scholarly journals FROM SPINOR GEOMETRY TO COMPLEX GENERAL RELATIVITY

2005 ◽  
Vol 02 (04) ◽  
pp. 675-731 ◽  
Author(s):  
GIAMPIERO ESPOSITO
Keyword(s):  
General Relativity ◽  
Minkowski Space ◽  
Dual Space ◽  
Conformal Gravity ◽  
Penrose Transform ◽  
Minkowski Space Time ◽  
Two Component ◽  
Spinor Geometry ◽  
Complex General Relativity ◽  
Component Spinor

An attempt is made of giving a self-contained introduction to holomorphic ideas in general relativity, following work over the last thirty years by several authors. The main topics are complex manifolds, two-component spinor calculus, conformal gravity, α-planes in Minkowski space-time, α-surfaces and twistor geometry, anti-self-dual space-times and Penrose transform, spin-3/2 potentials, heaven spaces and heavenly equations.

EXPLICIT TWO-COMPONENT SPINOR COMMUTATORS FOR QUANTIZED ELECTROMAGNETIC FIELDS

2005 ◽  
Vol 20 (28) ◽  
pp. 6365-6372
Author(s):  
J. G. CARDOSO
Keyword(s):  
Minkowski Space ◽  
Electromagnetic Fields ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Two Component ◽  
Quantum Version ◽  
Complete Set ◽  
Component Spinor

The quantum version of Maxwell's theory in real Minkowski space is utilized for building up a complete set of explicit two-component spinor commutators for electromagnetic fields. It is particularly pointed out that the relevant procedures may be of significance as regards the formulation of twistorial quantum field theories.

scholarly journals Theory of quantum gravity beyond Einstein and space-time dynamics with quantum inflation

2015 ◽  
Vol 30 (28n29) ◽  
pp. 1545002 ◽  
Author(s):  
Yue-Liang Wu
Keyword(s):  
General Relativity ◽  
Quantum Gravity ◽  
Minkowski Space ◽  
Gauge Field ◽  
Gravitational Force ◽  
Proper Time ◽  
Space Time ◽  
Coordinate Space ◽  
Gauge Symmetries ◽  
Minkowski Space Time

In this talk, I present a theory of quantum gravity beyond Einstein. The theory is established based on spinnic and scaling gauge symmetries by treating the gravitational force on the same footing as the electroweak and strong forces. A bi-frame space-time is initiated to describe the laws of nature. One frame space-time is a globally flat coordinate Minkowski space-time that acts as an inertial reference frame for the motions of fields, the other is a locally flat non-coordinate Gravifield space-time that functions as an interaction representation frame for the degrees of freedom of fields. The Gravifield is sided on both the globally flat coordinate space-time and locally flat non-coordinate space-time and characterizes the gravitational force. Instead of the principle of general coordinate invariance in Einstein theory of general relativity, some underlying principles with the postulates of coordinate independence and gauge invariance are motivated to establish the theory of quantum gravity. When transmuting the Gravifield basis into the coordinate basis in Minkowski space-time, it enables us to obtain equations of motion for all quantum fields and derive basic conservation laws for all symmetries. The gravity equation is found to be governed by the total energy–momentum tensor defined in the flat Minkowski space-time. When the spinnic and scaling gauge symmetries are broken down to a background structure that possesses the global Lorentz and scaling symmetries, we arrive at a Lorentz invariant and conformally flat background Gravifield space-time that is characterized by a cosmic vector with a non-zero cosmological mass scale. We also obtain the massless graviton and massive spinnon. The resulting universe is in general not isotropic in terms of conformal proper time and turns out to be inflationary in light of cosmic proper time. The conformal size of the universe has a singular at the cosmological horizon to which the cosmic proper time must be infinitely large. We show a mechanism for quantum inflation caused by the quantum loop contributions. The Gravifield behaves as a Goldstone-like field that transmutes the local spinnic gauge symmetry into the global Lorentz symmetry, which makes the spinnic gauge field becomes a hidden gauge field. As a consequence, the bosonic gravitational interactions can be described by the Goldstone-like Gravimetric field and space-time gauge field. The Einstein theory of general relativity is expected to be an effective low energy theory. Two types of gravity equation are resulted, one is the extension to Einstein’s equation of general relativity, and the other is a new type of gravitational equation that characterizes the spinnon dynamics.

scholarly journals DOTTED AND UNDOTTED ALGEBRAIC SPINOR FIELDS IN GENERAL RELATIVITY

