Related papers: Towards a definition of quantum integrability
The physics of many closed, conservative systems can be described by both classical and quantum theories. The dynamics according to classical theory is symplectic and admits linear instabilities which would initially seem at odds with a…
An adapted representation of quantum mechanics sheds new light on the relationship between quantum states and classical states. In this approach the space of quantum states splits into a product of the state space of classical mechanics and…
By the universal integrability objects we mean certain monodromy-type and transfer-type operators, where the representation in the auxiliary space is properly fixed, while the representation in the quantum space is not. This notion is…
Any single system whose space of states is given by a separable Hilbert space is automatically equipped with infinitely many hidden tensor-like structures. This includes all quantum mechanical systems as well as classical field theories and…
If quantum gravity respects the principles of quantum mechanics, suitably generalized, it may be that a more viable approach to the theory is through identifying the relevant quantum structures rather than by quantizing classical spacetime.…
We describe quantum and classical Hamiltonian dynamics in a common Hilbert space framework, that allows the treatment of mixed quantum-classical systems. The analysis of some examples illustrates the possibility of entanglement between…
A generalization of classical mechanics is obtained from a complex parametrization of the phase space. The formalism supports complex Hamiltonian functions describing non-conservative classical mechanical systems. A quantization scheme that…
Quantum computation is frequently mischaracterized as the simultaneous execution of exponentially many classical computations. This article offers a conceptual clarification of why this ``branchwise parallelism'' picture is misleading,…
The mathematical notion of incompleteness (eg of rational numbers, Turing-computable functions, and arithmetic proof) does not play a key role in conventional physics. Here, a reformulation of the kinematics of quantum theory is attempted,…
As a laboratory for loop quantum gravity, we consider the canonical quantization of the three-dimensional Chern-Simons theory on a noncompact space with the topology of a cylinder. Working within the loop quantization formalism, we define…
We describe our recent proposal of a path integral formulation of classical Hamiltonian dynamics. Which leads us here to a new attempt at hybrid dynamics, which concerns the direct coupling of classical and quantum mechanical degrees of…
We classify the completely integrable systems associated with classical root systems whose potential functions are meromorphic at an infinite point.
Computational complexity is a new quantum information concept that may play an important role in holography and in understanding the physics of the black hole interior. We consider quantum computational complexity for $n$ qubits using…
One of the most central and controversial element of quantum mechanics is the use of non zero vectors of a Hilbert space (or, more generally, of one dimension subspaces) for representing the state of a quantum system. In particular, the…
We derive an exact expression for the quantumness of a Hilbert space (defined in quant-ph/0302092), and show that in composite Hilbert spaces the signal states must contain at least some entangled states in order to achieve such a…
We discuss some conceptual issues that any approach to quantum gravity has to confront. In particular, it is argued that one has to find a theory that can be interpreted in a realist manner, because theories with an instrumentalist…
Through a new interpretation of Special Theory of Relativity and with a model given for physical space, we can find a way to understand the basic principles of Quantum Mechanics consistently from Classical Theory. It is supposed that…
Motivated by the question whether quantum gravity can "smear out" the classical singularity we analyze a certain quantum space and its quantum-mechanical completeness. Classical singularity is understood as a geodesic incompleteness, while…
The definitions of classical and quantum singularities in general relativity are reviewed. The occurence of quantum mechanical singularities in certain spherically symmetric and cylindrically symmetric (including infinite line…
It is shown for classical and quantum ensembles that there is a unique quantity which has the properties of a "volume". This quantity is a function of the ensemble entropy, and hence provides a geometric interpretation for the latter. It…