We describe the symplectic structure and Hamiltonian dynamics for a class of Grassmannian manifolds. Using the two dimensional sphere (S) and disc (D) as illustrative cases, we write their path integral representations using coherent state techniques. These path integrals can be evaluated exactly by semiclassical methods, thus providing examples of localisation formula. Along the way, we also g...

We present a new method of formulating the classical theory of SU(N + 1) non-Abelian Chern-Simons (NACS) particles for arbitrary N ≥ 1 using the symplectic reduction of CP (N) manifold from S2N+1. Quantizing the theory using BRST formulation and coherent state path integral method , we obtain a quantum mechanical model for SU(N + 1) NACS particles.

Using the ‘quantum optical approach’ we propose a model of multiplicity distributions in high energy collisions based on squeezed coherent states. We show that the k-mode squeezed coherent state is the most general one in describing hadronic mulitiplicity distributions in particle collision processes, describing not only pp collisions but e+e−, νp and diffractive collisions as well. The reason ...

The outline of a recent approach to quantum gravity is presented. Novel ingredients include: (1) Affine kinematical variables; (2) Affine coherent states; (3) Projection operator approach toward quantum constraints; (4) Continuous-time regularized functional integral representation without/with constraints; and (5) Hard core picture of nonrenormalizability. The “diagonal representation” for ope...

Systems with constraints pose problems when they are quantized. Moreover, the Dirac procedure of quantization prior to reduction is preferred. The projection operator method of quantization, which can be most conveniently described by coherent state path integrals, enables one to directly impose a regularized form of the quantum constraints. This procedure also overcomes conventional difficulti...

We develop the formulation of the spin(SU(2)) coherent state path integrals based on arbitrary starting vectors. The resultant action in the path integral expression extensively depends on the vector; it differs from the conventional one in that it has a generalized form having some additional terms. We also study, as physical applications, the geometric phases associated with the CS path integ...

We construct integrable models on flag manifold by using the symplectic structure explicitly given in the Bruhat coordinatization of flag manifold. They are non-commutative integrable and some of the conserved quantities are given by the Casimir invariants. We quantize the systems using the coherent state path integral technique and find the exact expression for the propagator for some special ...

We present a review of the applications of the Wigner distribution function in various areas of signal processing: amplitude and phase retrieval, signal recognition, characterization of arbitrary signals, optical systems and devices, and coupling coefficient estimation in phase space. Although reference is made to specific signals and systems, the mathematical formulation is general and can be ...

Coherent states can be used for diverse applications in quantum physics including the construction of coherent state path integrals. Most definitions make use of a lattice regularization; however, recent definitions employ a continuous-time regularization that may involve a Wiener measure concentrated on continuous phase space paths. The introduction of constraints is both natural and economica...

We investigate the quantum coherent dynamics of an externally driven effective two-level system subjected to a slow Ohmic environment characteristic of biomolecular protein-solvent reservoirs in photosynthetic light harvesting complexes. By means of the numerically exact quasi adiabatic propagator path integral (QUAPI) method we are able to include non-Markovian features of the environment and ...