Related papers: Stratified Pseudobundles and Quantization
We use tools from the theory of dynamical systems with symmetries to stratify Uhlmann's standard purification bundle and derive a new connection for mixed quantum states. For unitarily evolving systems, this connection gives rise to the…
We examine various properties of double field theory and the doubled string sigma model in the context of geometric quantisation. In particular we look at T-duality as the symplectic transformation related to an alternative choice of…
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…
A quantization scheme based on the extension of phase space with application of constrained quantization technic is considered. The obtained method is similar to the geometric quantization. For constrained systems the problem of scalar…
We study how the spin-statistics theorem relates to the geometric structures on phase space that are introduced in quantisation procedures (namely a U(1) bundle and connection). The relation can be proved in both the relativistic and the…
In the Hamiltonian approach on a single spatial plaquette, we construct a quantum (lattice) gauge theory which incorporates the classical singularities. The reduced phase space is a stratified K\"ahler space, and we make explicit the…
We review the definition of geometric quantization, which begins with defining a mathematical framework for the algebra of observables that holds equally well for classical and quantum mechanics. We then discuss prequantization, and go into…
Quantization together with quantum dynamics can be simultaneously formulated as the problem of finding an appropriate flat connection on a Hilbert bundle over a contact manifold. Contact geometry treats time, generalized positions and…
A general noncommutative-geometric theory of principal bundles is presented. Quantum groups play the role of structure groups. General quantum spaces play the role of base manifolds. A differential calculus on quantum principal bundles is…
An operator generalisation of the notion of geometric phase has been recently proposed purely based on physical grounds. Here we provide a mathematical foundation for its existence, while uncovering new geometrical structures in quantum…
In this paper we investigate the possibility of constructing a complete quantization procedure consisting of geometric and deformation quantization. The latter assigns a noncommutative algebra to a symplectic manifold, by deforming the…
This work has the purpose of applying the concept of Geometric Calculus (Clifford Algebras) to the Fibre Bundle description of Quantum Mechanics. Thus, it is intended to generalize that formulation to curved spacetimes [the base space of…
We develop a wave mechanics formalism for qubit geometry using holomorphic functions and Mobius transformations, providing a geometric perspective on quantum computation. This framework extends the standard Hilbert space description,…
Quantization identifies the cotangent bundle of projective space with the (non-Hermitian) rank-$1$ projections of a Hilbert space. We use this identification to study the natural geometric structures of these cotangent bundles and those of…
We develop a mathematically well-defined path integral formalism for general symplectic manifolds. We argue that in order to make a path integral quantization covariant under general coordinate transformations on the phase space and involve…
It was shown recently that stochastic quantization can be made into a well defined quantization scheme on (pseudo-)Riemannian manifolds using second order differential geometry, which is an extension of the commonly used first order…
We extend Berezin's quantization $q:M\to\mathbb{P}\mathcal{H}$ to holomorphic symplectic manifolds, which involves replacing the state space $\mathbb{P}\mathcal{H}$ with its complexification $\text{T}^*\mathbb{P}\mathcal{H}.$ We show that…
It is possible to reproduce the quantum features of quantum states, starting from a classical statistical theory and then limiting the amount of knowledge that an agent can have about an individual system [5, 18].These are so called…
Fedosov has described a geometro-algebraic method to construct in a canonical way a deformation of the Poisson algebra associated with a finite-dimensional symplectic manifold ("phase space"). His algorithm gives a non-commutative, but…
In this paper, a way is given to obtain explicitly the representations of the Poincar\'e group as can be prescribed by Geometric Quantization. Thus one obtains some forms of the Space of Quantum States of the different relativistic free…