Related papers: Examples of Enhanced Quantization: Bosons, Fermion…
A careful study of the classical/quantum connection with the aid of coherent states offers new insights into various technical problems. This analysis includes both canonical as well as closely related affine quantization procedures. The…
Canonical quantization relies on Cartesian, canonical, phase-space coordinates to promote to Hermitian operators, which also become the principal ingredients in the quantum Hamiltonian. While generally appropriate, this procedure can also…
The rules of canonical quantization normally offer good results, but sometimes they fail, e.g., leading to quantum triviality ($=$ free) for certain examples that are classically nontrivial ($\ne$ free). A new procedure, called Enhanced…
Following Dirac, the rules of canonical quantization include classical and quantum contact transformations of classical and quantum phase space variables. While arbitrary classical canonical coordinate transformations exist that is not the…
We apply the quantization scheme introduced in [arXiv:1204.2870] to a particle on a circle. We find that the quantum action functional restricted to appropriate coherent states can be expressed as the classical action plus…
The basic ideas of second quantization and Fock space are extended to density operator states, used in treatments of open many-body systems. This can be done for fermions and bosons. While the former only requires the use of a…
Studying quantum entanglement in systems of indistinguishable particles, in particular anyons, poses subtle challenges. Here, we investigate a model of one-dimensional anyons defined by a generalized algebra. This algebra has the special…
Quantum mechanics for a four-state-system is derived from classical statistics. Entanglement, interference, the difference between identical fermions or bosons and the unitary time evolution find an interpretation within a classical…
The quantization of systems with first- and second-class constraints within the coherent-state path-integral approach is extended to quantum systems with fermionic degrees of freedom. As in the bosonic case the importance of path-integral…
Quantum coherence is critical resource for applications in quantum technology, among which quantum-enhanced sensing represents a typical example.Compared with quantum metrology with entangled states of multiple qubits, bosonic…
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…
A generalized version of the coupled coherent states method for coherent states of arbitrary Lie groups is developed. In contrast to the original formulation, which is restricted to frozen-Gaussian basis sets, the extended method is…
Canonical quantization has taught us great things. A common example is that of the harmonic oscillator, which is like swinging a ball on a string back and forth. However, the half-harmonic oscillator blocks the ball at the bottom and then…
Quantum systems in nonequilibrium conditions, where coherent many-body interactions compete with dissipative effects, can feature rich phase diagrams and emergent critical behavior. Associated collective effects, together with the…
Canonical quantization may be approached from several different starting points. The usual approaches involve promotion of c-numbers to q-numbers, or path integral constructs, each of which generally succeeds only in Cartesian coordinates.…
It is shown here and in the preceeding paper (quant-ph/0201129) that vector coherent state theory, the theory of induced representations, and geometric quantization provide alternative but equivalent quantizations of an algebraic model. The…
One classical theory, as determined by an equation of motion or set of classical trajectories, can correspond to many unitarily {\em in}equivalent quantum theories upon canonical quantization. This arises from a remarkable ambiguity, not…
We obtain sufficient conditions for the efficient simulation of a continuous variable quantum algorithm or process on a classical computer. The resulting theorem is an extension of the Gottesman-Knill theorem to continuous variable quantum…
The nature of the classical canonical phase-space variables for gravity suggests that the associated quantum field operators should obey affine commutation relations rather than canonical commutation relations. Prior to the introduction of…
The Affine Coherent State Quantization procedure is applied to the case of a FRLW universe in the presence of a cosmological constant. The quantum corrections alter the dynamics of the system in the semiclassical regime, providing a…