Related papers: Pauli-Villars regularisation and Born-Infeld kinem…
We revise the use of 8-dimensional conformal, complex (Cartan) domains as a base for the construction of conformally invariant quantum (field) theory, either as phase or configuration spaces. We follow a gauge-invariant Lagrangian approach…
A pseudo-velocity concept, based on the extension of a linear body, is defined by a special relativity experiment. It suggests an analogy with the covariance properties of Wiener's process, ultimately implying that the scaling behavior of…
Extending the commutator algebra of quantum $\kappa$-Poincar\'e symmetry to the whole of the phase space, and assuming that this algebra is to be covariant under action of deformed Lorentz generators, we derive the transformation properties…
This paper suggests a generalization of the Born--Infeld action (1932) for the case of electroweak and gravitational fields. Basic notions one deals with are Dirac matrices, $\gamma_{a}$, and dimensionless covariant derivatives, $\pi_{a} =…
Recently, a number of interesting relations have been discovered between generalised Pauli/Dirac groups and certain finite geometries. Here, we succeeded in finding a general unifying framework for all these relations. We introduce…
We show that General Relativity can be formulated as a constrained topological theory for flat 2-connections associated to the Poincar\'e 2-group. Matter can be consistently coupled to gravity in this formulation. We also show that the edge…
Within loop quantum gravity we construct a coarse-grained approximation for the Einstein-Maxwell theory that yields effective Maxwell equations in flat spacetime comprising Planck scale corrections. The corresponding Hamiltonian is defined…
We study the cohomology (cocycles) of Lie superalgebras for the generalised complex of forms: superforms, pseudoforms and integral forms. We argue that these cocycles might be interpreted in the light of a new brane scan as generators of…
An infinite family of classical superintegrable Hamiltonians defined on the N-dimensional spherical, Euclidean and hyperbolic spaces are shown to have a common set of (2N-3) functionally independent constants of the motion. Among them, two…
We obtain a Lorentz covariant wave equation whose complex wave function transforms under a Lorentz boost according to the following rule, $\Psi(x)\rightarrow e^{\frac{i}{\hbar}f(x)}\Psi(x)$. We show that the spacetime dependent phase $f(x)$…
Relativistic invariance in Euclidean formulations of quantum mechanics is discussed. Relativistic treatments of quantum theory are needed to study hadronic systems at sub-hadronic distance scales. Euclidean formulations of relativistic…
The $\kappa$-deformation of the (2+1)D anti-de Sitter, Poincar\'e and de Sitter groups is presented through a unified approach in which the curvature of the spacetime (or the cosmological constant) is considered as an explicit parameter.…
The diffculties of relativistic particle theories formulated my means of canonical quantization, such as Klein-Gordon and Dirac theories, ultimately led theoretical physicists to turn on quantum field theory to model elementary particle…
In this study, we construct a 1+1-dimensional, relativistic, free, complex scalar Quantum Field Theory on the noncommutative spacetime known as lightlike $\kappa$-Minkowski. The associated $\kappa$-Poincar\'e quantum group of isometries is…
We investigate regularization of scalar one-loop integrals in the Pauli- Villars subtraction scheme. The results depend on the number of sub- tractions, in particular the finite terms that survive after the diver- gences have been absorbed…
A spacetime interpretation of deformed relativity symmetry groups was recently proposed by resorting to Finslerian geometries, seen as the outcome of a continuous limit endowed with first order corrections from the quantum gravity regime.…
In the recently proposed generalization of the Yang-Mills theory the group of gauge transformation gets essentially enlarged. This enlargement involves an elegant mixture of the internal and space-time symmetries. The resulting group is an…
We revisit a model of composite gravity, in the form of a reparametrization invariant, non-polynomial, metric-independent action for scalar fields. Previously, the emergence of a composite massless spin 2 particle, the graviton, was…
Quantum-mechanical observables for spatial and spacetime localization are considered from a lattice-theoretic perspective. It is shown that when replacing the lattice of all complex orthogonal projections underlying the Born rule by the…
We study space-time symmetries in scalar quantum field theory (including interacting theories) on static space-times. We first consider Euclidean quantum field theory on a static Riemannian manifold, and show that the isometry group is…