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marcus

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## Main Question or Discussion Point

This paper shows an interesting new approach to a theory of geometry + matter. Impressive preliminary results:

http://arxiv.org/abs/1101.6078

==quote Barrett's introduction==

This article concerns the problem of constructing a quantum theory of gravity coupled to matter. Many approaches to quantum gravity assume that the main difficulty lies in reconciling the dynamics of general relativity with quantum mechanics, and therefore start by describing a purely gravitational theory without matter fields. This article however takes the opposite point of view: that

At energies below the Planck scale it should be possible to describe the theory to a good approximation with continuum fields and an effective action. In the framework due to Alain Connes[C], the fields of the standard model and gravity are packaged very effectively into geometry and matter on a certain non-commutative Kaluza-Klein space consisting of the product of a standard (commutative) four-manifold and a non-commutative ‘internal space’.

In this article a new proposal is given for the action of gravity coupled to standard model matter at high energies near (but not exceeding) the Planck scale. This is done by generalising Sakharov’s idea of induced gravity in which the gravitational terms in the action are induced by matter interactions [SK]. The generalisation is to propose an induced action for all the bosonic fields in Connes’ framework. For this idea to work, it is necessary for the space- time geometry to exhibit discreteness at the Planck scale, so that there is a natural cut-off at the corresponding energy.

Implementing this proposal by defining a functional integral over the matter and gravitational fields with the required discreteness requires some non-trivial mathematical framework. It is noted that the main qualitative features that are required for the bosonic part of the functional integral are found in the construction of various topological gauge theories using the techniques of higher category theory and state sum models. However, as yet a model which realises all of the requirements remains to be defined, and in particular it is not yet known how to code the standard model geometry into state sum models. Some general perspectives are offered for a programme in which this might be realised.

==endquote==

It should be clear to anyone who reads this that the paper is the

Some of the themes here (like Sakharov induced g.) are ones that have been repeatedly raised here (by e.g. Atyy and others whose names escape me at the moment) at PF Beyond forum. Barrett and Connes separately published a major result in Connes' Noncommutative Geometry, realizing the Standard Model, at about the same time in 2006 ( http://arxiv.org/abs/hep-th/0608221 ).

Barrett does both LQG and NCG.

He will be giving a talk at the March 2011 QG school. (Which I see now has 107 registered participants.)

Have to go, more later.

http://arxiv.org/abs/1101.6078

**Induced standard model and unification**==quote Barrett's introduction==

This article concerns the problem of constructing a quantum theory of gravity coupled to matter. Many approaches to quantum gravity assume that the main difficulty lies in reconciling the dynamics of general relativity with quantum mechanics, and therefore start by describing a purely gravitational theory without matter fields. This article however takes the opposite point of view: that

**the gravity-matter interaction is in fact the most important feature of the dynamics**. The simplest hypothesis is that the dynamics of the gravitational field itself is a side-effect of the gravity-matter interaction.At energies below the Planck scale it should be possible to describe the theory to a good approximation with continuum fields and an effective action. In the framework due to Alain Connes[C], the fields of the standard model and gravity are packaged very effectively into geometry and matter on a certain non-commutative Kaluza-Klein space consisting of the product of a standard (commutative) four-manifold and a non-commutative ‘internal space’.

In this article a new proposal is given for the action of gravity coupled to standard model matter at high energies near (but not exceeding) the Planck scale. This is done by generalising Sakharov’s idea of induced gravity in which the gravitational terms in the action are induced by matter interactions [SK]. The generalisation is to propose an induced action for all the bosonic fields in Connes’ framework. For this idea to work, it is necessary for the space- time geometry to exhibit discreteness at the Planck scale, so that there is a natural cut-off at the corresponding energy.

Implementing this proposal by defining a functional integral over the matter and gravitational fields with the required discreteness requires some non-trivial mathematical framework. It is noted that the main qualitative features that are required for the bosonic part of the functional integral are found in the construction of various topological gauge theories using the techniques of higher category theory and state sum models. However, as yet a model which realises all of the requirements remains to be defined, and in particular it is not yet known how to code the standard model geometry into state sum models. Some general perspectives are offered for a programme in which this might be realised.

==endquote==

It should be clear to anyone who reads this that the paper is the

**starting point**of an interesting line of investigation, not an endpoint.Some of the themes here (like Sakharov induced g.) are ones that have been repeatedly raised here (by e.g. Atyy and others whose names escape me at the moment) at PF Beyond forum. Barrett and Connes separately published a major result in Connes' Noncommutative Geometry, realizing the Standard Model, at about the same time in 2006 ( http://arxiv.org/abs/hep-th/0608221 ).

Barrett does both LQG and NCG.

He will be giving a talk at the March 2011 QG school. (Which I see now has 107 registered participants.)

Have to go, more later.

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