scholarly journals The Raychaudhuri equation for a quantized timelike geodesic congruence

2021 ◽  
Vol 81 (10) ◽  
Author(s):  
Shibendu Gupta Choudhury ◽  
Ananda Dasgupta ◽  
Narayan Banerjee
Keyword(s):  
Recent Attempt ◽  
Raychaudhuri Equation ◽  
Timelike Geodesic ◽  
Quantum Regime ◽  
Operator Form ◽  
Domain Of Applicability ◽  
Quantum Version ◽  
Adjoint Extension

AbstractA recent attempt to arrive at a quantum version of Raychaudhuri’s equation is looked at critically. It is shown that the method, and even the idea, has some inherent problems. The issues are pointed out here. We have also shown that it is possible to salvage the method in some limited domain of applicability. Although no generality can be claimed, a quantum version of the equation should be useful in the context of ascertaining the existence of a singularity in the quantum regime. The equation presented in the present work holds for arbitrary $$n+1$$ n + 1 dimensions. An important feature of the Hamiltonian in the operator form is that it admits a self-adjoint extension quite generally. Thus, the conservation of probability is ensured.

Pluralism and the Liar

2017 ◽  
Author(s):  
Cory Wright ◽  
Bradley Armour-Garb
Keyword(s):  
Alternative Treatment ◽  
Liar Paradox ◽  
Recent Attempt ◽  
In Virtue Of ◽  
The Liar ◽  
The Liar Paradox

Pluralists maintain that there is more than one truth property in virtue of which bearers are true. Unfortunately, it is not yet clear how they diagnose the liar paradox or what resources they have available to treat it. This chapter considers one recent attempt by Cotnoir (2013b) to treat the Liar. It argues that pluralists should reject the version of pluralism that Cotnoir assumes, discourse pluralism, in favor of a more naturalized approach to truth predication in real languages, which should be a desideratum on any successful pluralist conception. Appealing to determination pluralism instead, which focuses on truth properties, it then proposes an alternative treatment to the Liar that shows liar sentences to be undecidable.

Generalized Riemann spaces

1956 ◽  
Vol 52 (4) ◽  
pp. 623-625 ◽  
Author(s):  
John Moffat
Keyword(s):  
Curvature Tensor ◽  
Physical Theory ◽  
Dimensional Space ◽  
Riemann Space ◽  
Recent Attempt ◽  
Fundamental Tensor ◽  
Fundamental Properties ◽  
Complex Symmetric ◽  
Definition Of ◽  
Generalized Curvature Tensor

ABSTRACTThe recent attempt at a physical interpretation of non-Riemannian spaces by Einstein (1, 2) has stimulated a study of these spaces (3–8). The usual definition of a non-Riemannian space is one of n dimensions with which is associated an asymmetric fundamental tensor, an asymmetric linear affine connexion and a generalized curvature tensor. We can also consider an n-dimensional space with which is associated a complex symmetric fundamental tensor, a complex symmetric affine connexion and a generalized curvature tensor based on these. Some aspects of this space can be compared with those of a Riemann space endowed with two metrics (9). In the following the fundamental properties of this non-Riemannian manifold will be developed, so that the relation between the geometry and physical theory may be studied.

scholarly journals Applied philosophy and psychotherapy: Heraclitus as case study

2002 ◽  
Vol 58 (3) ◽  
Author(s):  
Johann Beukes
Keyword(s):  
Recent Attempt ◽  
Philosophical Counselling ◽  
Post Modernism ◽  
Applied Philosophy

This article investigates a recent attempt to apply philosophy within the discipline of psychotherapy and to investigate the somewhat undefined realm of philosophical counselling. After introducing the claims of this interdisciplinary exercise and after addressing the problems involved in crossing the boundaries between philosophy and psychotherapy, the article elaborates on  Alex Howard’s (2000) [Philosophy for counselling and psychotherapy: Pythagoras to post-modernism. London: Macmillan] attempt to make explicit use of philosophy in psychotherapy, using his interpretation and application of Heraclitus’ philosophy as case study.

