Related papers: On the dimensional reduced theories
We write the Dirac equation in curved 4-dimensional Lorentzian spacetime using concepts from the analysis of partial differential equations as opposed to geometric concepts.
The un-reduction procedure introduced previously in the context of Mechanics is extended to covariant Field Theory. The new covariant un-reduction procedure is applied to the problem of shape matching of images which depend on more than one…
The concept of a particle is ambiguous in quantum field theory. It is generally agreed that particles depend not only on spacetime, but also on coordinates used to parametrise spacetime points. One of us has in contrast proposed a…
It is shown that trajectories of free motion of the particles in deformed ("quantum") four dimensional space-time are quadratic curves.
Attention is focused on quantum spaces of physical importance, i.e. Manin plane, q-deformed Euclidean space in three or four dimensions as well as q-deformed Minkowski space. There are algebra isomorphisms that allow to identify quantum…
We propose a new axiom system for unitary quantum field theories on curved space-time backgrounds, by postulating that the partition function and the correlators extend analytically to a certain domain of complex-valued metrics. Ordinary…
A theory of quantum measurement was introduced some time ago that was based on the notion of the so-called separation status. This separation status had a spatial, local character, so that the theory worked only in special cases.…
We study the semiclassical partition function in the frame work of the Morse theory, to clarify the phase factor of the partition function and to relate it to the eta invariant of Atiyah. Converting physical system with potential into a…
We investigate the question of unitarity of evolution between hypersurfaces in quantum field theory in curved spacetime from the perspective of the general boundary formulation. Unitarity thus means unitarity of the quantum operator that…
We expound in detail a method frequently used to reduce the Dirac equation in D-dimensional (D >= 4) spherically symmetric spacetimes to a pair of coupled partial differential equations in two variables. As a simple application of these…
Dimension reduction is a technique used to transform data from a high-dimensional space into a lower-dimensional space, aiming to retain as much of the original information as possible. This approach is crucial in many disciplines like…
The soft breaking of gauge or other symmetries is the typical Quantum Field Theory phenomenon. In many cases one can apply the Stuckelberg procedure, which means introducing some additional field (or fields) and restore the gauge symmetry.…
Numerical simulation is an important non-perturbative tool to study quantum field theories defined in non-commutative spaces. In this contribution, a selection of results from Monte Carlo calculations for non-commutative models is…
A discrete-time Quantum Walk (QW) is essentially an operator driving the evolution of a single particle on the lattice, through local unitaries. Some QWs admit a continuum limit, leading to familiar PDEs (e.g. the Dirac equation). Recently…
In the studies of the squeezing it is customary to focus more attention on the particular squeezed states and their evolution than on the dynamical operations that could squeeze simultaneously some wider families of quantum states,…
Coupled problems with various combinations of multiple physics, scales, and domains are found in numerous areas of science and engineering. A key challenge in the formulation and implementation of corresponding coupled numerical models is…
Quantum field theory unifies concepts from quantum theory and from special relativity. Its mathematically rigorous description is quite intricate and is only partially understood; this is particularly true for the construction of operators…
A relation between dimensional reduction and space-time symmetry gauging is outlined.
Application of the so-called refined algebraic quantization scheme for constrained systems to the relativistic particle provides an inner product that defines a unique Fock representation for a scalar field in curved space-time. The…
The relation between quantum measurement and thermodynamically irreversible processes is investigated. The reduction of the state vector is fundamentally asymmetric in time and shows an observer-relatedness which may explain the double…