Related papers: Partial Komori fields and imperative Komori fields
This survey contains a selection of topics unified by the concept of positive semi-definiteness (of matrices or kernels), reflecting natural constraints imposed on discrete data (graphs or networks) or continuous objects (probability or…
This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…
Students of quantum mechanics encounter discrete quantum numbers in a somewhat incoherent and bewildering number of ways. For each physical system studied, quantum numbers seem to be introduced in its own specific way, some enumerating from…
The Jacobian conjecture over a field of characteristic zero is considered directly in view of the nonlinear partial differential equations it is associated with. Exploring the integrals of such partial differential equations, this work…
What is computable with limited resources? How can we verify the correctness of computations? How to measure computational power with precision? Despite the immense scientific and engineering progress in computing, we still have only…
A `covariant' field that transforms like a relativistic field operator is required to be a linear combination of `canonical' fields that transform like annihilation and creation operators and with invariant coefficients. The Invariant…
The central theme of this thesis is to study some aspects of noncommutative quantum mechanics and noncommutative quantum field theory. We explore how noncommutative structures can emerge and study the consequences of such structures in…
Moving from the consideration that matter fields must be treated in terms of their fundamental quantum counterparts, we show straightforward arguments, within the framework of ordinary quantum mechanics and quantum field theory, in order to…
The quantum mechanical formalism doesn't support our intuition, nor does it elucidate the key concepts that govern the behaviour of the entities that are subject to the laws of quantum physics. The arrays of complex numbers are kin to the…
In the classical theory, an electromagnetic field obeying Maxwell's equations cannot be absorbed quickly by matter, so that it remains a zero point field. Splitting the total, genuine electromagnetic field into the sum of a conventional…
Semifields are semirings in which every nonzero element has a multiplicative inverse. A rough classification uses the characteristic of the semifield, that is the isomorphism type of the semifield generated by the two neutral elements. For…
In classical external gauge fields that fall off less fast than the inverse of the evolution parameter (time) of the system the implementability of a unitary perturbative scattering operator ($S$-matrix) is not guaranteed, although the…
There is debate as to whether quantum field theory is, at bottom, a quantum theory of fields or particles. One can take a field approach to the theory, using wave functionals over field configurations, or a particle approach, using wave…
We study a class of perturbative scalar quantum field theories where dynamics is characterized by Lorentz-invariant or Lorentz-breaking non-local operators of fractional order and the underlying spacetime has a varying spectral dimension.…
A problem is a multivalued function from a set of \emph{instances} to a set of \emph{solutions}. We consider only instances and solutions coded by sets of integers. A problem admits preservation of some computability-theoretic weakness…
We review the status of (scalar) quantum field theory on curved spacetimes using a novel formulation in terms of non linear functionals over the smooth configuration fields. In particular, this entails also a new foundation of locally…
Non-well-founded trees are used in mathematics and computer science, for modelling non-well-founded sets, as well as non-terminating processes or infinite data-structures. Categorically, they arise as final coalgebras for polynomial…
Point splitting has been suggested as a way to deal with anomalous commutators in quantum field theory. It has been pointed out by D.G. Boulware[4] that in order to obtain a mathematically consistent theory the Hamiltonian operator must be…
Theories of classification distinguish classes with some good structure theorem from those for which none is possible. Some classes (dense linear orders, for instance) are non-classifiable in general, but are classifiable when we consider…
We analyze a class of quantum operations based on a geometrical representation of $d-$level quantum system (or qudit for short). A sufficient and necessary condition of complete positivity, expressed in terms of the quantum Fourier…