Square Root Actions, Metric Signature, and the Path-Integral of Quantum Gravity

We consider quantization of the Baierlein-Sharp-Wheeler form of the gravitational action, in which the lapse function is determined from the Hamiltonian constraint. This action has a square root form, analogous to the actions of the relativistic particle and Nambu string. We argue that path-integral quantization of the gravitational action should be based on a path integrand $\exp[ \sqrt{i} S ]$ rather than the familiar Feynman expression $\exp[ i S ]$, and that unitarity requires integration over manifolds of both Euclidean and Lorentzian signature. We discuss the relation of this path integral to our previous considerations regarding the problem of time, and extend our approach to include fermions.Comment: 32 pages, latex. The revision is a more general treatment of the regulator. Local constraints are now derived from a requirement of regulator independenc

Locally optimal symplectic control of multimode Gaussian states

The relaxation of a system to a steady state is a central point of interest in many attempts to advance control over the quantum world. In this paper, we consider control through instantaneous Gaussian unitary operations on the ubiquitous lossy channel, and find locally optimal conditions for the cooling and heating of a multimode Gaussian state subject to losses and possibly thermal noise. This is done by isolating the parameters that encode entropy and temperature and by deriving an equation for their evolution. This equation is in such a form that it grants clear insight into how relaxation may be helped by instantaneous quantum control. It is thus shown that squeezing is a crucial element in optimising the rate of change of entropic properties under these channels. Exact relaxation times for heating and cooling are derived, up to an arbitrarily small distance from the fixed point of the lossy channel with locally optimal strategies. Keywords: Gaussian states, coherent control, open quantum system

Lower bound of minimal time evolution in quantum mechanics

We show that the total time of evolution from the initial quantum state to final quantum state and then back to the initial state, i.e., making a round trip along the great circle over S^2, must have a lower bound in quantum mechanics, if the difference between two eigenstates of the 2\times 2 Hamiltonian is kept fixed. Even the non-hermitian quantum mechanics can not reduce it to arbitrarily small value. In fact, we show that whether one uses a hermitian Hamiltonian or a non-hermitian, the required minimal total time of evolution is same. It is argued that in hermitian quantum mechanics the condition for minimal time evolution can be understood as a constraint coming from the orthogonality of the polarization vector \bf P of the evolving quantum state \rho={1/2}(\bf 1+ \bf{P}\cdot\boldsymbol{\sigma}) with the vector \boldsymbol{\mathcal O}(\Theta) of the 2\times 2 hermitian Hamiltonians H ={1/2}({\mathcal O}_0\boldsymbol{1}+ \boldsymbol{\mathcal O}(\Theta)\cdot\boldsymbol{\sigma}) and it is shown that the Hamiltonian H can be parameterized by two independent parameters {\mathcal O}_0 and \Theta.Comment: 4 pages, no figure, revtex

Fundamental Constants and the Problem of Time

We point out that for a large class of parametrized theories, there is a constant in the constrained Hamiltonian which drops out of the classical equations of motion in configuration space. Examples include the mass of a relativistic particle in free fall, the tension of the Nambu string, and Newton's constant for the case of pure gravity uncoupled to matter or other fields. In the general case, the classically irrelevant constant is proportional to the ratio of the kinetic and potential terms in the Hamiltonian. It is shown that this ratio can be reinterpreted as an {\it unconstrained} Hamiltonian, which generates the usual classical equations of motion. At the quantum level, this immediately suggests a resolution of the "problem of time" in quantum gravity. We then make contact with a recently proposed transfer matrix formulation of quantum gravity and discuss the semiclassical limit. In this formulation, it is argued that a physical state can obey a (generalized) Poincar\'e algebra of constraints, and still be an approximate eigenstate of 3-geometry. Solutions of the quantum evolution equations for certain minisuperspace examples are presented. An implication of our proposal is the existence of a small, inherent uncertainty in the phenomenological value of Planck's constant.Comment: 46 pages + 5 figures, LaTex, NBI-HE-94-3

Lorentzian and Euclidean Quantum Gravity - Analytical and Numerical Results

We review some recent attempts to extract information about the nature of quantum gravity, with and without matter, by quantum field theoretical methods. More specifically, we work within a covariant lattice approach where the individual space-time geometries are constructed from fundamental simplicial building blocks, and the path integral over geometries is approximated by summing over a class of piece-wise linear geometries. This method of ``dynamical triangulations'' is very powerful in 2d, where the regularized theory can be solved explicitly, and gives us more insights into the quantum nature of 2d space-time than continuum methods are presently able to provide. It also allows us to establish an explicit relation between the Lorentzian- and Euclidean-signature quantum theories. Analogous regularized gravitational models can be set up in higher dimensions. Some analytic tools exist to study their state sums, but, unlike in 2d, no complete analytic solutions have yet been constructed. However, a great advantage of our approach is the fact that it is well-suited for numerical simulations. In the second part of this review we describe the relevant Monte Carlo techniques, as well as some of the physical results that have been obtained from the simulations of Euclidean gravity. We also explain why the Lorentzian version of dynamical triangulations is a promising candidate for a non-perturbative theory of quantum gravity.Comment: 69 pages, 16 figures, references adde

Top quark forward-backward asymmetry in R-parity violating supersymmetry

The interaction of bottom squark-mediated top quark pair production, occurring in the R-parity violating minimal supersymmetric standard model (MSSM), is proposed as an explanation of the anomalously large $t\bar{t}$ forward-backward asymmetry (FBA) observed at the Tevatron. We find that this model can give a good fit to top quark data, both the inclusive and invariant mass-dependent asymmetries, while remaining consistent (at the 2-$\sigma$ level) with the total and differential production cross-sections. The scenario is challenged by strong constraints from atomic parity violation (APV), but we point out an extra diagram for the effective down quark-Z vertex, involving the same coupling constant as required for the FBA, which tends to weaken the APV constraint, and which can nullify it for reasonable values of the top squark masses and mixing angle. Large contributions to flavor-changing neutral currents can be avoided if only the third generation of sparticles is light.Comment: 24 pages, 7 figures. v3: included LHC top production cross section data; model still consistent at 2 sigma leve

Ostomy closure rate during COVID-19 pandemic. An Italian multicentre observational study

During the corona virus disease 2019 (COVID-19) pandemic, most of the surgical procedures were performed for emergencies or oncologic reasons to the detriment of the remaining elective procedures for benign conditions. Ileostomy or colostomy creation are sequelae of oncologic or emergency colorectal surgery, but their closure does not fall within the definition of oncologic or emergency surgery. The aim of this retrospective multicentre observational study is to report the impact of COVID-19 pandemic on the ostomy closure rate in Italy. Data regarding ileostomy and colostomy creation and closure from 24 Italian centres, during the study period (March 2020–February 2021) and during the control period (March 2019–February 2020) were collected. Three hospitals (12.5%) were COVID free. The number of colostomies and ileostomies created and closed in the same period was lower (-18.8% and-30%, respectively) in the study period in comparison to the control period (p = 0.1915 and p = 0.0001, respectively), such as the ostomies closed in the analysed periods but created before (colostomy-36.2% and ileostomy-7.4%, p = 0.2211 and p = 0.1319, respectively). Overall, a 19.5% reduction in ostomies closed occurred in the study period. Based on the present study, a reduction in ostomy closure rate occurred in Italy between March 2020 and February 2021. During the pandemic, the need to change the clinical practice probably prolonged deterioration of quality of life in patients with ostomies, increasing number of stomas that will never be closed, and related management costs, even if these issues have not been investigated in this study