scholarly journals Spin-Mechanics with Nitrogen-Vacancy Centers and Trapped Particles

Micromachines ◽  
2021 ◽  
Vol 12 (6) ◽  
pp. 651
Author(s):  
Maxime Perdriat ◽  
Clément Pellet-Mary ◽  
Paul Huillery ◽  
Loïc Rondin ◽  
Gabriel Hétet
Keyword(s):  
Degrees Of Freedom ◽  
Theoretical Background ◽  
Nitrogen Vacancy ◽  
Full Potential ◽  
Strongly Coupled ◽  
Trapped Particles ◽  
Quantum Regime ◽  
Atomic Spins ◽  
Nitrogen Vacancy Centers ◽  
Mechanical Oscillators

Controlling the motion of macroscopic oscillators in the quantum regime has been the subject of intense research in recent decades. In this direction, opto-mechanical systems, where the motion of micro-objects is strongly coupled with laser light radiation pressure, have had tremendous success. In particular, the motion of levitating objects can be manipulated at the quantum level thanks to their very high isolation from the environment under ultra-low vacuum conditions. To enter the quantum regime, schemes using single long-lived atomic spins, such as the electronic spin of nitrogen-vacancy (NV) centers in diamond, coupled with levitating mechanical oscillators have been proposed. At the single spin level, they offer the formidable prospect of transferring the spins’ inherent quantum nature to the oscillators, with foreseeable far-reaching implications in quantum sensing and tests of quantum mechanics. Adding the spin degrees of freedom to the experimentalists’ toolbox would enable access to a very rich playground at the crossroads between condensed matter and atomic physics. We review recent experimental work in the field of spin-mechanics that employ the interaction between trapped particles and electronic spins in the solid state and discuss the challenges ahead. Our focus is on the theoretical background close to the current experiments, as well as on the experimental limits, that, once overcome, will enable these systems to unleash their full potential.

scholarly journals Vacuum Polarization in a Zero-Width Potential: Self-Adjoint Extension

Universe ◽  
2021 ◽  
Vol 7 (5) ◽  
pp. 127
Author(s):  
Yuri V. Grats ◽  
Pavel Spirin
Keyword(s):  
Scalar Field ◽  
Vacuum Polarization ◽  
Dimensional Regularization ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Field Approximation ◽  
Dimensional Euclidean Space ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Adjoint Extension

The effects of vacuum polarization associated with a massless scalar field near pointlike source with a zero-range potential in three spatial dimensions are analyzed. The “physical” approach consists in the usage of direct delta-potential as a model of pointlike interaction. We use the Perturbation theory in the Fourier space with dimensional regularization of the momentum integrals. In the weak-field approximation, we compute the effects of interest. The “mathematical” approach implies the self-adjoint extension technique. In the Quantum-Field-Theory framework we consider the massless scalar field in a 3-dimensional Euclidean space with an extracted point. With appropriate boundary conditions it is considered an adequate mathematical model for the description of a pointlike source. We compute the renormalized vacuum expectation value ⟨ϕ2(x)⟩ren of the field square and the renormalized vacuum averaged of the scalar-field’s energy-momentum tensor ⟨Tμν(x)⟩ren. For the physical interpretation of the extension parameter we compare these results with those of perturbative computations. In addition, we present some general formulae for vacuum polarization effects at large distances in the presence of an abstract weak potential with finite-sized compact support.

scholarly journals Transition radiation in the quantum regime as a diffractive phenomenon

2006 ◽  
Vol 355 (4-5) ◽  
pp. 289-292 ◽  
Author(s):  
D. Schildknecht ◽  
B.G. Zakharov
Keyword(s):  
Transition Radiation ◽  
Quantum Regime

scholarly journals Transport theory in metallic films: Crossover from the classical to the quantum regime

