Unified geometry of internal space with space-time

1975 ◽  
Vol 12 (12) ◽  
pp. 3789-3792 ◽  
Author(s):  
Y. M. Cho ◽  
Pong Soo Jang
Keyword(s):  
Space Time ◽  
Internal Space

scholarly journals A bulk localized state and new holographic renormalization group flow in 3D spin-3 gravity

2018 ◽  
Vol 33 (12) ◽  
pp. 1850061 ◽  
Author(s):  
Ryuichi Nakayama ◽  
Tomotaka Suzuki
Keyword(s):  
Renormalization Group ◽  
Scalar Field ◽  
Central Charge ◽  
Dimensional Space ◽  
Space Time ◽  
Internal Space ◽  
Conformal Weight ◽  
Weight Changes ◽  
Localized State ◽  
Bulk Space

We construct a localized state of a scalar field in 3D spin-3 gravity. 3D spin-3 gravity is thought to be holographically dual to [Formula: see text]-extended CFT on a boundary at infinity. It is known that while [Formula: see text] algebra is a nonlinear algebra, in the limit of large central charge [Formula: see text] a linear finite-dimensional subalgebra generated by [Formula: see text] [Formula: see text] and [Formula: see text] [Formula: see text] is singled out. The localized state is constructed in terms of these generators. To write down an equation of motion for a scalar field which is satisfied by this localized state, it is necessary to introduce new variables for an internal space [Formula: see text], [Formula: see text], [Formula: see text], in addition to ordinary coordinates [Formula: see text] and [Formula: see text]. The higher-dimensional space, which combines the bulk space–time with the “internal space,” which is an analog of superspace in supersymmetric theory, is introduced. The “physical bulk space–time” is a 3D hypersurface with constant [Formula: see text], [Formula: see text] and [Formula: see text] embedded in this space. We will work in Poincaré coordinates of AdS space and consider [Formula: see text]-quasi-primary operators [Formula: see text] with a conformal weight [Formula: see text] in the boundary and study two and three point functions of [Formula: see text]-quasi-primary operators transformed as [Formula: see text]. Here, [Formula: see text] and [Formula: see text] are [Formula: see text] generators in the hyperbolic basis for Poincaré coordinates. It is shown that in the [Formula: see text] limit, the conformal weight changes to a new value [Formula: see text]. This may be regarded as a Renormalization Group (RG) flow. It is argued that this RG flow will be triggered by terms [Formula: see text] added to the action.

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.

Gravitational interactions in the Dirac spinor fields and possible structure of local space-time of fermions

2021 ◽  
pp. 129-135
Author(s):  
V.G. Krechet ◽  
◽  
V.B. Oshurko ◽  
A.E. Baidin ◽  
◽  
...  
Keyword(s):  
General Relativity ◽  
Magnetic Moment ◽  
Spinor Field ◽  
Space Time ◽  
Spin Interaction ◽  
Internal Space ◽  
Dirac Spinor ◽  
Geometric Properties ◽  
Spinor Fields ◽  
Local Space

In the framework of general relativity, possible effects of the gravitational interactions in the Dirac spinor field are considered. It is shown that these interactions manifest locally as contact spin-spin interaction of the gravitational and spinor fields. This interaction leads to the classical rotation of particles with spin ħ /2. As a result, it leads to appearance of local internal space-time with specific geometric properties for each particle. New effect of an increase of the mass of spinor particles due to this interaction is found. Also, an explanation of the existence of a magnetic moment in Dirac spinor particles as a result of a local electro-spin-spin interaction has been proposed.

scholarly journals Group Contractions: Inonu, Wigner, and Einstein

1997 ◽  
Vol 12 (01) ◽  
pp. 71-78 ◽  
Author(s):  
Y.S. Kim
Keyword(s):  
Degrees Of Freedom ◽  
Small Mass ◽  
Space Time ◽  
Internal Space ◽  
Large Momentum ◽  
Energy Relation ◽  
Large Radius ◽  
Massless Particles ◽  
Massive Particles

