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marcus

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I was just reading a paper co-authored by Jerzy Lewandowski

which is dated June 24 2003----but also dated February 2003, I don't know which applies.

http://arxiv.org/gr-qc/0302059 [Broken]

It begins "the quantum holonomy operators and the quantum flux operators are the basic elements of quantum geometry..."

"...Recently, Sahlmann [1] proposed a new, more algebraic point of view. It opens the door to a representation theory of quantum geometry. The main idea is to spell out a definition of a *-algebra constructed from the holonomies and fluxes, that underlies all the loop quantum gravity framework, and to study its representations..."

Lewandowski calls a certain kind of holonomy-flux *-algebra a "Sahlmann algebra". In his papers Hanno Sahlmann is more modest and does not call the algebra that. (naming things after oneself is not customary in mathematics). Hanno is pretty young to have something named after him. I am trying to understand this a little better.

A good many of the key papers (1994--present) in loop quantum gravity (quantum-general-relativity in effect) have been by Ashtekar and Lewandowski---if there are central figures in LQG then those two would be my pick of the lot. Hanno Sahlmann just appeared---his thesis date is, I think, 2002.

In November 2002 Ashtekar, Lewandowski, and Sahlmann posted

http://arxiv.org/gr-qc/0211012 [Broken]

"Polymer and Fock representations for a Scalar field"

here is the abstract:

"In loop quantum gravity, matter fields can have support only on the polymer-like excitations of quantum geometry, and their algebras of observables and Hilbert spaces of states can not refer to a classical, background geometry. Therefore, to adequately handle the matter sector, one has to address two issues already at the kinematic level. First, one has to construct the appropriate background independent operator algebras and Hilberts spaces. Second, to make contact with low energy physics, one has to relate this polymer description of matter fields to the standard Fock description in Minkowski space. While this task has been completed for gauge fields, imporatant gaps remained in the treatment of scalar fields. The purpose of this letter is to fill these gaps."

edit: forgot earlier to include link to the first paper mentioned

which is dated June 24 2003----but also dated February 2003, I don't know which applies.

http://arxiv.org/gr-qc/0302059 [Broken]

It begins "the quantum holonomy operators and the quantum flux operators are the basic elements of quantum geometry..."

"...Recently, Sahlmann [1] proposed a new, more algebraic point of view. It opens the door to a representation theory of quantum geometry. The main idea is to spell out a definition of a *-algebra constructed from the holonomies and fluxes, that underlies all the loop quantum gravity framework, and to study its representations..."

Lewandowski calls a certain kind of holonomy-flux *-algebra a "Sahlmann algebra". In his papers Hanno Sahlmann is more modest and does not call the algebra that. (naming things after oneself is not customary in mathematics). Hanno is pretty young to have something named after him. I am trying to understand this a little better.

A good many of the key papers (1994--present) in loop quantum gravity (quantum-general-relativity in effect) have been by Ashtekar and Lewandowski---if there are central figures in LQG then those two would be my pick of the lot. Hanno Sahlmann just appeared---his thesis date is, I think, 2002.

In November 2002 Ashtekar, Lewandowski, and Sahlmann posted

http://arxiv.org/gr-qc/0211012 [Broken]

"Polymer and Fock representations for a Scalar field"

here is the abstract:

"In loop quantum gravity, matter fields can have support only on the polymer-like excitations of quantum geometry, and their algebras of observables and Hilbert spaces of states can not refer to a classical, background geometry. Therefore, to adequately handle the matter sector, one has to address two issues already at the kinematic level. First, one has to construct the appropriate background independent operator algebras and Hilberts spaces. Second, to make contact with low energy physics, one has to relate this polymer description of matter fields to the standard Fock description in Minkowski space. While this task has been completed for gauge fields, imporatant gaps remained in the treatment of scalar fields. The purpose of this letter is to fill these gaps."

edit: forgot earlier to include link to the first paper mentioned

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