Related papers: Seven Sphere Quantization
Interesting non-linear functions on the phase spaces of classical field theories can never be quantized immediately because the basic fields of the theory become operator valued distributions. Therefore, one is usually forced to find a…
We define formal geometric quantisation for proper Hamiltonian actions by possibly noncompact groups on possibly noncompact, prequantised symplectic manifolds, generalising work of Weitsman and Paradan. We study the functorial properties of…
We show that the classical mechanics of an algebraic model are implied by its quantizations. An algebraic model is defined, and the corresponding classical and quantum realizations are given in terms of a spectrum generating algebra.…
Geometric quantization is an attempt at using the differential-geometric ingredients of classical phase spaces regarded as symplectic manifolds in order to define a corresponding quantum theory. Generally, the process of geometric…
In this paper we study the groups of contactomorphisms of a closed contact manifold from a topological viewpoint. First we construct examples of contact forms on spheres whose Reeb flow has a dense orbit. Then we show that the unitary group…
The formalism of classical and quantum mechanics on phase space leads to symplectic and Heisenberg group representations, respectively. The Wigner functions give a representation of the quantum system using classical variables. The…
The main result is that the qc-scalar curvature of a seven dimensional quaternionic contact Einstein manifold is a constant. In addition, we characterize qc-Einstein structures with certain flat vertical connection and develop their local…
The classical soliton solution, quantized by means of suitable translational and rotational collective coordinates, is embedded into the one-particle irreductible representation of the Poincare group corresponding to a definite spin. It is…
The manifold of pure quantum states is a complex projective space endowed with the unitary-invariant geometry of Fubini and Study. According to the principles of geometric quantum mechanics, the detailed physical characteristics of a given…
This paper develops a systematic and geometric theory of optimal quantization on the unit sphere $\mathbb S^2$, focusing on finite uniform probability distributions supported on the spherical surface - rather than on lower-dimensional…
A generalized quantization principle is considered, which incorporates nontrivial commutation relations of the components of the variables of the quantized theory with the components of the corresponding canonical conjugated momenta…
A tensor invariant is defined on a quaternionic contact manifold in terms of the curvature and torsion of the Biquard connection involving derivatives up to third order of the contact form. This tensor, called quaternionic contact conformal…
The dynamics of states representing arbitrary N-level quantum systems, including dissipative systems, can be modelled exactly by the dynamics of classical coupled oscillators. There is a direct one-to-one correspondence between the quantum…
A general prescription for the treatment of constrained quantum motion is outlined. We consider in particular constraints defined by algebraic submanifolds of the quantum state space. The resulting formalism is applied to obtain solutions…
We study quantization of a self-interacting scalar field within the unfolded dynamics approach. To this end we find and analyze a classical unfolded system describing 4d off-shell scalar field with a general self-interaction potential. Then…
Hamiltonians whose symbols are not simply real valued, but matrix or, more generally, endomorphism valued functions appear in many places in physics, examples being the Dirac equation, multicomponent wave equations like electrodynamics in…
Using canonical quantisation, and eschewing the Schwinger-Keldysh path integral, we derive a version of the Worldline Quantum Field Theory (WQFT) formalism suitable for both scattering and bound configurations of the classical two-body…
We construct left invariant quaternionic contact (qc) structures on Lie groups with zero and non-zero torsion and with non-vanishing quaternionic contact conformal curvature tensor, thus showing the existence of non-flat quaternionic…
The Schr\"odinger cat states, constructed from Glauber coherent states and applied for description of qubits are generalized to the kaleidoscope of coherent states, related with regular n-polygon symmetry and the roots of unity. This…
Motivated by the construction of spectral manifolds in noncommutative geometry, we introduce a higher degree Heisenberg commutation relation involving the Dirac operator and the Feynman slash of scalar fields. This commutation relation…