TWISTOR GEOMETRY, SPINOR STRUCTURE AND NATURE OF SUPERSPACE

1989 ◽  
Vol 04 (05) ◽  
pp. 1111-1123 ◽  
Author(s):  
PRATUL BANDYOPADHYAY ◽  
PRADIP GHOSH
Keyword(s):  
Minkowski Space ◽  
Reflection Group ◽  
Internal Symmetry ◽  
Space Time ◽  
Base Space ◽  
Internal Space ◽  
Direction Vector ◽  
Spinor Structure ◽  
Minkowski Space Time ◽  
Time Point

The nature of superspace is studied here from the viewpoint of eight-component conformal spinors which can be split into two Cartan semispinors having two internal helicities corresponding to particle and anti-particle states. This leads to the generation of internal symmetry through reflection group. It is shown that each member of the doublet can be taken to behave as twistors in complexified Minkowski space-time. This helps us to introduce a spinor structure at each space-time point and the spinor coordinate gives rise to the internal helicity. This may be achieved through the introduction of a direction vector attached to each space-time point. Superspace here appears as a bundle space where the base space is the ordinary Minkowski space-time and the spinorial coordinates generated through the introduction of the direction vector from the fibre. This suggests that the internal space of hadrons is anisotropic in nature.

HOLOMORPHIC QUANTUM MECHANICS, CONFORMAL REFLECTION AND THE INTERNAL SYMMETRY OF HADRONS

1989 ◽  
Vol 04 (17) ◽  
pp. 4449-4467 ◽  
Author(s):  
PRATUL BANDYOPADHYAY
Keyword(s):  
Quantum Mechanics ◽  
Minkowski Space ◽  
Composite System ◽  
Conformal Geometry ◽  
Reflection Group ◽  
Internal Symmetry ◽  
Space Time ◽  
Internal Space ◽  
Minkowski Space Time ◽  
Antiparticle State

It is shown here that the holomorphic quantum mechanics in a complexified Minkowski space-time helps us to study the geometrical feature of the internal space of a particle and its relevance with conformal geometry. It is noted that the conformal reflection can be depicted in the formalism of an internal helicity which takes the value [Formula: see text] and [Formula: see text] for the particle and antiparticle state. This again can be described in the framework of holomorphic quantum mechanics in terms of the half-orbital angular momentum of a constituent in an anisotropic space in the sense of Minkowski space-time with a fixed lz value for the particle and antiparticle configuration when a composite system is considered. A massive or massless spinor moving with such characteristic in the configuration of a composite system can be depicted as a Cartan semispinor and behaves as a twistor. The doublet of such spinors with opposite helicities represent an eight-component conformal spinor. The internal symmetry group SU(3) for a composite system of hadrons can then be realized from the reflection group. This formalism reveals the microlocal region of a complexified Minkowski space-time as a twistor space.

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 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.

scholarly journals CHARGED PARTICLES AND THE ELECTRO-MAGNETIC FIELD IN NONINERTIAL FRAMES OF MINKOWSKI SPACE–TIME II: "APPLICATIONS: ROTATING FRAMES, SAGNAC EFFECT, FARADAY ROTATION, WRAP-UP EFFECT"

2010 ◽  
Vol 07 (02) ◽  
pp. 185-213 ◽  
Author(s):  
DAVID ALBA ◽  
LUCA LUSANNA
Keyword(s):  
Minkowski Space ◽  
Faraday Rotation ◽  
Rotating Disk ◽  
Space Time ◽  
Sagnac Effect ◽  
Electro Magnetic Field ◽  
Minkowski Space Time ◽  
Relativistic Extension ◽  
Rotating Frames ◽  
Electro Magnetic

We apply the theory of noninertial frames in Minkowski space–time, developed in the previous paper, to various relevant physical systems. We give the 3 + 1 description without coordinate singularities of the rotating disk and the Sagnac effect, with added comments on pulsar magnetosphere and on a relativistic extension of the Earth-fixed coordinate system. Then we study properties of Maxwell equations in noninertial frames like the wrap-up effect and the Faraday rotation in astrophysics.

scholarly journals Nature itself in a mirror space–time

2015 ◽  
Vol 93 (10) ◽  
pp. 1005-1008 ◽  
Author(s):  
Rasulkhozha S. Sharafiddinov
Keyword(s):  
Dirac Equation ◽  
Minkowski Space ◽  
Space Time ◽  
Point Of View ◽  
Classical Solutions ◽  
Left Handed ◽  
Minkowski Space Time ◽  
Energy And Momentum ◽  
The Right ◽  
Structure Of Matter

The unity of the structure of matter fields with flavor symmetry laws involves that the left-handed neutrino in the field of emission can be converted into a right-handed one and vice versa. These transitions together with classical solutions of the Dirac equation testify in favor of the unidenticality of masses, energies, and momenta of neutrinos of the different components. If we recognize such a difference in masses, energies, and momenta, accepting its ideas about that the left-handed neutrino and the right-handed antineutrino refer to long-lived leptons, and the right-handed neutrino and the left-handed antineutrino are short-lived fermions, we would follow the mathematical logic of the Dirac equation in the presence of the flavor symmetrical mass, energy, and momentum matrices. From their point of view, nature itself separates Minkowski space into left and right spaces concerning a certain middle dynamical line. Thereby, it characterizes any Dirac particle both by left and by right space–time coordinates. It is not excluded therefore that whatever the main purposes each of earlier experiments about sterile neutrinos, namely, about right-handed short-lived neutrinos may serve as the source of facts confirming the existence of a mirror Minkowski space–time.

scholarly journals Generalized Timelike Mannheim Curves in Minkowski Space-Time

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
M. Akyig~it ◽  
S. Ersoy ◽  
İ. Özgür ◽  
M. Tosun
Keyword(s):  
Minkowski Space ◽  
Sufficient Conditions ◽  
Space Time ◽  
Necessary And Sufficient Conditions ◽  
Minkowski Space Time ◽  
Mannheim Curve ◽  
Definition Of ◽  
Necessary And Sufficient

We give the definition of generalized timelike Mannheim curve in Minkowski space-time . The necessary and sufficient conditions for the generalized timelike Mannheim curve are obtained. We show some characterizations of generalized Mannheim curve.

scholarly journals Hermitian realizations of κ-Minkowski space–time

2015 ◽  
Vol 30 (03) ◽  
pp. 1550019 ◽  
Author(s):  
Domagoj Kovačević ◽  
Stjepan Meljanac ◽  
Andjelo Samsarov ◽  
Zoran Škoda
Keyword(s):  
Minkowski Space ◽  
Star Product ◽  
Plane Waves ◽  
Space Time ◽  
Star Products ◽  
Systematic Construction ◽  
Minkowski Space Time ◽  
Noncommutative Plane

General realizations, star products and plane waves for κ-Minkowski space–time are considered. Systematic construction of general Hermitian realization is presented, with special emphasis on noncommutative plane waves and Hermitian star product. Few examples are elaborated and possible physical applications are mentioned.

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