## FANDOM

118 Pages

Quantum Field Theory
... no spooky action at a distance (Einstein)
Early Results
Relativistic Quantum Mechanics Klein-Gordon Equation
Dirac Equation
The Dawn of QFT Spinors
Spin
Feynman Slash Notation
Antimatter
Klein-Gordon Field
Dirac Field
Renormalisation
Grassman Variable
Conformal Field Theory
Countdown to the Standard Model
From a framework to a model Yang-Mills Theory
Quantum Electrodynamics
Quantum Chromodynamics
Electroweak Theory
Higgs Mechanism
Standard Model
Semi-Classical Gravity and the Dark Age Hawking Radiation
Chandrashekhar Limit
Inflation
Problems with the Standard Model
Outlook
Beyond the Standard Model Beyond the Standard Model
Quantum Gravity
Theory of Everything
Related
Related De Donder-Weyl Theory

Quantum Gravity refers to a theory of Gravity that is compatible with Quantum Mechanics. It often refers to the theory of gravity being General Relativity. Usually, it is possible to quantise a fundamental force easily using the canonical method, which makes one realise that the force is mediated by particles, etc. However, this is not possible in the context of Gravity, because the Perturbation Series diverges, and the result is non-renormalisable.

## Why one can't quantise gravity ordinarilyEdit this section

In the standard way of "second" quantisation, one quantises the forces in a similar way to matter, assigning their quanta with fields (not wavefunctions though), and so on. However, when one does this for gravity, this results in a non-renormalisable divergent Perturbation Series.

Intuitively, one can think of it in this way:

If there is a system of particles with a non-vanishing Stress-Energy-Momentum Tensor, interacting gravitationally, thus through gravitons, then these gravitons themselves have a non-zero Stress-Energy-Momentum Tensor, and therefore interact gravitationally themselves. Therefore, there are more gravitons, ad infinitum. This results in a divergent series mathematically. However, this happens with Quantum Chromodynamics, too, so we do not lose faith so easily. Unfortunately, while in the case of Quantum Chromodynamics, the result is Renormalisable, it is not so in the case of gravity.

## Attempt to quantiseEdit this section

Below is an out line of the attempt to quantise gravity ordinarily [1]:

One firstly expands the Metric Tensor around the Minkowski Metric as follows:

$g_{\mu\nu}=\eta_{\mu\nu}+ \kappa\psi_{\mu\nu}$

Where $\psi_{\mu\nu}$ is the Graviton Field.

Now, write down the Einstein-Hilbert Action:

$S=\frac1{2\kappa^2} \int \mbox{d}^Dx \sqrt g R$

Expanding this Action results in a complicated non-polynomial action in $\psi$.If we quantise this perturbatively, the perturbation diverges, and the result is non-renormalisable.

## ReferencesEdit this section

1. Mohaupt, Thomas. "Introduction to String Theory". ArXiV: 30.