scholarly journals Twisted reality condition for spectral triple on two points

2016 ◽  
Author(s):  
Andrzej Sitarz ◽  
Ludwik Dabrowski
Keyword(s):  
Spectral Triple ◽  
Reality Condition

scholarly journals Missing the point in noncommutative geometry

Synthese ◽  
2021 ◽  
Author(s):  
Nick Huggett ◽  
Fedele Lizzi ◽  
Tushar Menon
Keyword(s):  
Scalar Field ◽  
Noncommutative Geometry ◽  
Smooth Manifold ◽  
Operational Definition ◽  
Spectral Triple ◽  
Fundamental Quantity

AbstractNoncommutative geometries generalize standard smooth geometries, parametrizing the noncommutativity of dimensions with a fundamental quantity with the dimensions of area. The question arises then of whether the concept of a region smaller than the scale—and ultimately the concept of a point—makes sense in such a theory. We argue that it does not, in two interrelated ways. In the context of Connes’ spectral triple approach, we show that arbitrarily small regions are not definable in the formal sense. While in the scalar field Moyal–Weyl approach, we show that they cannot be given an operational definition. We conclude that points do not exist in such geometries. We therefore investigate (a) the metaphysics of such a geometry, and (b) how the appearance of smooth manifold might be recovered as an approximation to a fundamental noncommutative geometry.

scholarly journals Reality of the Wigner Functions and Quantization

2009 ◽  
Vol 2009 ◽  
pp. 1-5 ◽  
Author(s):  
Sadollah Nasiri ◽  
Samira Bahrami
Keyword(s):  
Phase Space ◽  
Quantum Statistical Mechanics ◽  
Direct Consequence ◽  
Extended Phase Space ◽  
Extended Phase ◽  
Reality Condition ◽  
Energy Quantization ◽  
Extended Action ◽  
Space Formulation ◽  
Quantum Statistical

Here we use the extended phase space formulation of quantum statistical mechanics proposed in an earlier work to define an extended lagrangian for Wigner's functions (WFs). The extended action defined by this lagrangian is a function of ordinary phase space variables. The reality condition of WFs is employed to quantize the extended action. The energy quantization is obtained as a direct consequence of the quantized action. The technique is applied to find the energy states of harmonic oscillator, particle in the box, and hydrogen atom as the illustrative examples.

scholarly journals Physiological State and Learning Ability of Students in Normal and Virtual Reality Conditions: Complexity-Based Analysis (Preprint)

2020 ◽  
Author(s):  
Mohammad H Babini ◽  
Vladimir V Kulish ◽  
Hamidreza Namazi
Keyword(s):  
Virtual Reality ◽  
Fractal Theory ◽  
Physiological State ◽  
Three Dimensional ◽  
Physiological Signals ◽  
Learning Ability ◽  
Two Dimensional ◽  
Reality Condition ◽  
Computer Mediated ◽  
Dimensional Condition

BACKGROUND Education and learning are the most important goals of all universities. For this purpose, lecturers use various tools to grab the attention of students and improve their learning ability. Virtual reality refers to the subjective sensory experience of being immersed in a computer-mediated world, and has recently been implemented in learning environments. OBJECTIVE The aim of this study was to analyze the effect of a virtual reality condition on students’ learning ability and physiological state. METHODS Students were shown 6 sets of videos (3 videos in a two-dimensional condition and 3 videos in a three-dimensional condition), and their learning ability was analyzed based on a subsequent questionnaire. In addition, we analyzed the reaction of the brain and facial muscles of the students during both the two-dimensional and three-dimensional viewing conditions and used fractal theory to investigate their attention to the videos. RESULTS The learning ability of students was increased in the three-dimensional condition compared to that in the two-dimensional condition. In addition, analysis of physiological signals showed that students paid more attention to the three-dimensional videos. CONCLUSIONS A virtual reality condition has a greater effect on enhancing the learning ability of students. The analytical approach of this study can be further extended to evaluate other physiological signals of subjects in a virtual reality condition.

scholarly journals A spectral triple for noncommutative compact surfaces

2020 ◽  
Vol 120 ◽  
pp. 121-134
Author(s):  
Fredy Díaz García ◽  
Elmar Wagner
Keyword(s):  
Spectral Triple ◽  
Compact Surfaces

scholarly journals On the Koszul formula in noncommutative geometry

2020 ◽  
Vol 32 (10) ◽  
pp. 2050032 ◽  
Author(s):  
Jyotishman Bhowmick ◽  
Debashish Goswami ◽  
Giovanni Landi
Keyword(s):  
Scalar Curvature ◽  
Noncommutative Geometry ◽  
Spectral Triple ◽  
Fuzzy Sphere ◽  
Civita Connection ◽  
Canonical Metric ◽  
Levi Civita Connection

We prove a Koszul formula for the Levi-Civita connection for any pseudo-Riemannian bilinear metric on a class of centered bimodule of noncommutative one-forms. As an application to the Koszul formula, we show that our Levi-Civita connection is a bimodule connection. We construct a spectral triple on a fuzzy sphere and compute the scalar curvature for the Levi-Civita connection associated to a canonical metric.

scholarly journals KK-Theory and Spectral Flow in von Neumann Algebras

2012 ◽  
Vol 10 (2) ◽  
pp. 241-277 ◽  
Author(s):  
J. Kaad ◽  
R. Nest ◽  
A. Rennie
Keyword(s):  
Von Neumann Algebra ◽  
Von Neumann Algebras ◽  
Closed Ideal ◽  
Spectral Triple ◽  
Spectral Flow ◽  
Von Neumann ◽  
Selfadjoint Operators ◽  
Definition Of

AbstractWe present a definition of spectral flow for any norm closed ideal J in any von Neumann algebra N. Given a path of selfadjoint operators in N which are invertible in N/J, the spectral flow produces a class in Ko(J).Given a semifinite spectral triple (A, H, D) relative to (N, τ) with A separable, we construct a class [D] ∈ KK1(A, K(N)). For a unitary u ∈ A, the von Neumann spectral flow between D and u*Du is equal to the Kasparov product [u]A[D], and is simply related to the numerical spectral flow, and a refined C*-spectral flow.

scholarly journals DIFFERENTIAL CALCULUS ON FUZZY SPHERE AND SCALAR FIELD

1998 ◽  
Vol 13 (19) ◽  
pp. 3235-3243 ◽  
Author(s):  
URSULA CAROW-WATAMURA ◽  
SATOSHI WATAMURA
Keyword(s):  
Scalar Field ◽  
Dirac Operator ◽  
Differential Calculus ◽  
Spectral Triple ◽  
Fuzzy Sphere ◽  
Alternative Possibility ◽  
Operator Ordering

We find that there is an alternative possibility to define the chirality operator on the fuzzy sphere, due to the ambiguity of the operator ordering. Adopting this new chirality operator and the corresponding Dirac operator, we define Connes' spectral triple on the fuzzy sphere and the differential calculus. The differential calculus based on this new spectral triple is simplified considerably. Using this formulation the action of the scalar field is derived.

scholarly journals Twisted Reality Condition for Dirac Operators

2016 ◽  
Vol 19 (3) ◽  
Author(s):  
Tomasz Brzeziński ◽  
Nicola Ciccoli ◽  
Ludwik Dąbrowski ◽  
Andrzej Sitarz
Keyword(s):  
Dirac Operators ◽  
Reality Condition
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