Einstein's E = mc2 unifies the momentum-energy relation for massive and massless particles. According to Wigner, the internal space–time symmetries of massive and massless particles are isomorphic to O(3) and E(2) respectively. According to Inonu and Wigner, O(3) can be contracted to E(2) in the large-radius limit. It is noted that the O(3)-like little group for massive particles can be contracted to the E(2)-like little group for massless particles in the limit of large momentum and/or small mass. It is thus shown that transverse rotational degress of freedom for massive particles become contracted to gauge degrees of freedom for massless particles.

Charge conjugation and internal space-time symmetries

1982 ◽  
Vol 35 (10) ◽  
pp. 352-352
Author(s):  
M. Pavšić ◽  
E. Recami
Keyword(s):  
Space Time ◽  
Charge Conjugation ◽  
Internal Space

ON THE STRUCTURE OF PHYSICAL SPACE

2001 ◽  
Vol 16 (24) ◽  
pp. 4045-4055 ◽  
Author(s):  
DANIEL WISNIVESKY
Keyword(s):  
Electromagnetic Coupling ◽  
Lorentz Invariance ◽  
Electroweak Interaction ◽  
Physical Space ◽  
Building Blocks ◽  
Space Time ◽  
Coupling Constants ◽  
Internal Space ◽  
External Space ◽  
Physical Phenomena

In this paper we develop a theory based on the postulate that the environment where physical phenomena take place is the space of four complex parameters of the linear group of transformations. Using these parameters as fundamental building blocks we construct ordinary space–time and the internal space. Lorentz invariance is built in the definition of external space, while the symmetry of the internal space, S(1)×SU(2) results as a consequence of the identification of the external coordinates. Thus, special relativity and the electroweak interaction symmetry ensue from the properties of the basic building blocks of physical space. Since internal and external space are derived from a common structure, there is no need to bring into the theory any additional hypothesis to account for the microscopic nature of the internal space, nor to introduce symmetry breaking mechanisms that would normally be required to force a splitting of the internal and external symmetries. As an outcome of the existence of a basic structure underlying the external space–time, the weak and electromagnetic coupling constants are not independent and the Weinberg weak mixing angle is derived from the theory. In this new theory, there is an interrelationship between external and internal transformations, which leads to the quantization of electric charge. Finally we conclude that the electroweak gauge theory can be regarded as a consequence of Einstein's general theory of relativity. The proposed theory represents an extension of the normally accepted theory and includes it as a particular case. This paper is an attempt to formulate a new framework in which the physical phenomena take place, and to explore some of its consequences.

A new approach on electromagnetism with dual number coefficient octonion algebra

2016 ◽  
Vol 13 (09) ◽  
pp. 1630013 ◽  
Author(s):  
Bhupesh Chandra Chanyal ◽  
Sunil Kumar Chanyal ◽  
Özcan Bektaş ◽  
Salim Yüce
Keyword(s):  
Maxwell Equations ◽  
Wave Equations ◽  
Space Time ◽  
Internal Space ◽  
Field Equations ◽  
Octonion Algebra ◽  
New Approach ◽  
Dual Number ◽  
Symmetrical Form ◽  
Unit Formula

Dual number coefficient octonion (DNCO) is one of the kind of octonion, it has 16 components with an additional dual unit [Formula: see text]. Starting with DNCO algebra, we develop the generalized electromagnetic field equations of dyons regarding the DNCOS spaces, which has two octonionic space-times namely the octonionic internal space-time and the octonionic external space-time. Besides, the generalized four-potential components of dyons have been expressed with respect to the dual octonion form. Furthermore, we obtain the symmetrical form of Dirac–Maxwell equations, and the generalized potential wave equations for dyons in terms of the dual octonion. Finally, we conclude that dual octonion formulation is compact and simpler like octonion formulation.

Sign in / Sign up

Export Citation Format

Share Document