Related papers: An introduction to generalised functions in period…
Quantum gauge theory in the connection representation uses functions of holonomies as configuration observables. Physical observables (gauge and diffeomorphism invariant) are represented in the Hilbert space of physical states; physical…
We study some fundamental issues related to the Hilbert space representation of quantum mechanics in the presence of a minimal length and maximal momentum. In this framework, the maximally localized states and quasi-position representation…
In this paper the generalized quantum states, i.e. positive and normalized linear functionals on $C^{*}$-algebras, are studied. Firstly, we study normal states, i.e. states which are represented by density operators, and singular states,…
We study Heisenberg's matrix mechanics within an algebraic pre-Hilbert framework of arbitrary finite dimension. The commutator of the position and momentum matrices naturally generates a third Hermitian operator whose unbounded character…
If quantum gravity respects the principles of quantum mechanics, suitably generalized, it may be that a more viable approach to the theory is through identifying the relevant quantum structures rather than by quantizing classical spacetime.…
A generalized Hamilton-Jacobi representation describes microstates of the Schr\"odinger wave function for bound states. At the very points that boundary values are applied to the bound state Schr\"odinger wave function, the generalized…
In this sequence of papers, noncommutative analysis is used to give a consistent axiomatic approach to a unified conceptual foundation of classical and quantum physics. The present Part I defines the concepts of observables, states and…
Hilbert space operators may be mapped onto a space of ordinary functions (operator symbols) equipped with an associative (but noncommutative) star-product. A unified framework for such maps is reviewed. Because of its clear probabilistic…
In this paper, we extend the standard formalism of quantum mechanics to a quantum theory for a total system including one internal measuring apparatus. The internality of the measuring apparatus implies that different decomposition of a…
Colombeau's generalized functions are used to adapt the distributional approach to singular hypersurfaces in general relativity with signature change. Equations governing the dynamics of singular hypersurface is obtained and it is shown…
We prove that there exists essentially one {\it minimal} differential algebra of distributions $\A$, satisfying all the properties stated in the Schwartz impossibility result [L. Schwartz, Sur l'impossibilit\'e de la multiplication des…
A generalization of the Heisenberg algebra has been recently constructed. This generalized algebra has a characteristic function which depends on one of its generators. When this function is linear, $qJ_0+s$, it is possible to construct a…
Cirelli, Mani\`{a} and Pizzocchero generalized quantum mechanics by K\"{a}hler geometry. Furthermore they proved that any unital C$^{*}$-algebra is represented as a function algebra on the set of pure states with a noncommutative…
This paper studies the combinatoric structure of the set of all representations, up to equivalence, of a finite-dimensional semisimple Lie algebra. This has intrinsic interest as a previously unsolved problem in representation theory, and…
Colombeau generalized functions invariant under smooth (additive) one-parameter groups are characterized. This characterization is applied to generalized functions invariant under orthogonal groups of arbitrary signature, such as groups of…
Important characteristics of the loop approach to quantum gravity are a specific choice of the algebra A of observables and of a representation of A on a measure space over the space of generalized connections. This representation is…
A simple pedagogical introduction to the Colombeau algebra of generalised functions is presented, leading the standard definition.
We compare the classical Kolmogorov and quantum probability models. We show that the gap between these model is not so huge as it was commonly believed. The main structures of quantum theory (interference of probabilities, Born's rule,…
The basic notions of quantum mechanics are formulated in terms of separable infinite dimensional Hilbert space $\mathcal{H}$. In terms of the Hilbert lattice $\mathcal{L}$ of closed linear subspaces of $\mathcal{H}$ the notions of state and…
A quantization scheme based on the extension of phase space with application of constrained quantization technic is considered. The obtained method is similar to the geometric quantization. For constrained systems the problem of scalar…