Related papers: Fourier duality of quantum curves
Wave-particle duality is certainly one of the most curious concepts of contemporary physics, which ascribes mutually exclusive behaviors to quantum systems that cannot be observed simultaneously. In the context of two-path interferometers,…
We discuss the deformation quantization approach for the teaching of quantum mechanics. This approach has certain conceptual advantages which make its consideration worthwhile. In particular, it sheds new light on the relation between…
We elaborate on a construction of quantum LG superpotential associated to a tau-function of the KP hierarchy in the case that resulting quantum spectral curve lies in the quantum two-torus. This construction is applied to Hurwitz numbers,…
A theory of principal bundles possessing quantum structure groups and classical base manifolds is presented. Structural analysis of such quantum principal bundles is performed. A differential calculus is constructed, combining differential…
Motivated by the expectation that relativistic symmetries might acquire quantum features in Quantum Gravity, we take the first steps towards a theory of ''Doubly'' Quantum Mechanics, a modification of Quantum Mechanics in which the…
We explore the relationship between complexity and duality in quantum systems, focusing on how local and non-local operators evolve under time evolution. We find that non-local operators, which are dual to local operators under specific…
I conceptualise the role of dualities in quantum gravity, in terms of their functions for theory construction. I distinguish between two functions of duality in physical practice: namely, discovering and describing 'equivalent physics', vs.…
We provide a simple derivation of particle-vortex duality in d=2+1 dimensions. Our starting point is a relativistic form of flux attachment, designed to transmute the statistics of particles. From this seed, we derive a web of new…
We characterize the finite codimension sub-K-algebras of K[[t]] as the solutions of a computable finite family of higher differential operators. For this end, we establish a duality between such a sub-algebras and the finite codimension…
We consider the nature of quantum properties in non-relativistic quantum mechanics (QM) and relativistic QFTs, and examine the connection between formal quantization schemes and intuitive notions of wave-particle duality. Based on the map…
We discuss the meaning of geometrical constructions associated to loop quantum gravity states on a graph. In particular, we discuss the "twisted geometries" and derive a simple relation between these and Regge geometries.
We portray the structure of quantum gravity emerging from recent progress in understanding the quantum mechanics of an evaporating black hole. Quantum gravity admits two different descriptions, based on Euclidean gravitational path integral…
The pairwise correlations in a multi-qubit state are quantified through a linear variant of relative entropy. In particular, we derive the explicit expressions of total, quantum and classical bipartite correlations. Two different…
We study wave-particle duality by exploring for the first time effects of a quantum object's source. A single photon emitted from a pair of nonlocally entangled two-level atoms is specifically analyzed. Surprisingly, duality is found to be…
We describe a deformation of the observable algebra of quantum gravity in which the loop algebra is extended to framed loops. This allows an alternative nonperturbative quantization which is suitable for describing a phase of quantum…
The quantisation of the two-dimensional Liouville field theory is investigated using the path integral, on the sphere, in the large radius limit. The general form of the $N$-point functions of vertex operators is found and the three-point…
The stability of two quantum counter-streaming electron beams is investigated within the quantum plasma fluid equations for arbitrarily oriented wave vectors. The analysis reveals that the two quantum two-stream unstable branches are indeed…
Loop Quantum Gravity provides a natural truncation of the infinite degrees of freedom of gravity, obtained by studying the theory on a given finite graph. We review this procedure and we present the construction of the canonical theory on a…
We prove that Riemannian metrics in General Relativity in the \emph{`normal-coordinates'} gauge are in one-to-one correspondence with curvature 2-forms. We discuss how this can be used as a change of variables in the operator formalism to…
We study the boundary correlation functions in Liouville theory and in solvable statistical models of 2D quantum gravity. In Liouville theory we derive functional identities for all fundamental boundary structure constants, similar to the…