## You are here

Homequantum gravity theories

## Primary tabs

# quantum gravity theories

# 0.1 Quantum gravity theories

The goal of several *quantum gravity theories* is to define gravitational interactions in terms of relativistic quantum fields; this poses axiomatic, conceptual, logical and mathematical-fundamental problems and theoretical
challenges. In spite of their universal span, gravitational interactions are the
weakest known. Repeated experimental attempts failed so far to reliably detect the quanta of gravitational fields-
the gravitons- which are considered as ‘particles’ expected to be associated
with ‘gravitational waves’. Solving the theoretical problem of defining and mathematically treating gravitational interactions in quantum terms is thus the aim of Quantum Gravity theories. Recently, there are several quite different
mathematical/theoretical physics approaches that involve either Hamiltonian algebroids or graded ’Lie’ algebras/ superalgebras involving extensions of previous relativistic QFT approaches. Two such
approaches to Quantum Gravity (and respectively, dark matter) problems are
Noncommutative Geometry which was initially proposed by A. Connes, and (respectively) Quantum Geometry (mostly by theoreticians).

# References

- 1
A. Connes. 1994.
*Noncommutative Geometry*, Academic Press: New York. - 2
Abhay Ashtekar and Jerzy Lewandowski.2005. Quantum Geometry and Its Applications,

Quantum Geometry with Applications - 3
VÃ¡rilly, J. C.: 1997,
*An introduction to noncommutative geometry*, arXiv: phys/9709045

## Mathematics Subject Classification

18D25*no label found*18-00

*no label found*55U99

*no label found*81-00

*no label found*81P05

*no label found*81Q05

*no label found*

- Forums
- Planetary Bugs
- HS/Secondary
- University/Tertiary
- Graduate/Advanced
- Industry/Practice
- Research Topics
- LaTeX help
- Math Comptetitions
- Math History
- Math Humor
- PlanetMath Comments
- PlanetMath System Updates and News
- PlanetMath help
- PlanetMath.ORG
- Strategic Communications Development
- The Math Pub
- Testing messages (ignore)

- Other useful stuff
- Corrections