Related papers: Semi-Classical Quantum Fields Theories and Frobeni…
We present a uniform framework for the treatment of a large class of toy models of quantum theory. Specifically, we will be interested in theories of wavefunctions valued in commutative involutive semirings, and which give rise to some…
A new form of quasiclassical space-time dynamics for constrained systems reveals how quantum effects can be derived systematically from canonical quantization of gravitational systems. These quasiclassical methods lead to additional fields,…
We show that it is possible to still use semiclassical gravity together with quantum field theory beyond the regimes where the field state is coherent. In particular, we identify families of cat states (superposition of…
A topological quantum field theory of non-abelian differential forms is investigated from the point of view of its possible applications to description of polynomial invariants of higher-dimensional two-component links. A path-integral…
We show that the quantum family of all maps from a finite space to a finite dimensional compact quantum semigroup has a canonical quantum semigroup structure.
An algebraic formalism for description of quantum states of charged particle with spin moving in two-dimensional space under influence of singular magnetic field is developed in terms of graded algebras. The fundamental assumption is that…
It is shown that the Foldy-Wouthuysen transformation for relativistic particles in strong external fields provides the possibility of obtaining a meaningful classical limit of the relativistic quantum mechanics. The full agreement between…
Particle aspects of two-dimensional conformal field theories are investigated, using methods from algebraic quantum field theory. The results include asymptotic completeness in terms of (counterparts of) Wigner particles in any vacuum…
Effect algebras are one of the generalizations of Boolean algebras proposed in the quest for a quantum logic. Frobenius algebras are a tool of categorical quantum mechanics, used to present various families of observables in abstract, often…
Unlike ferromagnetism, antiferromagnetism cannot readily be included in the quasiclassical Keldysh theory because of the rapid spatial variation in the directions of the magnetic moments. The quasiclassical framework is useful because it…
We discuss the semiclassical approximation to transport problems in quantum chaotic systems. The figures of merit are moments of the transmission matrix and of the time delay matrix. After reviewing a few results obtained by treating these…
It is pointed out that quantum states, in general, contain a new kind of orders that cannot be characterized by symmetry. A concept of quantum order is introduced to describe such orders. As two concrete examples, we discussed quantum…
The paper is dedicated to the study of algebraic manifolds whose quantum cohomology or a part of it is a semisimple Frobenius manifold. Theorem 1.8.1 says, roughly speaking, that the sum of $(p,p)$--cohomology spaces is a maximal Frobenius…
Semi-classical gravity attempts to define a hybrid theory in which a classical gravitational field is coupled to a unitarily evolving quantum state. Although semi-classical gravity is inconsistent with observation, a viable theory of this…
We briefly review a recently developed semiclassical theory for quantum oscillations in the spatial (particle and kinetic energy) densities of finite fermion systems and present some examples of its results. We then discuss the inclusion of…
For classical field theories with probabilistic initial conditions the classical field observables are an idealization. Their arbitrarily precise values poorly reflect the characteristic uncertainty in the presence of substantial…
In the present paper we propose a new approach to quantum fields in terms of category algebras and states on categories. We define quantum fields and their states as category algebras and states on causal categories with partial involution…
This thesis provides an introduction to the various category theory ideas employed in topological quantum field theory. These theories are viewed as symmetric monoidal functors from topological cobordism categories into the category of…
The motion of neutral particles with magnetic moments in an inhomogeneous magnetic field is described in a semi-classical framework. The concept of Coherent Internal States is used in the formulation of the semiclassical approximation from…
A classical (or quantum) superintegrable system on an n-dimensional Riemannian manifold is an integrable Hamiltonian system with potential that admits 2n-1 functionally independent constants of the motion that are polynomial in the momenta,…