Related papers: Wavelet representation of light-front quantum fiel…
Reparametrization invariant theories have a vanishing Hamiltonian and enforce their dynamics through a constraint. We specifically choose the Dirac procedure of quantization before the introduction of constraints. Consequently, for field…
We describe the quantum theory of massless (p,0)-forms that satisfy a suitable holomorphic generalization of the free Maxwell equations on Kaehler spaces. These equations arise by first-quantizing a spinning particle with a U(1)-extended…
Light-Front Field Theory (LFFT) is a good candidate to describe bound states. In LFFT covariance is non-manifest. Burkardt and Langnau claim that, even for scattering amplitudes, rotational invariance is broken. We will take a different…
The classical electromagnetic field of a spinless point electron is described in a formalism with extended causality by discrete finite point-vector fields with discrete and localized point interactions. These fields are taken as a…
I give a quantum theoretical description of kinematically invariant vacuua on the algebra of free fields restricted to a light front and discuss the relation between the light-front Hamiltonian, P-, the vacuum, and Poincare invariance. This…
Some basic topics in Light-Front (LF) quantized field theory are reviewed. Poincar\`e algebra and the LF Spin operator are discussed. The local scalar field theory of the conventional framework is shown to correspond to a non-local…
In a representation theoretic approach a free q-relativistic wave equation must be such, that the space of solutions is an irreducible representation of the q-Poincare algebra. It is shown how this requirement uniquely determines the q-wave…
We use an algebraic approach based on representations of de Sitter group to construct covariant quantum fields in arbitrary dimensions. We study the complementary and the discrete series which correspond to light and massless fields and…
We present a new $6D$ infinite spin field theory in the light-front formulation. The Lorentz-covariant counterparts of these fields depend on 6-vector coordinates and additional spinor variables. Casimir operators in this realization are…
In this work we analyze complex scalar fields using a new framework where the object of noncommutativity $\theta^{\mu\nu}$ represents independent degrees of freedom. In a first quantized formalism, $\theta^{\mu\nu}$ and its canonical…
Linearity allows several versions of reality to simultaneously exist in the state vector. But it implies that there is no interaction between versions, and that there will never be perception of more than one version. It also implies, in…
Complex numbers appear in the Hilbert space formulation of quantum mechanics, but not in the formulation in phase space. Quantum symmetries are described by complex, unitary or antiunitary operators defining ray representations in Hilbert…
This short review summarizes recent developments and results in connection with point-form dynamics of relativistic quantum systems. We discuss a Poincare invariant multichannel formalism which describes particle production and annihilation…
This work is a continuation of our previous works concerning linear canonical transformations and phase space representation of quantum theory. It is mainly focused on the description of an approach which allows to establish spinorial…
Using the Cartan formulation of General Relativity, we construct a well defined lattice-regularized theory capable to describe large non-perturbative quantum fluctuations of the frame field (or the metric) and of the spin connection. To…
Quantum simulation of quantum field theory is a flagship application of quantum computers that promises to deliver capabilities beyond classical computing. The realization of quantum advantage will require methods to accurately predict…
In this paper we continue the development of Quantum Holonomy Theory, which is a candidate for a fundamental theory, by constructing separable strongly continuous representations of its algebraic foundation, the quantum…
The renormalization problem of (2+1)-dimensional Yang-Mills theory quantized on the light front is considered. Extra fields analogous to those used in Pauli-Villars regularization are introduced to restore perturbative equivalence between…
We discuss the light-cone quantization of gauge theories as a calculational tool for representing hadrons as QCD bound-states of relativistic quarks and gluons, and also as a novel method for simulating quantum field theory on a computer.…
A finite-dimensional pseudo-unitary framework is set up for describing the dynamics of free elementary particles in a purely relativistic quantum mechanical way. States of any individual particles or antiparticles are defined as suitably…