scholarly journals COMPLEX GRAVITY AND NONCOMMUTATIVE GEOMETRY

2001 ◽  
Vol 16 (05) ◽  
pp. 759-766 ◽  
Author(s):  
ALI H. CHAMSEDDINE
Keyword(s):  
Noncommutative Geometry ◽  
Space Time ◽  
Specific Form ◽  
Antisymmetric Tensor ◽  
Gauge Invariant ◽  
Diffeomorphism Invariance ◽  
Open Strings ◽  
Noncommutative Spaces

The presence of a constant background antisymmetric tensor for open strings or D-branes forces the space-time coordinates to be noncommutative. An immediate consequence of this is that all fields get complexified. By applying this idea to gravity one discovers that the metric becomes complex. Complex gravity is constructed by gauging the symmetry U(1, D-1). The resulting action gives one specific form of nonsymmetric gravity. In contrast to other theories of nonsymmetric gravity the action is both unique and gauge invariant. It is argued that for this theory to be consistent one must prove the existence of generalized diffeomorphism invariance. The results are easily generalized to noncommutative spaces.

scholarly journals THE ADHM CONSTRUCTION OF INSTANTONS ON NONCOMMUTATIVE SPACES

2011 ◽  
Vol 23 (03) ◽  
pp. 261-307 ◽  
Author(s):  
SIMON BRAIN ◽  
WALTER D. VAN SUIJLEKOM
Keyword(s):  
Euclidean Space ◽  
Noncommutative Geometry ◽  
Space Time ◽  
Point Of View ◽  
Noncommutative Space ◽  
Special Cases ◽  
Noncommutative Spaces ◽  
Coordinate Algebra ◽  
Classical Construction

We present an account of the ADHM construction of instantons on Euclidean space-time ℝ4 from the point of view of noncommutative geometry. We recall the main ingredients of the classical construction in a coordinate algebra format, which we then deform using a cocycle twisting procedure to obtain a method for constructing families of instantons on noncommutative space-time, parametrized by solutions to an appropriate set of ADHM equations. We illustrate the noncommutative construction in two special cases: the Moyal–Groenewold plane [Formula: see text] and the Connes–Landi plane [Formula: see text].

SPIN-1/2 GAUGE FIELD REVISITED

1993 ◽  
Vol 08 (28) ◽  
pp. 2643-2648
Author(s):  
KAZUNARI SHIMA
Keyword(s):  
Gauge Symmetry ◽  
Gauge Field ◽  
Lagrange Multiplier ◽  
Space Time ◽  
Antisymmetric Tensor ◽  
Gauge Invariant ◽  
Rank Tensor ◽  
Higher Spin

The gauge symmetry for spin-1/2 field proposed in the previous paper by using second rank tensor-spinors is re-investigated. The constraints which are essential for eliminating higher spin components are re-examined and reformulated by using a traceless antisymmetric tensor-spinor Lagrange multiplier in a gauge-invariant way. The gauge symmetry is compatible with the space-time with (anti)self-dual Riemann curvatures.

scholarly journals The effects of quantum spectrum of 4 + n-dimensional water around a DNA on pure water in four dimensional universe

Open Physics ◽  
2019 ◽  
Vol 17 (1) ◽  
pp. 831-838
Author(s):  
Massimo Fioranelli ◽  
Alireza Sepehri ◽  
Maria Grazia Roccia ◽  
Mahdieh Ghasemi
Keyword(s):  
String Theory ◽  
Extra Dimension ◽  
Extra Dimensions ◽  
Pure Water ◽  
Space Time ◽  
Dimensional Manifold ◽  
Curved Space ◽  
Open Strings ◽  
Long Time ◽  
Quantum Spectrum

