Symmetry behavior in the Einstein universe: Gaussian approximation in the Schrödinger picture

1988 ◽  
Vol 38 (6) ◽  
pp. 1853-1858 ◽  
Author(s):  
S. K. Kim ◽  
W. Namgung ◽  
K. S. Soh ◽  
J. H. Yee
Keyword(s):  
Gaussian Approximation ◽  
Einstein Universe ◽  
Schrödinger Picture

Gaussian approximation of the Gross-Neveu model in the functional Schrödinger picture

1989 ◽  
Vol 40 (8) ◽  
pp. 2647-2653 ◽  
Author(s):  
S. K. Kim ◽  
J. Yang ◽  
K. S. Soh ◽  
J. H. Yee
Keyword(s):  
Gaussian Approximation ◽  
Schrödinger Picture ◽  
Gross Neveu Model

scholarly journals QUANTUM EVOLUTION OF SCALAR FIELDS IN ROBERTSON-WALKER SPACE-TIME

1996 ◽  
Vol 11 (21) ◽  
pp. 3957-3971 ◽  
Author(s):  
H.C. REIS ◽  
O.J.P. ÉBOLI
Keyword(s):  
Field Theory ◽  
Energy Momentum Tensor ◽  
Gaussian Approximation ◽  
Scalar Fields ◽  
Momentum Tensor ◽  
Space Time ◽  
Quantum Evolution ◽  
Coupling Constant ◽  
Pure States ◽  
Schrödinger Picture

We study the λɸ4 field theory in a flat Robertson-Walker space-time using the functional Schrödinger picture. We introduce a simple Gaussian approximation to analyze the time evolution of pure states and we establish the renormalizability of the approximation. We also show that the energy–momentum tensor in this approximation is finite once we consider the usual mass and coupling constant renormalizations.

scholarly journals QUANTUM EVOLUTION OF INHOMOGENEITIES IN CURVED SPACE

1999 ◽  
Vol 14 (10) ◽  
pp. 1633-1650 ◽  
Author(s):  
H. C. REIS
Keyword(s):  
Energy Momentum Tensor ◽  
Gaussian Approximation ◽  
Equations Of Motion ◽  
Momentum Tensor ◽  
Quantum Evolution ◽  
Coupling Constant ◽  
Curved Space ◽  
Semiclassical Gravity ◽  
Nonperturbative Approximation ◽  
Schrödinger Picture

We obtain the renormalized equations of motion for matter and semiclassical gravity in an inhomogeneous space–time. We use the functional Schrödinger picture and a simple Gaussian approximation to analyze the time evolution of the λϕ4 model, and we establish the renormalizability of this nonperturbative approximation. We also show that the energy–momentum tensor in this approximation is finite once we consider the usual mass and coupling constant renormalizations, without the need of further geometrical counterterms.

scholarly journals Gaussian approximation of the (2+1)-dimensional Thirring model in the functional Schrödinger picture

1994 ◽  
Vol 50 (10) ◽  
pp. 6542-6546 ◽  
Author(s):  
Seungjoon Hyun ◽  
Geon Hyoung Lee ◽  
Jae Hyung Yee
Keyword(s):  
Gaussian Approximation ◽  
Thirring Model ◽  
Schrödinger Picture

scholarly journals Multiple particle filtering for tracking wireless agents via Monte Carlo likelihood approximation

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Stephan Schlupkothen ◽  
Gerd Ascheid
Keyword(s):  
Monte Carlo ◽  
Computational Complexity ◽  
Particle Filtering ◽  
Gaussian Approximation ◽  
State Of The Art ◽  
Approximation Techniques ◽  
Accurate Localization ◽  
Likelihood Approximation ◽  
Current State ◽  
Multiple Particle

