Related papers: Covariant Canonical Quantization
We investigate the algebraic properties of the quantum counterpart of the classical canonical transformations using the symbol-calculus approach to quantum mechanics. In this framework we construct a set of pseudo-differential operators…
We investigate the canonical quantization of gravity coupled to pointlike matter in 2+1 dimensions. Starting from the usual point particle action in the first order formalism, we introduce auxiliary variables which make the action locally…
The limitations of the approach based on using fields restricted to the lightfront (Lightfront Quantization or p$\to \infty $ Frame Approach) which drive quantum fields towards canonical and ultimately free fields are well known. Here we…
We define covariantly a deformation of a given algebra, then we will see how it can be related to a deformation quantization of a class of observables in Quantum Field Theory. Then we will investigate the operator order related to this…
This paper is one of a series of papers on coherent spaces and their applications, defined in the recent book 'Coherent Quantum Mechanics' by the first author. The paper studies coherent quantization -- the way operators in the quantum…
Quantum canonical transformations corresponding to time-dependent diffeomorphisms of the configuration space are studied. A special class of these transformations which correspond to time-dependent dilatations is used to identify a…
In this work, we study the classical and quantum properties of the unique commutative Lorentz-covariant connection for loop quantum gravity. This connection has been found after solving the second-class constraints inherited from the…
Different quantum mechanical operators can correspond to the same classical quantity. Hermitian operators differing only by operator ordering of the canonical coordinates and momenta at one moment of time are the most familiar example.…
The algebra of polynomials in operators that represent generalized coordinate and momentum and depend on the Planck constant is defined. The Planck constant is treated as the parameter taking values between zero and some nonvanishing $h_0$.…
Classical mechanics, in the operatorial formulation of Koopman and von Neumann, can be written also in a functional form. In this form two Grassmann partners of time make their natural appearance extending in this manner time to a three…
Canonical quantization has served wonderfully for the quantization of a vast number of classical systems. That includes single classical variables, such as $p$ and $q$, and numerous classical Hamiltonians $H(p,q)$, as well as field…
Via K$\ddot{a}$hker polarization we geometrically quantize free fields in the spaces of motions, namely the space of solutions of equations of motion. We obtain the correct results just as that given by the canonical quantization. Since we…
This paper is a generalization of previous work on the use of classical canonical transformations to evaluate Hamiltonian path integrals for quantum mechanical systems. Relevant aspects of the Hamiltonian path integral and its measure are…
In this work, a classical-quantum correspondence for two-level pseudo-Hermitian systems is proposed and analyzed. We show that the presence of a complex external field can be described by a pseudo-Hermitian Hamiltonian if there is a…
In quantum time (QT) schemes, time is promoted to a degree of freedom, allowing Lorentz covariance to be made explicit for single particles. We ask whether this can be lifted to QFT, so that Lorentz covariance becomes manifest at the…
Modification of the right-hand-side of canonical commutation relations (CCR) naturally occurs if one considers a harmonic oscillator with indefinite frequency. Quantization of electromagnetic field by means of such a non-CCR algebra…
Since there are quantization ambiguities in constructing the Hamiltonian constraint operator in isotropic loop quantum cosmology, it is crucial to check whether the key features of loop quantum cosmology are robust against the ambiguities.…
Following an article by John von Neumann on infinite tensor products, we develop the idea that the usual formalism of quantum mechanics, associated with unitary equivalence of representations, stops working when countable infinities of…
We give a manifestly invariant definition of the Lagrangian complex germ with the minimal degree of accuracy required to define the canonical operator. The equivalence with the traditional definition is proved, and the canonical operator is…
In classical canonical correlation analysis (CCA), the goal is to determine the linear transformations of two random vectors into two new random variables that are most strongly correlated. Canonical variables are pairs of these new random…