Related papers: Polymer representations and geometric quantization
We present a general procedure for constructing new Hilbert spaces for loop quantum gravity on non-compact spatial manifolds. Given any fixed background state representing a non-compact spatial geometry, we use the Gel'fand-Naimark-Segal…
We construct a general quantization procedure for square integrable functions on well-behaved connected exponential Lie groups. The Lie groups in question should admit at least one co-adjoint orbit of maximal possible dimension. The…
We study finite dimensional algebras that appear as fibers of quantum orders over a given point of variety of center. We present the formula for the number of irreducible representations and check it for it for the algebra of twisted…
In this paper, we begin a quantization program for nilpotent orbits of a real semisimple Lie group. These orbits and their covers generalize the symplectic vector space. A complex structure polarizing the orbit and invariant under a maximal…
When two or more subsystems of a quantum system interact with each other they can become entangled. In this case the individual subsystems can no longer be described as pure quantum states. For systems with only 2 subsystems this…
To illustrate the conceptual problems for the low-energy symmetries in the continuum of spacetime emerging from the discrete quantum geometry, Galileo symmetries are investigated in the polymer particle representation of a non-relativistic…
Within the Hamiltonian framework, the propositions about a classical physical system are described in the Borel {\sigma}-algebra of a symplectic manifold (the phase space) where logical connectives are the standard set operations.…
The corner symmetry algebra organises the physical charges induced by gravity on codimension-$2$ corners of a manifold. In this letter, we initiate a study of the quantum properties of this group using as a toy model the corner symmetry…
Coherent state theory is shown to reproduce three categories of representations of the spectrum generating algebra for an algebraic model: (i) classical realizations which are the starting point for geometric quantization; (ii) induced…
Recent research in the geometric formulation of quantum theory has implied that Weyl Geometry can be used to merge quantum theory and general relativity consistently as classical field theories. In the Weyl Geometric framework, it seems…
Free scalar field theory on 2 dimensional flat spacetime, cast in diffeomorphism invariant guise by treating the inertial coordinates of the spacetime as dynamical variables, is quantized using LQG type `polymer' representations for the…
We construct, using the quantum dilogarithm, a series of *-representations of quantized cluster varieties. This includes a construction of infinite dimensional unitary projective representations of their discrete symmetry groups - the…
Much of the work in loop quantum gravity and quantum geometry rests on a mathematically rigorous integration theory on spaces of distributional connections. Most notably, a diffeomorphism invariant representation of the algebra of basic…
We present a new family of quantum Weyl algebras where the polynomial part is the quantum analog of functions on homogeneous spaces corresponding to symmetric matrices, skew symmetric matrices, and the entire space of matrices of a given…
We consider scalar-tensor theories of gravity defined in Weyl integrable space-time and show that in the ADM formalism Weyl transformations corresponding to change of frames induce canonical transformations between different representations…
Quantum mechanics is among the most important and successful mathematical model for describing our physical reality. The traditional formulation of quantum mechanics is linear and algebraic. In contrast classical mechanics is a geometrical…
Quantum geometry governs a wide range of transport and optical phenomena in quantum materials. Recent works have explored analogue electromagnetism and gravity in terms of the quantum geometric tensor, whose real and imaginary parts…
A simplified construction of representations is presented for the quantized enveloping algebra Uq(g), with g being a simple complex Lie algebra belonging to one of the four principal series A, B, C or D. The carrier representation space is…
Physical systems, characterized by an ensemble of interacting elementary constituents, can be represented and studied by different algebras of observables or operators. For example, a fully polarized electronic system can be investigated by…
The method of geometric quantization is applied to a particle moving on an arbitrary Riemannian manifold $Q$ in an external gauge field, that is a connection on a principal $H$-bundle $N$ over $Q$. The phase space of the particle is a…