Abstract The localization of multiple wireless agents via, for example, distance and/or bearing measurements is challenging, particularly if relying on beacon-to-agent measurements alone is insufficient to guarantee accurate localization. In these cases, agent-to-agent measurements also need to be considered to improve the localization quality. In the context of particle filtering, the computational complexity of tracking many wireless agents is high when relying on conventional schemes. This is because in such schemes, all agents’ states are estimated simultaneously using a single filter. To overcome this problem, the concept of multiple particle filtering (MPF), in which an individual filter is used for each agent, has been proposed in the literature. However, due to the necessity of considering agent-to-agent measurements, additional effort is required to derive information on each individual filter from the available likelihoods. This is necessary because the distance and bearing measurements naturally depend on the states of two agents, which, in MPF, are estimated by two separate filters. Because the required likelihood cannot be analytically derived in general, an approximation is needed. To this end, this work extends current state-of-the-art likelihood approximation techniques based on Gaussian approximation under the assumption that the number of agents to be tracked is fixed and known. Moreover, a novel likelihood approximation method is proposed that enables efficient and accurate tracking. The simulations show that the proposed method achieves up to 22% higher accuracy with the same computational complexity as that of existing methods. Thus, efficient and accurate tracking of wireless agents is achieved.

scholarly journals Gauge × gauge = gravity on homogeneous spaces using tensor convolutions

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
L. Borsten ◽  
I. Jubb ◽  
V. Makwana ◽  
S. Nagy
Keyword(s):  
Homogeneous Spaces ◽  
Gauge Fields ◽  
Convolution Product ◽  
Tensor Fields ◽  
Einstein Universe ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Static Einstein Universe ◽  
Definition Of ◽  
Gauge Gravity

Abstract A definition of a convolution of tensor fields on group manifolds is given, which is then generalised to generic homogeneous spaces. This is applied to the product of gauge fields in the context of ‘gravity = gauge × gauge’. In particular, it is shown that the linear Becchi-Rouet-Stora-Tyutin (BRST) gauge transformations of two Yang-Mills gauge fields generate the linear BRST diffeomorphism transformations of the graviton. This facilitates the definition of the ‘gauge × gauge’ convolution product on, for example, the static Einstein universe, and more generally for ultrastatic spacetimes with compact spatial slices.

scholarly journals Medium induced QCD cascades: broadening and rescattering during branching

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
E. Blanco ◽  
K. Kutak ◽  
W. Płaczek ◽  
M. Rohrmoser ◽  
R. Straka
Keyword(s):  
Momentum Transfer ◽  
Quark Gluon Plasma ◽  
Evolution Equations ◽  
Gaussian Approximation ◽  
Gluon Plasma ◽  
Jet Quenching ◽  
Diffusive Approximation

Abstract We study evolution equations describing jet propagation through quark-gluon plasma (QGP). In particular we investigate the contribution of momentum transfer during branching and find that such a contribution is sizeable. Furthermore, we study various approximations, such as the Gaussian approximation and the diffusive approximation to the jet-broadening term. We notice that in order to reproduce the BDIM equation (without the momentum transfer in the branching) the diffusive approximation requires a very large value of the jet-quenching parameter $$ \hat{q} $$ q ̂ .

scholarly journals Cavalier Use of Inferential Statistics Is a Major Source of False and Irreproducible Scientific Findings

Mathematics ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 603
Author(s):  
Leonid Hanin
Keyword(s):  
Sample Size ◽  
Gaussian Approximation ◽  
Statistical Significance ◽  
Statistical Analyses ◽  
Random Sample Size ◽  
P Values ◽  
The Central Limit Theorem ◽  
Fixed Sample ◽  
Large Numbers ◽  
Significance Levels

I uncover previously underappreciated systematic sources of false and irreproducible results in natural, biomedical and social sciences that are rooted in statistical methodology. They include the inevitably occurring deviations from basic assumptions behind statistical analyses and the use of various approximations. I show through a number of examples that (a) arbitrarily small deviations from distributional homogeneity can lead to arbitrarily large deviations in the outcomes of statistical analyses; (b) samples of random size may violate the Law of Large Numbers and thus are generally unsuitable for conventional statistical inference; (c) the same is true, in particular, when random sample size and observations are stochastically dependent; and (d) the use of the Gaussian approximation based on the Central Limit Theorem has dramatic implications for p-values and statistical significance essentially making pursuit of small significance levels and p-values for a fixed sample size meaningless. The latter is proven rigorously in the case of one-sided Z test. This article could serve as a cautionary guidance to scientists and practitioners employing statistical methods in their work.

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