Related papers: Central extensions and quantum physics
We study a (1+1)-dimensional quantum circuit consisting of Haar-random unitary gates and projective measurements that conserve a total $U(1)$ charge and thus have $U(1)$ symmetry. In addition to a measurement-induced entanglement transition…
Different routes towards the canonical formulation of a classical theory result in different canonically equivalent Hamiltonians, while their quantum counterparts are related through appropriate unitary transformation. However, for…
A consistent classical mechanics formulation is presented in such a way that, under quantization, it gives a noncommutative quantum theory with interesting new features. The Dirac formalism for constrained Hamiltonian systems is strongly…
It is shown that the non-commutativity in quantum Hall system may get modified. The self-adjoint extension of the corresponding Hamiltonian leads to a family of non-commutative geometries labeled by the self-adjoint extension parameters. We…
In quantum field theory, particle creation occurs, in general, when an intense external field, such as an electromagnetic field, breaks time translational invariance. This leads to an ambiguity in the definition of the vacuum state. In…
The mechanism of the transition of a dynamical system from quantum to classical mechanics is one of the remaining challenges of quantum theory. Currently, it is considered to occur via decoherence caused by entanglement and/or stochastic…
We extend the Composite Boson theory to study slightly im-balanced bi-layer Quantum Hall systems. In the global $ U(1) $ symmetry breaking excitonic superfluid side, as the imbalance increases, the system supports continuously changing…
We propose an operator constraint equation for the wavefunction of the Universe that admits genuine evolution. While the corresponding classical theory is equivalent to the canonical decomposition of General Relativity, the quantum theory…
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 infinite group of deformed diffeomorphisms of the spacetime continuum is put into the basis of the gauge theory of gravity. This gives rise to some new ways for unification of gravity with other gauge interactions.
The notion of quantum embedding is considered for two classes of examples: quantum coadjoint orbits in Lie coalgebras and quantum symplectic leaves in spaces with non-Lie permutation relations. A method for constructing irreducible…
The product of two unitaries can normally be expressed as a single exponential through the famous Baker-Campbell-Hausdorff formula. We present here a counterexample in quantum optics, by showing that an expression in terms of a single…
The construction and analysis of deformations of quantum field theories by warped convolutions is extended to a class of globally hyperbolic spacetimes. First, we show that any four-dimensional spacetime which admits two commuting and…
A field theory with local transformations belonging to the quantum group SU_q(n) is defined on a classical spacetime, with gauge potentials belonging to a quantum Lie algebra. Gauge transformations are defined for the potentials which lead…
The conditions leading to a nontrivial renormalization of the topological charge in four--dimensional Yang--Mills theory are discussed. It is shown that if the topological term is regarded as the limit of a certain nontopological…
Dimensional reduction of various gravity and supergravity models leads to effectively two-dimensional field theories described by gravity coupled G/H coset space sigma-models. The transition matrices of the associated linear system provide…
Gauge symmetries emerge from a redundant description of the effective action for light degrees of freedom after the decoupling of heavy modes. This redundant description avoids the use of explicit constraints in configuration space. For…
Quantum mechanics in the presence of $\delta$-function potentials is known to be plagued by UV divergencies which result from the singular nature of the potentials in question. The standard method for dealing with these divergencies is by…
In grand unified theories with large numbers of fields, renormalization effects significantly modify the scale at which quantum gravity becomes strong. This in turn can modify the boundary conditions for coupling constant unification, if…
We study some basic quantum confinement effects through investigation a deformed harmonic oscillator algebra. We show that spatial confinement effects on a quantum harmonic oscillator can be represented by a deformation function within the…