Related papers: That strange procedure called quantisation
A problem with an instructive description of measurement process for sufficiently separated entangled quantum systems is well known. More precise and crafty experiments together with new technological challenges raise questions about…
The way of finding all the constraints in the Hamiltonian formulation of singular (in particular, gauge) theories is called the Dirac procedure. The constraints are naturally classified according to the correspondig stages of this…
We consider quantum mechanics on constrained surfaces which have non-Euclidean metrics and variable Gaussian curvature. The old controversy about the ambiguities involving terms in the Hamiltonian of order hbar^2 multiplying the Gaussian…
The constrained Hamiltonian systems admitting no gauge conditions are considered. The methods to deal with such systems are discussed and developed. As a concrete application, the relationship between the Dirac and reduced phase space…
A modification of the canonical quantization procedure for systems with time-dependent second-class constraints is discussed and applied to the quantization of the relativistic particle in a plane wave. The time dependence of constraints…
Generalised quantifiers, which include Henkin's branching quantifiers, have been introduced by Mostowski and Lindstr\"om and developed as a substantial topic application of logic, especially model theory, to linguistics with work by…
A quantization over a manifold can be seen as a way to construct a differential operator with prescribed principal symbol. The quantization map is moreover required to be a linear bijection. It is known that there is in general no natural…
We introduce a hierarchical classification of theories that describe systems with fundamentally limited information content. This property is introduced in an operational way and gives rise to the existence of mutually complementary…
The Dirac quantization `procedure' for constrained systems is well known to have many subtleties and ambiguities. Within this ill-defined framework, we explore the generality of a particular interpretation of the Dirac procedure known as…
I extend upon the paper by Batalin and Marnelius, in which they show how to construct and quantize a gauge theory from a Hamiltonian system with second class constraints. Among the avenues explored, their technique is analyzed in relation…
Pedagogical introduction into the problem of the mathematical description of the quantum correlation (entanglement) of composite quantum systems is represented. The notion is substantiated about the fact that the conventional algorithm of…
It is known that the quantization of a system defined on a topologically non-trivial configuration space is ambiguous in that many inequivalent quantum systems are possible. This is the case for multiply connected spaces as well as for…
We use Dirac's method for the quantization of constrained systems in order to quantize a spatially flat Friedmann-Lema\^{i}tre-Robertson-Walker spacetime in the context of $f(Q)$ cosmology. When the coincident gauge is considered, the…
A covariant quantization method for physical systems with reducible constraints is presented.
This paper explores in some detail a recent proposal (the Rieffel induction/refined algebraic quantization scheme) for the quantization of constrained gauge systems. Below, the focus is on systems with a single constraint and, in this…
We discuss in detail the uniform discretization approach to the quantization of totally constrained theories. This approach allows to construct the continuum theory of interest as a well defined, controlled, limit of well behaved discrete…
A method of quantizing parametrized systems is developed that is based on a kind of ``gauge invariant'' quantities---the so-called perennials (a perennial must also be an ``integral of motion''). The problem of time in its particular form…
Conventional canonical quantization procedures directly link various c-number and q-number quantities. Here, we advocate a different association of classical and quantum quantities that renders classical theory a natural subset of quantum…
This paper introduces a new notion of quantum recursion of which the control flow of the computation is quantum rather than classical as in the notions of recursion considered in the previous studies of quantum programming. A typical…
An alternative to Dirac's constrained quantization procedure is explained.