Related papers: On Ordering of Operators in Canonical Quantization…
We have previously presented a version of the Weak Equivalence Principle for a quantum particle as an exact analog of the classical case, based on the Heisenberg picture analysis of free particle motion. Here, we take that to a full…
The classical theory for a massive free particle moving on the group manifold $AdS_3 \cong SL(2, \mathbb{R})$ is analysed in detail. In particular a symplectic structure and two different sets of canonical coordinates are explicitly found,…
We derive general form of finite-dimensional approximations of path integrals for both bosonic and fermionic canonical systems in terms of symbols of operators determined by operator ordering. We argue that for a system with a given quantum…
The similarity between classical and quantum physics is large enough to make an investigation of quantization methods a worthwhile endeavour. As history has shown, Dirac's canonical quantization method works reasonably well in the case of…
A certain notion of canonical equivalence in quantum mechanics is proposed. It is used to relate quantal systems with discrete ones. Discrete systems canonically equivalent to the celebrated harmonic oscillator as well as the quartic and…
In this Paper we present an approach to Quantum Mechanical Canonical Transformations. Our main result is that Time Dependent Quantum Canonical Transformations can always be cast in the form of Squeezing Operators. We revise the main…
Geometrical formulation of classical mechanics with forces that are not necessarily potential-generated is presented. It is shown that a natural geometrical "playground" for a mechanical system of point particles lacking Lagrangian and/or…
The basic elements of the geometric approach to a consistent quantization formalism are summarized, with reference to the methods of the old quantum mechanics and the induced representations theory of Lie groups. A possible relationship…
This paper concerns the quantisation of a rigid body in the framework of ``covariant quantum mechanics'' on a curved spacetime with absolute time. The basic idea is to consider the multi-configuration space, i.e. the configuration space for…
A formulation of quantum mechanics with additive and multiplicative (q-)difference operators instead of differential operators is studied from first principles. Borel-quantisation on smooth configuration spaces is used as guiding…
It is discussed an opportunity to introduce new class of quantum algorithms based on possibility to express amplitude of transition between two states of quantum system as sum of some function along all possible classical paths. Continuous…
The classical limit $\hbar$->0 of quantum mechanics is known to be delicate, in particular there seems to be no simple derivation of the classical Hamilton equation, starting from the Schr\"odinger equation. In this paper I elaborate on an…
Path integrals are a central tool when it comes to describing quantum or thermal fluctuations of particles or fields. Their success dates back to Feynman who showed how to use them within the framework of quantum mechanics. Since then, path…
Classical mechanics involves position and momentum variables that must be special coordinates chosen to promote to suitable quantum operators. Since classical variables may be broadly chosen, only unique variables should be chosen. We will…
In this talk we briefly review the concept of supersymmetric quantum mechanics using a model introduced by Witten. A quasi-classical path-integral evaluation for this model is performed, leading to a so-called supersymmetric quasi-classical…
We describe our recent proposal of a path integral formulation of classical Hamiltonian dynamics. Which leads us here to a new attempt at hybrid dynamics, which concerns the direct coupling of classical and quantum mechanical degrees of…
We axiomatize path integral quantization of symplectic manifolds. We prove that this path integral formulation of quantization is equivalent to an abstract operator formulation, ie. abstract coherent state (or Berezin) quantization. We use…
Quantum canonical transformations have attracted interest since the beginning of quantum theory. Based on their classical analogues, one would expect them to provide a powerful quantum tool. However, the difficulty of solving a nonlinear…
Canonical transformations are ubiquitous in Hamiltonian mechanics, since they not only describe the fundamental invariance of the theory under phase-space reparameterisations, but also generate the dynamics of the system. In the first part…
An extension of the classical action principle obtained in the framework of the gauge transformations, is used to describe the motion of a particle. This extension assigns many, but not all, paths to a particle. Properties of the particle…