2004 ◽  
Vol 13 (08) ◽  
pp. 1637-1659 ◽  
Author(s):  
E. CAPELAS DE OLIVEIRA ◽  
W. A. RODRIGUES
Keyword(s):  
General Relativity ◽  
Ad Hoc ◽  
Unified Theory ◽  
Spinor Fields ◽  
Covariant Derivatives ◽  
Clifford Bundle ◽  
Two Component ◽  
Theory Of Gravitation ◽  
Derivatives Of ◽  
Component Spinor

We investigate using Clifford algebra methods the theory of algebraic dotted and undotted spinor fields over a Lorentzian spacetime and their realizations as matrix spinor fields, which are the usual dotted and undotted two component spinor fields. We found that some ad hoc rules postulated for the covariant derivatives of Pauli sigma matrices and also for the Dirac gamma matrices in General Relativity cover important physical meaning, which is not apparent in the usual matrix presentation of the theory of two components dotted and undotted spinor fields. We discuss also some issues related to the previous one and which appear in a proposed "unified" theory of gravitation and electromagnetism which use two components dotted and undotted spinor fields and also paravector fields, which are particular sections of the even subundle of the Clifford bundle of spacetime.

scholarly journals SPINOR GEOMETRY

2012 ◽  
Vol 27 (22) ◽  
pp. 1250126 ◽  
Author(s):  
A. NICOLAIDIS ◽  
V. KIOSSES
Keyword(s):  
Quantum Mechanics ◽  
String Theory ◽  
Minkowski Space ◽  
Conformal Symmetry ◽  
Space Time ◽  
Large Network ◽  
Dirac Spinor ◽  
Minkowski Space Time ◽  
Spinor Geometry ◽  
Relational Logic

It has been proposed that quantum mechanics and string theory share a common inner syntax, the relational logic of C. S. Peirce. Along this line of thought we consider the relations represented by spinors. Spinor composition leads to the emergence of Minkowski space–time. Inversely, the Minkowski space–time is istantiated by the Weyl spinors, while the merger of two Weyl spinors gives rise to a Dirac spinor. Our analysis is applied also to the string geometry. The string constraints are represented by real spinors, which create a parametrization of the string worldsheet identical to the Enneper–Weierstass representation of minimal surfaces. Further, a spinorial study of the AdS3 space–time reveals a Hopf fibration AdS3 → AdS2. The conformal symmetry inherent in AdS3 is pointed out. Our work indicates the hidden ties between logic-quantum mechanics-string theory-geometry and vindicates the Wheeler's proposal of pregeometry as a large network of logical propositions.

On generalized partially null Mannheim curves in Minkowski space-time

2016 ◽  
Vol 46 (1) ◽  
pp. 159-170 ◽  
Author(s):  
Emilija Nešović ◽  
Milica Grbović
Keyword(s):  
Minkowski Space ◽  
Space Time ◽  
Minkowski Space Time

scholarly journals Ray-tracing in pseudo-complex General Relativity

2014 ◽  
Vol 442 (1) ◽  
pp. 121-130 ◽  
Author(s):  
T. Schönenbach ◽  
G. Caspar ◽  
P. O. Hess ◽  
T. Boller ◽  
A. Müller ◽  
...  
Keyword(s):  
General Relativity ◽  
Ray Tracing ◽  
Complex General Relativity

scholarly journals A MAXWELL-LIKE FORMULATION OF GRAVITATIONAL THEORY IN MINKOWSKI SPACE–TIME

2007 ◽  
Vol 16 (06) ◽  
pp. 1027-1041 ◽  
Author(s):  
EDUARDO A. NOTTE-CUELLO ◽  
WALDYR A. RODRIGUES
Keyword(s):  
Gravitational Field ◽  
Minkowski Space ◽  
Gravitational Theory ◽  
Space Time ◽  
Lorentzian Geometry ◽  
Field Equations ◽  
Yang Mills ◽  
Minkowski Space Time ◽  
Clifford Bundle ◽  
Gauge Fixing

Using the Clifford bundle formalism, a Lagrangian theory of the Yang–Mills type (with a gauge fixing term and an auto interacting term) for the gravitational field in Minkowski space–time is presented. It is shown how two simple hypotheses permit the interpretation of the formalism in terms of effective Lorentzian or teleparallel geometries. In the case of a Lorentzian geometry interpretation of the theory, the field equations are shown to be equivalent to Einstein's equations.

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