Three-dimensional group manifold reductions of gravity

2005 ◽  
Author(s):  
Román Linares
Keyword(s):  
Three Dimensional ◽  
Dimensional Group ◽  
Group Manifold

QUANTUM FIELDS ON CURVED MOMENTUM SPACE

2012 ◽  
Vol 09 (06) ◽  
pp. 1261002
Author(s):  
MICHELE ARZANO
Keyword(s):  
Momentum Space ◽  
Three Dimensional ◽  
Point Function ◽  
Commutative Field ◽  
Group Manifold ◽  
Poincaré Algebra ◽  
Definition Of ◽  
Group Symmetries ◽  
Field Quantization ◽  
Relativistic Particles

Relativistic particles with momentum space described by a group manifold provide a very interesting link between gravity, quantum group symmetries and non-commutative field theories. We discuss how group valued momenta emerge in the context of three-dimensional Einstein gravity and describe the related non-commutative field theory. As an application we introduce a non-commutative heat-kernel, calculate the associated spectral dimension and comment on its non-trivial behavior. In four spacetime dimensions the only known example of momenta living on a group manifold is encountered in the context of the κ-Poincaré algebra introduced by Lukierski et al. 20 years ago. I will discuss the construction of a one-particle Hilbert space from the classical κ-deformed phase space and show how the group manifold structure of momentum space leads to an ambiguity in the quantization procedure. The tools introduced in the discussion of field quantization lead to a natural definition of deformed two-point function.

scholarly journals Generalized spinning particles on $${\mathcal {S}}^2$$ in accord with the Bianchi classification

2021 ◽  
Vol 81 (3) ◽  
Author(s):  
Anton Galajinsky
Keyword(s):  
External Field ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Degrees Of Freedom ◽  
Scalar Potential ◽  
Three Dimensional ◽  
Dirac Monopole ◽  
Spinning Particles ◽  
Group Manifold ◽  
Internal Degrees Of Freedom

AbstractMotivated by recent studies of superconformal mechanics extended by spin degrees of freedom, we construct minimally superintegrable models of generalized spinning particles on $${\mathcal {S}}^2$$ S 2 , the internal degrees of freedom of which are represented by a 3-vector obeying the structure relations of a three-dimensional real Lie algebra. Extensions involving an external field of the Dirac monopole, or the motion on the group manifold of SU(2), or a scalar potential giving rise to two quadratic constants of the motion are discussed. A procedure how to build similar models, which rely upon real Lie algebras with dimensions $$d=4,5,6$$ d = 4 , 5 , 6 , is elucidated.

Analysis and Simulation of a Micro Hydrocyclone Device for Particle Liquid Separation

2012 ◽  
Vol 134 (2) ◽  
Author(s):  
P. Bagdi ◽  
P. Bhardwaj ◽  
A. K. Sen
Keyword(s):  
Stokes Equations ◽  
Separation Efficiency ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Group Model ◽  
Operational Parameters ◽  
Lab On Chip ◽  
Dimensional Group ◽  
Simulation Results ◽  
On Chip

This paper presents a three-dimensional simulation of a micro hydrocyclone for the separation of micron sized particles from liquid in a particulated sample. A theoretical analysis is performed to demonstrate the working principle of the micro hydrocyclone and develop design models. The geometry of the proposed device is designed based on the Bradley model, since it offers a lower cut-size, thus making it suitable for microfluidics applications. The operational parameters of the hydrocyclone are derived from a dimensional group model. The particle separation process inside the micro hydrocyclone is simulated by solving fluid flows using Navier-Stokes equations and particle dynamics using the Lagrangian approach in a Eulerean fluid. First, the numerical model is validated by comparing the simulation results with the experimental results for a macroscale hydrocyclone reported in the literature. Then, the micro hydrocyclone is simulated and the simulation results are presented and discussed in the context of the functioning of the micro hydrocyclone. Finally, the effects of inlet velocity, vortex finder diameter, particle size, and density on the separation efficiency are investigated. The proposed device can be easily integrated with micro-environments; thus, is suitable for lab-on-chip and microsystems development.

scholarly journals E6(6) exceptional Drinfel’d algebras

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Emanuel Malek ◽  
Yuho Sakatani ◽  
Daniel C. Thompson
Keyword(s):  
Tangent Bundle ◽  
Leibniz Algebra ◽  
Baxter Equation ◽  
Duality Group ◽  
Dimensional Group ◽  
Drinfel’D Double ◽  
Group Manifold ◽  
Natural Generalisation ◽  
M Theory ◽  
Selection Of

Abstract The exceptional Drinfel’d algebra (EDA) is a Leibniz algebra introduced to provide an algebraic underpinning with which to explore generalised notions of U-duality in M-theory. In essence, it provides an M-theoretic analogue of the way a Drinfel’d double encodes generalised T-dualities of strings. In this note we detail the construction of the EDA in the case where the regular U-duality group is E6(6). We show how the EDA can be realised geometrically as a generalised Leibniz parallelisation of the exceptional generalised tangent bundle for a six-dimensional group manifold G, endowed with a Nambu-Lie structure. When the EDA is of coboundary type, we show how a natural generalisation of the classical Yang-Baxter equation arises. The construction is illustrated with a selection of examples including some which embed Drinfel’d doubles and others that are not of this type.