Abstract Recently, a method for calculating the quantum spectrum of black holes has been proposed. We show that this method can be applied for radiations of 4 + n - dimensional water around a DNA. In this model, DNA acts like a black hole and produces a curved space-time in a water around it. In these conditions, molecules of water in four dimensional universe are entangled with some DNA-like structures in extra dimension. Consequently, the effects of structures of water in extra dimensions can be observed in four dimensions. The entangled structures emit some quantum spectrum which can be transmitted to pure waters. These waves produce a curved space-time in pure water and make an entanglement between structure of water on four and DNA-like structures in extra dimensions. As a result, some signatures of DNAs can be observed in pure water. This model helps us to understand the reason for the emergence of life on the earth. To explain the model better, we unify Darwin’s theory with string theory in a new Darwinian’s string theory. In this theory, a zero dimensional manifold decays into two types of closed strings. One type decays into open strings and then these strings join to each other and form cosmos. Another type decays into open strings which form biological matters like DNAs and molecules of water in universe and anti-DNAs and anti-water in anti-universe. Thus, DNAs and molecules water are connected to each other and anti-DNAs and molecules of anti-water in anti-universe through some closed strings. These strings helps to molecules of water to store their informations in extra dimension and have long time memory. Because, information that are transformed into extra dimensions through closed strings, could be returned into universe. Also, these closed strings could have the main role in DNA transduction. Because, they connect two tubes one including water and DNA and another pure water in universe to two tubes including anti-DNA and water in anti-universe and transform properties of DNA into pure water. As a result, Darwinian string theory can confirm both water memory and DNA transduction. Finally, this theory response to this question that why memory of water couldnt remain for a long time. In this model, open strings which connects atoms in universe with anti-atoms in anti-universe interact with open strings which connects molecules of water and anti-water and decrease their entanglement. This causes that exchanging information between water and anti-water decreases and memory is dis-appeared.

scholarly journals Quantum geometrodynamics with intrinsic time development

2016 ◽  
Vol 25 (13) ◽  
pp. 1645008 ◽  
Author(s):  
Chopin Soo
Keyword(s):  
Paradigm Shift ◽  
Time Development ◽  
Gauge Invariant ◽  
Problem Of Time ◽  
Diffeomorphism Invariance ◽  
Intrinsic Time ◽  
Natural Extensions ◽  
The Universe ◽  
Quantum Geometrodynamics ◽  
Einstein’S General Relativity

Quantum geometrodynamics with intrinsic time development is presented. Paradigm shift from full spacetime covariance to spatial diffeomorphism invariance yields a nonvanishing Hamiltonian, a resolution of the ‘problem of time’ and gauge-invariant temporal ordering in an ever expanding universe. Einstein’s general relativity is a particular realization of a wider class of theories; and the framework prompts natural extensions and improvements with the consequent dominance of Cotton–York potential at early times when the universe was small.

scholarly journals SCHWINGER'S RESULT ON PARTICLE PRODUCTION FROM COMPLEX PATHS WKB APPROXIMATION

2000 ◽  
Vol 15 (23) ◽  
pp. 3717-3731 ◽  
Author(s):  
S. BISWAS ◽  
A. SHAW ◽  
B. MODAK
Keyword(s):  
Electric Field ◽  
Particle Production ◽  
Complex Space ◽  
Space Time ◽  
Wkb Approximation ◽  
Uniform Electric Field ◽  
Gauge Invariant ◽  
Transmission Coefficients ◽  
Loop Approximation ◽  
Complex Trajectory

This paper presents the derivation of Schwinger's gauge-invariant result of Im ℒ eff up to one loop approximation, for particle production in an uniform electric field through the method of complex trajectory WKB approximation (CWKB). The CWKB proposed by one of the authors1 looks upon particle production as being due to the motion of a particle in complex space–time plane, thereby requiring tunneling paths both in space and time. Recently2,3 there have been some efforts to calculate the reflection and the transmission coefficients for particle production in an uniform electric field that differ from our expressions for the same. In this paper we clarify the confusion in this regard and establish the correctness of CWKB.

scholarly journals Integrability conditions for the Bianchi identities as transformations in Schwarzschild space-time

1999 ◽  
Vol 41 (2) ◽  
pp. 260-270
Author(s):  
J. F. Q. Fernandes ◽  
A. W.-C. Lun
Keyword(s):  
Space Time ◽  
Gauge Invariant ◽  
Bianchi Identities ◽  
Schwarzschild Geometry ◽  
Integrability Conditions ◽  
The Relationship ◽  
Coordinate Gauge

AbstractWe investigate the relationship between the Bardeen-Press and the Regge-Wheeler equations for perturbations of the Schwarzschild geometry. We examine how tetrad and coordinate gauge invariant Regge-Wheeler field quantities arise naturally from the perturbed Bianchi identities in the modified Newman-Penrose (compacted spincoefficient) formalism. The integrability conditions for the Bianchi identities then provide the transformation identities relating these quantities to the Bardeen-Press quantities. The relationships between the Bardeen-Press quantities of opposite spin-weight also arise naturally in our approach.

