# Charged and Electromagnetic Fields from Relativistic Quantum Geometry

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## Abstract

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## 1. Introduction

## 2. RQG Revisited

#### 2.1. Gauge-Invariance and Quantum Dynamics

#### 2.2. Charged Geometry and Vector Field Dynamics

## 3. Quantum Field Dynamics

#### 3.1. Dynamics of the Complex Fields

#### 3.2. Dynamics of the Vector Fields

## 4. Final Remarks

## Author Contributions

## Conflicts of Interest

## References

- Weyl, H. Philosophy of Mathematics and Natural Science; Princeton University Press: Princeton, UK, 1949. [Google Scholar]
- Cvetic, M.; Gibbons, G.W.; Pope, C.N. Super-geometrodynamics. J. High Energy Phys.
**2015**, 2015, 029. [Google Scholar] [CrossRef] - Wheeler, J.A. On the nature of quantum geometrodynamics. Ann. Phys.
**1957**, 2, 604–614. [Google Scholar] [CrossRef] - Wheeler, J.A. Superspace and the Nature of Quantum Geometrodynamics. In Battelle Rencontres, 1967 Lectures in Mathematics and Physics; De Witt, C.M., Wheeler, J.A., Eds.; W.A. Benjamin: New York, NY, USA, 1968. [Google Scholar]
- Gibbons, G.W. Soliton States and Central Charges in Extended Supergravity Theories. Lect. Notes Phys.
**1982**, 160, 145–151. [Google Scholar] - Gibbons, G.W.; Hull, C.M. A bogomolny bound for general relativity and solitons in N=2 supergravity. Phys. Lett. B
**1982**, 109, 190–194. [Google Scholar] [CrossRef] - Rácz, I. Cauchy problem as a two-surface based ‘geometrodynamics’. Class. Quantum Gravity
**2015**, 32, 015006. [Google Scholar] [CrossRef] - Prugovečki, E. Liouville dynamics for optimal phase-space representations of quantum mechanics. Ann. Phys.
**1978**, 110, 102–121. [Google Scholar] [CrossRef] - Prugovečki, E. Consistent formulation of relativistic dynamics for massive spin-zero particles in external fields. Phys. Rev. D
**1978**, 18, 3655–3675. [Google Scholar] [CrossRef] - Prugovečki, E. A Poincaré gauge-invariant formulation of general-relativistic quantum geometry. Nuo. Cim. A
**1987**, 97, 597–628. [Google Scholar] [CrossRef] - Ridao, L.S.; Bellini, M. Towards relativistic quantum geometry. Phys. Lett. B
**2015**, 751, 565–571. [Google Scholar] [CrossRef] - Ridao, L.S.; Bellini, M. Discrete modes in gravitational waves from the big-bang. Astrophys. Space Sci.
**2015**, 357, 94. [Google Scholar] [CrossRef] - Bellini, M. Inflationary back-reaction effects from Relativistic Quantum Geometry. Phys. Dark Univ.
**2016**, 11, 64–67. [Google Scholar] [CrossRef]

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Arcodía, M.R.A.; Bellini, M.
Charged and Electromagnetic Fields from Relativistic Quantum Geometry. *Universe* **2016**, *2*, 13.
https://doi.org/10.3390/universe2020013

**AMA Style**

Arcodía MRA, Bellini M.
Charged and Electromagnetic Fields from Relativistic Quantum Geometry. *Universe*. 2016; 2(2):13.
https://doi.org/10.3390/universe2020013

**Chicago/Turabian Style**

Arcodía, Marcos R. A., and Mauricio Bellini.
2016. "Charged and Electromagnetic Fields from Relativistic Quantum Geometry" *Universe* 2, no. 2: 13.
https://doi.org/10.3390/universe2020013