scholarly journals LORENTZ GAUGE THEORY AND SPINOR INTERACTION

2008 ◽  
Vol 23 (08) ◽  
pp. 1282-1285 ◽  
Author(s):  
NAKIA CARLEVARO ◽  
ORCHIDEA MARIA LECIAN ◽  
GIOVANNI MONTANI
Keyword(s):  
Gauge Theory ◽  
Gauge Field ◽  
Lorentz Group ◽  
Flat Space ◽  
Stationary Solutions ◽  
Space Time ◽  
Pauli Equation ◽  
Relativistic Limit ◽  
Curved Space

A gauge theory of the Lorentz group, based on the different behavior of spinors and vectors under local transformations, is formulated in a flat space-time and the role of the torsion field within the generalization to curved space-time is briefly discussed. The spinor interaction with the new gauge field is then analyzed assuming the time gauge and stationary solutions, in the non-relativistic limit, are treated to generalize the Pauli equation.

scholarly journals FERMION DYNAMICS BY INTERNAL AND SPACETIME SYMMETRIES

2009 ◽  
Vol 24 (06) ◽  
pp. 415-427 ◽  
Author(s):  
NAKIA CARLEVARO ◽  
ORCHIDEA MARIA LECIAN ◽  
GIOVANNI MONTANI
Keyword(s):  
Gauge Theory ◽  
Stationary Solutions ◽  
Gauge Fields ◽  
Spacetime Symmetries ◽  
Lorentz Transformations ◽  
Relativistic Limit ◽  
Spinor Structure ◽  
Flat Spacetime ◽  
Fermion Fields

This paper is devoted to introduce a gauge theory of the Lorentz group based on the ambiguity emerging in dealing with isometric diffeomorphism-induced Lorentz transformations. The behaviors under local transformations of fermion fields and spin connections (assumed to be ordinary world vectors) are analyzed in flat spacetime and the role of the torsion field, within the generalization to curved spacetime, is briefly discussed. The fermion dynamics is then analyzed including the new gauge fields and assuming time-gauge. Stationary solutions of the problem are also analyzed in the non-relativistic limit, to study the spinor structure of an hydrogen-like atom.

scholarly journals COVARIANT WIGNER FUNCTION APPROACH TO THE BOLTZMANN EQUATION FOR MIXING FERMIONS IN CURVED SPACE–TIME

2003 ◽  
Vol 18 (24) ◽  
pp. 4469-4484 ◽  
Author(s):  
KAZUHIRO YAMAMOTO
Keyword(s):  
Boltzmann Equation ◽  
Wigner Function ◽  
Gravitational Effect ◽  
Space Time ◽  
Function Approach ◽  
Order Effects ◽  
Relativistic Limit ◽  
Curved Space ◽  
The Boltzmann Equation ◽  
Flavor Oscillation

Based on the covariant Wigner function approach we derive the quantum Boltzmann equation for fermions with flavor mixing in general curved space–time. This work gives a rigorous theoretical framework to investigate the flavor oscillation phenomena taking the gravitational effect into account. It is shown that the Boltzmann equation of the lowest order of the expansion with respect to ℏ reproduces the previous result which was derived in the relativistic limit on the Minkowski background space–time. It is demonstrated that the familiar formula for the vacuum neutrino oscillation can be obtained by solving the Boltzmann equation. Higher order effects of the ℏ-expansion are also briefly discussed.

Zum Übergang von der Wellenoptik zur geometrischen Optik in der allgemeinen Relativitätstheorie

1967 ◽  
Vol 22 (9) ◽  
pp. 1328-1332 ◽  
Author(s):  
Jürgen Ehlers
Keyword(s):  
General Relativity ◽  
Maxwell Equations ◽  
Expansion Method ◽  
Flat Space ◽  
Space Time ◽  
Moving Medium ◽  
Formal Similarity ◽  
Curved Space ◽  
Optical Metric ◽  
Series Expansion Method

The transition from the (covariantly generalized) MAXWELL equations to the geometrical optics limit is discussed in the context of general relativity, by adapting the classical series expansion method to the case of curved space time. An arbitrarily moving ideal medium is also taken into account, and a close formal similarity between wave propagation in a moving medium in flat space time and in an empty, gravitationally curved space-time is established by means of a normal hyperbolic optical metric.

A gauge theory of the Weyl group

1974 ◽  
Vol 340 (1622) ◽  
pp. 249-262 ◽  
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Conservation Laws ◽  
Weyl Group ◽  
Lorentz Group ◽  
Space Time ◽  
Gauge Fields ◽  
Field Equations ◽  
Covariant Derivatives ◽  
The World

The construction of field theory which exhibits invariance under the Weyl group with parameters dependent on space–time is discussed. The method is that used by Utiyama for the Lorentz group and by Kibble for the Poincaré group. The need to construct world-covariant derivatives necessitates the introduction of three sets of gauge fields which provide a local affine connexion and a vierbein system. The geometrical implications are explored; the world geometry has an affine connexion which is not symmetric but is semi-metric. A possible choice of Lagrangian for the gauge fields is presented, and the resulting field equations and conservation laws discussed.

