Related papers: Effective constrained polymeric theories and their…
In polymeric quantum theories, a natural question pertains to the so called continuum limit, corresponding to the limit where the `discreteness parameter' $\lambda$ approaches zero. In particular one might ask whether the limit exists and,…
A simple example is used to show that renormalization group limit cycles of effective quantum theories can be studied in a new way. The method is based on the similarity renormalization group procedure for Hamiltonians. The example contains…
A rather non-standard quantum representation of the canonical commutation relations of quantum mechanics systems, known as the polymer representation has gained some attention in recent years, due to its possible relation with Planck scale…
We introduce two possible ways of defining effective constraints of quantum systems and applied this effective constraint method to models of WDW Quantum Cosmology and Loop Quantum Cosmology. We analyze effective Hamiltonian constraint on…
There is widespread interest in many-body quantum systems that exhibit limit-cycle or time-crystalline behaviour. An ideal quantum limit cycle would be realized using fully coherent driving (to minimize noise) and also have a continuous…
It is shown that several prescriptions for the effective continuum limit of the flat Friedmann-Lemaitre-Robertson-Walker loop quantum cosmology can be understood as the exact classical limit of the Wheeler-DeWitt quantization of certain…
Linear-constraint loops are programs whose transition relation is specified by a system of linear inequalities. The termination problem asks, given a loop, whether it admits an infinite computation. Decidability of termination remains open…
Self-consistent Hamiltonian formulation of scalar theory on the null plane is constructed following Dirac method. The theory contains also {\it constraint equations}. They would give, if solved, to a nonlinear and nonlocal Hamiltonian. The…
The investigation of quantum-classical correspondence may lead to gain a deeper understanding of the classical limit of quantum theory. We develop a quantum formalism on the basis of a linear-invariant theorem, which gives an exact…
There is good evidence that full general relativity is non-integrable or even chaotic. We point out the severe repercussions: differentiable Dirac observables and a reduced phase space do not exist in non-integrable constrained systems and…
We present a new method for the quantization of totally constrained systems including general relativity. The method consists in constructing discretized theories that have a well defined and controlled continuum limit. The discrete…
The effective classical/quantum dynamics of a particle constrained on a closed line embedded in a higher dimensional configuration space is analyzed. By considering explicit examples it is shown how different reduction mechanisms produce…
The Dirac method is used to analyze the classical and quantum dynamics of a particle constrained on a circle. The method of Lagrange multipliers is scrutinized, in particular in relation to the quantization procedure. Ordering problems are…
The existence of a classical limit describing interacting particles in a second-quantized theory of identical particles with bosonic symmetry is proved. This limit exists in addition to a previously established classical limit with a…
Within a perturbative cosmological regime of loop quantum gravity corrections to effective constraints are computed. This takes into account all inhomogeneous degrees of freedom relevant for scalar metric modes around flat space and results…
It is well known that a minimal distance emerges in quantum field theories owing to the need to regularize the UV divergences. The macroscopical limit at large minimal distance, weak spatial resolution, is investigated for a self…
We propose that whatever quantity controls the Heisenberg uncertainty relations (for a given complementary pair of observables) it should be identified with an effective Planck parameter. With this definition it is not difficult to find…
Quantum cosmology has traditionally been studied at the level of symmetry-reduced minisuperspace models, analyzing the behavior of wave functions. However, in the absence of a complete full setting of quantum gravity and detailed knowledge…
A new framework for deriving equations of motion for constrained quantum systems is introduced, and a procedure for its implementation is outlined. In special cases the framework reduces to a quantum analogue of the Dirac theory of…
A general quantum constraint of the form $C= - \partial_T^2 \otimes B - I\otimes H$ (realized in particular in Loop Quantum Cosmology models) is studied. Group Averaging is applied to define the Hilbert space of solutions and the relational…