Lagrange multiplier and Wess-Zumino variable as large extra dimensions in the torus universe

Abstract

We study the effect of the topology of universe by gauging the non-relativistic particle model on the torus and 3-torus, using the symplectic formalism of constrained systems and embedding those models on extended phase-spaces. Also, we obtain the generators of the gauge transformations for gauged models. Extracting the corresponding Poisson structure of the existed constraints, we show the effect of the topology on the canonical structure of the phase-spaces of those models and suggest some phenomenology to prove the topology of the universe and probable non-commutative structure of the space. In addition, we show that the number of large extra dimensions in the Phase-spaces of the gauged embeded models are exactly two. Moreover, in the classical form, we talk over MOND theory in order to study the origin of the terms appeared in the gauged theory, which modify the Newton's second law.

Major revision: text and contents corrected and recovered thanks to unknown journal referee. Many refs added. Final version which will be published in the journal

References in corpus (45)

• A Large Mass Hierarchy from a Small Extra Dimension
• An Alternative to Compactification
• The Hierarchy Problem and New Dimensions at a Millimeter
• Dirichlet-Branes and Ramond-Ramond Charges
• Phenomenology, Astrophysics and Cosmology of Theories with Sub-Millimeter Dimensions and TeV Scale Quantum Gravity
• Hilbert Space Representation of the Minimal Length Uncertainty Relation
• Potential Sensitivity of Gamma-Ray Burster Observations to Wave Dispersion in Vacuo
• Noncommutative Perturbative Dynamics
• Tests of the Gravitational Inverse-Square Law below the Dark-Energy Length Scale
• A high resolution foreground cleaned CMB map from WMAP
• Sub-millimeter tests of the gravitational inverse-square law: A search for "large" extra dimensions
• Sub-millimeter Tests of the Gravitational Inverse-square Law
• Cosmic Topology
• Particle Physics Implications of a Recent Test of the Gravitational Inverse Square Law
• Circles in the Sky: Finding Topology with the Microwave Background Radiation
• Constraining the Topology of the Universe
• Features and New Physical Scales in Primordial Observables: Theory and Observation
• An infrared background--TeV gamma-ray crisis?
• MOND theory
• Minimal Length Uncertainty Relation and the Hydrogen Spectrum
• The MOND limit from space-time scale invariance
• Minimum Length Cutoff in Inflation and Uniqueness of the Action
• Cosmic microwave background anisotropies in multi-connected flat spaces
• Extending the WMAP Bound on the Size of the Universe
• Can COBE see the shape of the universe?
• Cutoff in the TeV Energy Spectrum of Markarian 421 During Strong Flares in 2001
• Dual equivalence between Self-Dual and Maxwell-Chern-Simons models coupled to dynamical U(1) charged matter
• Do we Live in a "Small Universe"?
• Sub-millimeter Spatial Oscillations of Newton's Constant: Theoretical Models and Laboratory Tests
• Phenomenology of Particle Production and Propagation in String-Motivated Canonical Noncommutative Spacetime
• Brane world corrections to Newton's law
• Cosmic microwave background constraints on multi-connected spherical spaces
• On the IR/UV mixing and experimental limits on the parameters of canonical noncommutative spacetimes
• Gravitational waves in bimetric MOND
• A spatial correlation analysis for a toroidal universe
• A search for cosmic topology in the final WMAP data
• BFT Method for Mixed Constrained Systems and Chern-Simons Theory
• Obtaining gauge invariant actions via symplectic embedding formalism
• Constraint structure in modified Faddeev-Jackiw method
• The BFT Method With Chain Structure
• UV/IR mode mixing and the CMB
• QCD gauge symmetries through Faddeev-Jackiw symplectic method
• Symplectic Embedding of a Massive Vector-Tensor Theory with Topological Coupling
• Puzzles in astrophysics in the past and present
• The complete Faddeev-Jackiw treatment of the $U_{EM}(1)$ gauged SU(2) WZW model

Cited by in corpus (6)

• Particle on a Torus Knot: Constrained Dynamics and Semi-Classical Quantization in a Magnetic Field
• Particle on a torus knot: Symplectic analysis
• Symplectic gauge invariant reformulation of a free particle system on toric geometry
• Spinning Toroidal Brane Cosmology; A Classical and Quantum Survey
• Supervariable approach to particle on a torus knot: A model for Hodge theory
• Dynamical Structure of the Fields in the Light Cone Coordinates