1995 ◽  
Vol 51 (11) ◽  
pp. 7325-7328 ◽  
Author(s):  
L. Sheng ◽  
D. Y. Xing ◽  
Z. D. Wang
Keyword(s):  
Transport Theory ◽  
Metallic Films ◽  
Quantum Regime

BOUNDS ON f(G) GRAVITY FROM ENERGY CONDITIONS

2010 ◽  
Vol 25 (27) ◽  
pp. 2325-2332 ◽  
Author(s):  
PUXUN WU ◽  
HONGWEI YU
Keyword(s):  
General Relativity ◽  
Dark Energy ◽  
Energy Density ◽  
Modified Gravity ◽  
Energy Conditions ◽  
Model Parameters ◽  
Effective Energy ◽  
Raychaudhuri Equation ◽  
Accelerating Expansion

The f(G) gravity is a theory to modify the general relativity and it can explain the present cosmic accelerating expansion without the need of dark energy. In this paper the f(G) gravity is tested with the energy conditions. Using the Raychaudhuri equation along with the requirement that the gravity is attractive in the FRW background, we obtain the bounds on f(G) from the SEC and NEC. These bounds can also be found directly from the SEC and NEC within the general relativity context by the transformations: ρ → ρm + ρE and p → pm + pE, where ρE and pE are the effective energy density and pressure in the modified gravity. With these transformations, the constraints on f(G) from the WEC and DEC are obtained. Finally, we examine two concrete examples with WEC and obtain the allowed region of model parameters.

scholarly journals What Constitutions Can Do (but Courts Sometimes Don’t): Property, Speech, and the Influence of Constitutional Norms on Private Law

2004 ◽  
Vol 17 (1) ◽  
pp. 61-81 ◽  
Author(s):  
Oliver Gerstenberg
Keyword(s):  
Human Rights ◽  
Property Rights ◽  
Freedom Of Expression ◽  
Social Democracy ◽  
Recent Attempt ◽  
Private Law ◽  
Human Rights Norms ◽  
The Right ◽  
Higher Law

In this paper I want to address, against the background of the ECtHR’s recent attempt to resolve the clash between property rights and the right to freedom of expression in its decision in Appleby v. UK, two questions, both of which I take to be related to the overarching theme of “social democracy”. First, there is the problem of the influence of “higher law”-of human rights norms and constitutional norms-on private law norms; second, the question of the role of adjudication in “constitutionalizing” private law, in other words, the question of the “judicial cognizability” of constitutional norms within private law.

Requirements for Amicus Curiae Participation in International Investment ArbitrationA Deconstruction of the Procedural Wall Erected in Joint ICSID Cases ARB/10/25 and ARB/10/15

2013 ◽  
Vol 12 (3) ◽  
pp. 365-390 ◽  
Author(s):  
Christian Schliemann
Keyword(s):  
International Law ◽  
International Investment ◽  
Recent Attempt ◽  
Arbitral Tribunal ◽  
Amicus Curiae ◽  
Legal Rules ◽  
Investment Arbitration ◽  
Legal Standard ◽  
Investment Law

Abstract The legal standard on amicus curiae participation in international investment arbitration has been forged by the judicial development of legal rules and, in parallel, the modification of normative sources, such as the ICSID Arbitration Rules. Current and future decisions by arbitral tribunals on the participation of amicus curiae in a given dispute must abide by this consolidated standard. In June 2012, the arbitral tribunal in Joint ICSID Cases No. ARB/10/15 and No. ARB/10/25 released a procedural order, rejecting an amicus petition. This Order contains various deviations from the applicable legal standard and severely restricts the options for amicus participation. The recent attempt to strengthen the legitimacy of international investment arbitration by allowing for greater amicus participation and the acknowledgement of the interdependence of investment law and other areas of international law is thereby put in peril.

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