Related papers: Perturbative anomalies in quantum mechanics
We show that certain global anomalies can be detected in an elementary fashion by analyzing the way the symmetry algebra is realized on the torus Hilbert space of the anomalous theory. Distinct anomalous behaviours imprinted in the Hilbert…
We review the homotopy algebraic perspective on perturbative quantum field theory: classical field theories correspond to homotopy algebras such as $A_\infty$- and $L_\infty$-algebras. Furthermore, their scattering amplitudes are encoded in…
We describe a cohomological framework for measurement based quantum computation, in which symmetry plays a central role. Therein, the essential information about the computational output is contained in topological invariants, namely…
For nonrelativistic Hamiltonians which are shape invariant, analytic expressions for the eigenvalues and eigenvectors can be derived using the well known method of supersymmetric quantum mechanics. Most of these Hamiltonians also possess…
The origin of the anomalies is analyzed. It is shown that they are due to the fact that the generators of the symmetry do not leave invariant the domain of definition of the Hamiltonian and then a term, normally forgotten in the Heisenberg…
We study two-dimensional Hamiltonians in phase space with noncommutativity both in coordinates and momenta. We consider the generator of rotations on the noncommutative plane and the Lie algebra generated by Hermitian rotationally invariant…
Finite-dimensional Quantum Mechanics can be geometrically formulated as a proper classical-like Hamiltonian theory in a projective Hilbert space. The description of composite quantum systems within the geometric Hamiltonian framework is…
We study the commutation relations, uncertainty relations and spectra of position and momentum operators within the framework of quantum group % symmetric Heisenberg algebras and their (Bargmann-) Fock representations. As an effect of the…
One of the more popular objections towards shape dynamics is the suspicion that anomalies in the spatial Weyl symmetry will arise upon quantization. The purpose of this short paper is to establish the tools required for an investigation of…
A unique classification of the topological effects associated to quantum mechanics on manifolds is obtained on the basis of the invariance under diffeomorphisms and the realization of the Lie-Rinehart relations between the generators of the…
In a recent paper it was shown that if a Hamiltonian H has an unbroken PT symmetry, then it also possesses a hidden symmetry represented by the linear operator C. The operator C commutes with both H and PT. The inner product with respect to…
Cohomological methods are applied for the special set of solutions corresponding to rotating branes in arbitrary dimensions, AdS black holes (which can be embedded in ten or eleven dimensions), and gauge supergravities. A new class of…
We construct Lie algebras arising from commutators of the harmonic Hamiltonian and the perturbed anharmonic Hamiltonian. From there we form a very specific element of the associated Lie group and transform the unperturbed Hamiltonian into…
We recently introduced a particular nonlinear generalization of quantum mechanics which has the property that it is exactly solvable in terms of the eigenvalues and eigenfunctions of the Hamiltonian of the usual linear quantum mechanics…
We propose a method for reduction of quantum systems with arbitrary first class constraints. An appropriate mathematical setting for the problem is homology of associative algebras. For every such an algebra $A$ and its subalgebra B with an…
In this second paper of our series we focus on the classical pure gravity sector of spherically symmetric black hole perturbations and expand the reduced Hamiltonian to second order. To compare our manifestly gauge invariant formalism with…
We develop the Hamiltonian theory of axial perturbations around a general time-dependent spherical background spacetime. Using the fact that the linearized constraints are gauge generators, we isolate the physical and unconstrained axial…
The observable algebra O of SO_q(3)-symmetric quantum mechanics is generated by the coordinates of momentum and position spaces (which are both isomorphic to the SO_q(3)-covariant real quantum space R_q^3). Their interrelations are…
Stationary quantum stochastic process j is introduced as a *-homomorphism embedding an involutive graded algebra $\tilde K=\oplus_{i=1}^{\infty}K_i$ into a ring of (abelian) cohomologies of the one-parameter group $\alpha$ consisting of…
Symmetry is an important property of quantum mechanical systems which may dramatically influence their behavior in and out of equilibrium. In this paper, we study the effect of symmetry on tripartite entanglement properties of typical…