Clifford algebra to a graph. I describe the structure of these Clifford graph algebras and provide many examples and pictures. I describe which graphs correspond to isomorphic Clifford algebras and also discuss…

Comprehensive - that is, gauge and family - unification using spinors has many attractive features, but it has been challenged to explain chirality. Here, by combining an orbifold construction with more traditional ideas, we address that…

We introduce the Umbral calculus into Clifford analysis starting from the abstract of the Heisenberg commutation relation $[\frac{d}{dx}, x] = {\bf id}$. The Umbral Clifford analysis provides an effective framework in continuity and…

We introduce a concept of an embedding of a quadratic space in an associative algebra. The general properties of such embeddings are analyzed by linking it to the Clifford algebra. Conversely, there isa simple description of the standard…

Classification of quantum spinor fields according to quantum bilinear covariants is introduced in a context of quantum Clifford algebras on Minkowski spacetime. Once the bilinear covariants are expressed in terms of algebraic spinor fields,…