Related papers: The Bargmann representation for the quantum mechan…
The convenience of coherent state representation is discussed from the viewpoint of what is in a broad sense called the measurement problem in quantum mechanics. Standard quantum theory in coherent state representation is intrinsically…
We formulate a general principle that supplants a Boolean \sigma-algebra of intrinsic properties of a classical system by a \sigma-complex (a union of \sigma-algebras) of extrinsic properties of a quantum system that are elicited by…
The Hermiticity condition in quantum mechanics required for the characterisation of (a) physical observables and (b) generators of unitary motions can be relaxed into a wider class of operators whose eigenvalues are real and whose…
Bohmian mechanics is the most naively obvious embedding imaginable of Schr\"odinger's equation into a completely coherent physical theory. It describes a world in which particles move in a highly non-Newtonian sort of way, one which may at…
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…
The minimal representations of Sp(r,R) can be realized on a Hilbert space of holomorphic functions. This is the analogue of the Brylinski-Kostant model. It can also be realized on a Hilbert space of L^2 functions on R^r. This is the…
A classical representation for quantum eigenstates of a particle bound in $\lambda z^{2m}$ $(\lambda >0, m=1,2,...)$ potentials is developed. It is represented by ensembles of classical trajectories with energy distributions that can take…
It is well known that the quantum double structure plays an important role in three dimensional quantum gravity coupled to matter field. In this paper, we show how this algebraic structure emerges in the context of three dimensional…
An algebraic treatment of shape-invariant potentials in supersymmetric quantum mechanics is discussed. By introducing an operator which reparametrizes wave functions, the shape-invariance condition can be related to a oscillator-like…
We review some aspects of the relation between ordinary coherent states and q-deformed generalized coherent states with some of the simplest cases of quantum Lie algebras. In particular, new properties of (q-)coherent states are utilized to…
Pure quantum spin-$s$ states can be represented by $2s$ points on the sphere, as shown by Majorana in 1932 --- the description has proven particularly useful in the study of rotational symmetries of the states, and a host of other…
A study on a method for the establishment of a phase space representation of quantum theory is presented. The approach utilizes the properties of Gaussian distribution, the properties of Hermite polynomials, Fourier analysis and the current…
The author summarizes the Quantum Bayesian viewpoint of quantum mechanics, developed originally by C. M. Caves, R. Schack, and himself. It is a view crucially dependent upon the tools of quantum information theory. Work at the Perimeter…
An extended Wigner function formalism is introduced for describing the quantum dynamics of particles with internal degrees of freedom in the presence of spatially inhomogeneous fields. The approach is used for quantitative simulations of…
Several finite dimensional quasi-probability representations of quantum states have been proposed to study various problems in quantum information theory and quantum foundations. These representations are often defined only on restricted…
We present a complete theory, which is a generalization of Bargmann's theory of factors for ray representations. We apply the theory to the generally covariant formulation of the Quantum Mechanics.
Doplicher, Fredenhagen, and Roberts (1994, 1995) proposed a simple model of a particle in quantum spacetime. We give a new formulation of the model and propose some small changes and additions which improve the physical interpretation. In…
We survey some of the main conceptual developments in the study of PT-symmetric and pseudo-Hermitian Hamiltonian operators that have taken place during the past ten years or so. We offer a precise mathematical description of a quantum…
Quantization of the system comprising gravitational, fermionic and electromagnetic fields is developed in the loop representation. As a result we obtain a natural unified quantum theory. Gravitational field is treated in the framework of…
We give a review of the tomographic probability representation of quantum mechanics. We present the formalism of quantum states and quantum observables using the formalism of standard probability distributions and classical-like random…