Sectional Curvature and Chaos in Dynamical Problems: Toward the Invariant Measure of Chaos in Hamiltonian Systems

1993 ◽  
Vol 46 (7) ◽  
pp. 427-437 ◽  
Author(s):  
Marek Szydłowski ◽  
Adam Krawiec
Keyword(s):  
General Relativity ◽  
Invariant Measure ◽  
Coordinate System ◽  
Sectional Curvature ◽  
Hamiltonian Systems ◽  
Invariant Theory ◽  
Space Time ◽  
Gauge Invariant ◽  
Time Coordinate ◽  
Physical Description

Chaotic phenomena in general relativity are investigated. In relativistic astrophysical problems no space-time coordinate system is privileged in any way as far as the physical description of phenomena is concerned. Effects which depend on the choice of the particular coordinate system should be treated as an artifact of the incorrect methods. To avoid such difficulties the gauge invariant theory of chaos is proposed.

scholarly journals A LARGE CLASS OF NEW GRAVITATIONAL AND AXIONIC BACKGROUNDS FOR FOUR-DIMENSIONAL SUPERSTRINGS

1994 ◽  
Vol 09 (08) ◽  
pp. 1361-1393 ◽  
Author(s):  
E. KIRITSIS ◽  
C. KOUNNAS ◽  
D. LÜST
Keyword(s):  
Superstring Vacua ◽  
Large Class ◽  
Space Time ◽  
Antisymmetric Tensor ◽  
Tensor Fields ◽  
Background Fields ◽  
Killing Symmetries ◽  
Calabi Yau Manifolds

A large class of new 4D superstring vacua with nontrivial/singular geometries, space–time supersymmetry and other background fields (axion, dilaton) are found. Killing symmetries are generic and are associated with nontrivial dilaton and antisymmetric tensor fields. Duality symmetries preserving N = 2 superconformal invariance are employed to generate a large class of explicit metrics for noncompact 4D Calabi–Yau manifolds with Killing symmetries. We comment on some of our solutions which have interesting singularity properties and cosmological interpretation.

EXACT SOLUTIONS FOR SELF-DUAL SU(2) GAUGE THEORY WITH AXIAL SYMMETRY

2001 ◽  
Vol 16 (11) ◽  
pp. 685-692 ◽  
Author(s):  
G. ZET ◽  
V. MANTA ◽  
C. BANDAC
Keyword(s):  
Gauge Theory ◽  
Axial Symmetry ◽  
Dimensional Space ◽  
Space Time ◽  
Field Equations ◽  
Metric Tensor ◽  
Gauge Invariant ◽  
Local Gauge ◽  
Dimensional Space Time ◽  
Strength Tensor

A model of SU(2) gauge theory is constructed in terms of local gauge-invariant variables defined over a four-dimensional space–time endowed with axial symmetry. A metric tensor gμν is defined starting with the components [Formula: see text] of the strength tensor and its dual [Formula: see text]. The components gμν are interpreted as new local gauge-invariant variables. Imposing the condition that the new metric coincides with the initial metric we obtain the field equations for the considered ansatz. We obtain the same field equations using the condition of self-duality. It is concluded that the self-dual variables are compatible with the axial symmetry of the space–time. A family of analytical solutions of the gauge field equations is also obtained. The solutions have the confining properties. All the calculations are performed using the GRTensorII computer algebra package, running on the MapleV platform.

scholarly journals Noncommutative geometry and structure of space–time

2018 ◽  
Vol 31 (1) ◽  
pp. 15-27
Author(s):  
Ali H. Chamseddine
Keyword(s):  
Noncommutative Geometry ◽  
Space Time
Sign in / Sign up

Export Citation Format

Share Document