4 + n -dimensional Topoisomerase-like Waves

2018 ◽  
Author(s):  
Alireza Sepehri
Keyword(s):  
Extra Dimensions ◽  
Dimensional Space ◽  
Space Time ◽  
Dimensional Manifold ◽  
Curved Space ◽  
New Model ◽  
Exchange Information ◽  
Dimensional Space Time ◽  
Dimensional Object

In this paper, we propose a new model which allows to consider all evolutions of DNA from viewpoint of an observer on 11-dimensional manifold. In this model, DNA is an 4 + n-dimensional object in 11 dimensional space-time which is compacted to 4-dimensional manifold. This leads to the emergence of a curved space-time around DNA and production of some new waves. To exchange information between DNAs, it is needed that waves play the role of topoisomerases in extra dimensions. These topoisomerase-like waves open packings of DNA, read it’s information and compact it again. The shape and properties of these waves are completely different from gravitational and electromagnetic ones. By reducing dimensions from 11 to 4, the topoisomerase-like waves obtain the properties of known fields like gravitons and photons.

Time, Topology, and the Twin Paradox

2011 ◽  
Author(s):  
Jean‐Pierre Luminet
Keyword(s):  
High Speed ◽  
Reference Frames ◽  
Thought Experiment ◽  
Flat Space ◽  
Space Time ◽  
Twin Paradox ◽  
Theory Of Relativity ◽  
Apparent Paradox ◽  
Curved Space ◽  
Gravitational Fields

This chapter notes that the twin paradox is the best-known thought experiment associated with Einstein's theory of relativity. An astronaut who makes a journey into space in a high-speed rocket will return home to find he has aged less than his twin who stayed on Earth. This result appears puzzling, as the homebody twin can be considered to have done the travelling with respect to the traveller. Hence, it is called a “paradox”. In fact, there is no contradiction, and the apparent paradox has a simple resolution in special relativity with infinite flat space. In general relativity (dealing with gravitational fields and curved space-time), or in a compact space such as the hypersphere or a multiply connected finite space, the paradox is more complicated, but its resolution provides new insights about the structure of space–time and the limitations of the equivalence between inertial reference frames.

THE ASYMPTOTICALLY FREE AND ASYMPTOTICALLY CONFORMALLY INVARIANT GRAND UNIFICATION THEORIES IN CURVED SPACE-TIME

1990 ◽  
Vol 05 (20) ◽  
pp. 1599-1604 ◽  
Author(s):  
I.L. BUCHBINDER ◽  
I.L. SHAPIRO ◽  
E.G. YAGUNOV
Keyword(s):  
Renormalization Group ◽  
Gravitational Field ◽  
Gauge Group ◽  
Flat Space ◽  
Space Time ◽  
Grand Unification ◽  
Curved Space ◽  
Conformally Invariant ◽  
Renormalization Group Equations ◽  
The One

GUT’s in curved space-time is considered. The set of asymptotically free and asymptotically conformally invariant models based on the SU (N) gauge group is constructed. The general solutions of renormalization group equations are considered as the special ones. Several SU (2N) models, which are finite in flat space-time (on the one-loop level) and asymptotically conformally invariant in external gravitational field are also presented.

One-loop effective action for the gauge field in curved space-time

1998 ◽  
Vol 117 (1) ◽  
pp. 1208-1213 ◽  
Author(s):  
V. Ch. Zhukovskii ◽  
I. V. Mamsurov
Keyword(s):  
Gauge Field ◽  
Effective Action ◽  
Space Time ◽  
Curved Space

A Class of Energetically Rigid Gravitational Fields

1974 ◽  
Vol 29 (11) ◽  
pp. 1527-1530 ◽  
Author(s):  
H. Goenner
Keyword(s):  
Flat Space ◽  
Second Fundamental Form ◽  
Momentum Tensor ◽  
Space Time ◽  
Curved Space ◽  
Geometrical Properties ◽  
Gravitational Fields ◽  
The Second Fundamental Form ◽  
Perfect Fluids ◽  
Higher Dimensional

In Einstein's theory, the physics of gravitational fields is reflected by the geometry of the curved space-time manifold. One of the methods for a study of the geometrical properties of space-time consists in regarding it, locally, as embedded in a higher-dimensional flat space. In this paper, metrics admitting a 3-parameter group of motion are considered which form a generalization of spherically symmetric gravitational fields. A subclass of such metrics can be embedded into a five- dimensional flat space. It is shown that the second fundamental form governing the embedding can be expressed entirely by the energy-momentum tensor of matter and the cosmological constant. Such gravitational fields are called energetically rigid. As an application gravitating perfect fluids are discussed.

Sign in / Sign up

Export Citation Format

Share Document