scholarly journals Limits of JT gravity

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Daniel Grumiller ◽  
Jelle Hartong ◽  
Stefan Prohazka ◽  
Jakob Salzer
Keyword(s):  
Boundary Conditions ◽  
Light Cone ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Hamiltonian Reduction ◽  
Dilaton Gravity ◽  
Group Manifold ◽  
Particle Action

Abstract We construct various limits of JT gravity, including Newton-Cartan and Carrollian versions of dilaton gravity in two dimensions as well as a theory on the three-dimensional light cone. In the BF formulation our boundary conditions relate boundary connection with boundary scalar, yielding as boundary action the particle action on a group manifold or some Hamiltonian reduction thereof. After recovering in our formulation the Schwarzian for JT, we show that AdS-Carroll gravity yields a twisted warped boundary action. We comment on numerous applications and generalizations.

Matching angular and vector descriptions of three-dimensional group point objects

2012 ◽  
Vol 48 (6) ◽  
pp. 537-549 ◽  
Author(s):  
Ya. A. Furman ◽  
I. L. Egoshina ◽  
R. V. Eruslanov
Keyword(s):  
Three Dimensional ◽  
Dimensional Group

ON TYPE II SUPERSTRINGS: THE σ MODEL AND COMPACTIFICATION TO D=4

1991 ◽  
Vol 06 (22) ◽  
pp. 4009-4039 ◽  
Author(s):  
LEONARDO CASTELLANI ◽  
RICCARDO D’ AURIA ◽  
DAVIDE FRANCO
Keyword(s):  
Dimensional Reduction ◽  
Geometric Construction ◽  
Covering Space ◽  
Type Ii ◽  
Internal Target ◽  
Dimensional Group ◽  
Group Manifold ◽  
Target Manifold

We present a geometric construction of the σ model describing type II superstrings propagating on an arbitrary Mtarget. Specializing the covering space of the internal target manifold to be the nine-dimensional group manifold SU(2)3, we discuss the massless vertices both in the (4+9)-dimensional a model and in the D=4 superconformal theory, and show how they are related via dimensional reduction.

scholarly journals Scaling behavior of three-dimensional group field theory

2009 ◽  
Vol 26 (18) ◽  
pp. 185012 ◽  
Author(s):  
Jacques Magnen ◽  
Karim Noui ◽  
Vincent Rivasseau ◽  
Matteo Smerlak
Keyword(s):  
Field Theory ◽  
Three Dimensional ◽  
Scaling Behavior ◽  
Dimensional Group ◽  
Group Field Theory

TRANSVERSE ISOTROPIC CRUST STRUCTURE BENEATH THE NORTHWEST AND CENTRAL NORTH ANATOLIA REVEALED BY SEISMIC SURFACE WAVES PROPAGATION

2020 ◽  
Vol 5 (2) ◽  
pp. 41-50
Author(s):  
Özcan Çakır
Keyword(s):  
Surface Waves ◽  
Lower Crust ◽  
Transverse Isotropy ◽  
Three Dimensional ◽  
Phase Speed ◽  
Upper Crust ◽  
One Dimensional ◽  
Dimensional Group ◽  
Single Station ◽  
Seismic Surface Waves

The Anatolian crust, which is abnormally hot, is widely deformed by subduction related volcanism. Suture zones, transform faults, thrusts and folds and metamorphic core complexes add to the geological complexity. Volcanic provinces such as Western, Central and Eastern Anatolia and Galatea are recognized as distinct features in the region. The middle-to-lower crust depths appear to be intruded by horizontal sills and the upper crust by vertical dykes. Both horizontal sills and vertical dykes leave anisotropic signs detected as Vertical Transverse Isotropy (VTI) that is explored by Love and Rayleigh surface wave inversions, i.e., Love-Rayleigh wave discrepancy which arises because the dykes and sills act differently against the Love and Rayleigh surface waves. The current study gives emphasis to the Northwest and Central North Anatolia utilizing both single-station and two-station tomography techniques to recover the two-dimensional group and phase speed charts from which one-dimensional dispersion inversions are implemented. The one-dimensional inversions are joined to construct the three-dimensional crust of the studied region. The shear-wave anisotropy is used to locate the anisotropy in the crust. The vertical dykes in the upper crust fit into negative VTI around -10% while the horizontal sills in the middle-to-lower crust yield positive VTI around 12%. The vertical magma flows within the vertical dykes and the horizontal magma flows within the horizontal sills contribute constructively to the anisotropy created by the special shape orientations of sills and dykes. The earthquakes hypocenter distribution and high and low speeds alongside the VTI provide significant clues to differentiate between diverse geological districts.

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