Related papers: Dimensional reduction of the Dirac equation in arb…
In this paper we present a theory of reduction of quantum systems in the presence of symmetries and constraints. The language used is that of Lie--Jordan Banach algebras, which are discussed in some detail together with spectrum properties…
A 3d generally covariant field theory having some unusual properties is described. The theory has a degenerate 3-metric which effectively makes it a 2d field theory in disguise. For 2-manifolds without boundary, it has an infinite number of…
A pure Dirac's method for abelian and non-abelian massive theories in three dimensions is performed. Our analysis is developed on the extended phase space reporting the relevant structure of the theories, namely, the extended action, the…
We study the Dirac--Klein-Gordon system in $1+2$ spacetime dimensions. We show global existence of the solutions, as well as sharp time decay and linear scattering. One key advance is that we provide the first asymptotic stability result…
Many theories of quantum gravity live in higher dimensions, and their reduction to four dimensions via mechanisms such as Kaluza-Klein compactification or brane world models have associated problems. We propose a novel mechanism of…
We construct an analogue of Dirac's reduction for an arbitrary local or non-local Poisson bracket in the general setup of non-local Poisson vertex algebras. This leads to Dirac's reduction of an arbitrary non-local Poisson structure. We…
We establish a finite-dimensional version of the Arveson-Stinespring dilation theorem for unital completely positive maps on operator systems. This result can be seen as a general principle to deduce finite-dimensional dilation theorems…
In the first part of this paper, we generalize Dirac reduction to the extent of non-local Poisson vertex superalgebra and non-local SUSY Poisson vertex algebra cases. Next, we modify this reduction so that we explain the structures of…
We develop a new method which extends Dynamic Mode Decomposition (DMD) to incorporate the effect of control to extract low-order models from high-dimensional, complex systems. DMD finds spatial-temporal coherent modes, connects local-linear…
We are interested in the cubic Dirac equation with mass $m \in [0, 1]$ in two space dimensions, which is also known as the Soler model. We conduct a thorough study on this model with initial data sufficiently small in high regularity…
We perform a brief review on Dirac's procedure applied to the well known Einstein's linearized gravity in $N > 2$ dimensions. Considering it as a gauge theory and therefore the manifestation of second class constraints in analogy with the…
We study covariant equations in quantum cosmology of an extended minisuperspace obtained by the Eisenhart--Duval lift. We find that a Dirac-type equation is naturally introduced in the extended minisuperspace. Explicit forms of the…
Divide and Conquer (DC) is conceptually well suited to high-dimensional optimization by decomposing a problem into multiple small-scale sub-problems. However, appealing performance can be seldom observed when the sub-problems are…
Exact solutions of the Dirac equation in external electromagnetic background fields are very helpful for understanding non-perturbative phenomena in quantum electrodynamics (QED). However, for the limited set of known solutions, the field…
It is proposed that the Dirac equation, as normally interpreted, incorporates intrinsic redundancies whose removal necessarily leads to an enormous gain in calculating power and physical interpretation. Streamlined versions of the Dirac…
The general procedure of constructing a consistent covariant Dirac-type bracket for models with mixed first and second class constraints is presented. The proposed scheme essentially relies upon explicit separation of the initial…
Within the context of infinite-dimensional representations of the rotation group the Dirac monopole problem is studied in details. Irreducible infinite-dimensional representations, being realized in the indefinite metric Hilbert space, are…
In a Minkowski spacetime, one may transform the Dirac wave function under the spin group, as one transforms coordinates under the Poincar\'e group. This is not an option in a curved spacetime. Therefore, in the equation proposed…
We study the $(1+1)$-dimensional Dirac oscillator within a class of doubly special relativity (DSR) models generated by linear-fractional (projective) transformations on momentum space that preserve both the invariant speed of light and a…
We consider a 5-dimensional scalar-tensor theory which is a direct generalization of the original 4-dimensional Brans-Dicke theory to 5-dimensions. By assuming that there is a hypersurface-orthogonal spacelike Killing vector field in the…