BRST quantization of Ashtekar variables

[kodama]

TL;DR Summary

if LQG is wrong

if LQG is wrong

what about BRST quantization of Ashtekar variables?

is that more ambitious than LQGmethods ?

 

[ohwilleke]

TL;DR Summary: if LQG is wrong

if LQG is wrong

what about BRST quantization of Ashtekar variables?

is that more ambitious than LQGmethods ?

This post is too skeletal to respond meaningfully to and doesn't really spell out how the dots would be connected.

What about LQG would be wrong? Do Ashetkar variables make any sense outside LQG type theories? What would BRST quantization of Ashtekar variables even amount to?

Is there any literature going down this road or is this just your out of the blue flight of fancy?

 

[kodama]

This post is too skeletal to respond meaningfully to and doesn't really spell out how the dots would be connected.

What about LQG would be wrong? Do Ashetkar variables make any sense outside LQG type theories? What would BRST quantization of Ashtekar variables even amount to?

Is there any literature going down this road or is this just your out of the blue flight of fancy?

Somewhere in this forum there are posts where Mitchel Porter and Urs Schreiber discuss LQG. Urs Schreiber stated reformulating GR in terms of SU(2) connections is mathematically viable, that there is a mathematical theorem that lets you do this, but that LQG method of quantization is completely wrong. Specifically, LQG uses "generalized" connections unrelated to Asketar and therefore is unphysical. He's not a fan of spinfoam either. Mitchel Porter called LQG technically wrong, but he seems to think that there could be ways to use Ashketar variables.

if LQG is wrong, what are other ways to turn SU(2) Ashektar variables into a viable quantum theory, for example, BRST quantization? I also have in mind Woit's proposal where he joins Ashektar variables to the weak force.

 

[mitchell porter]

A few words on what "BRST quantization" is, from a sum-over-histories perspective. Gauge theory and general relativity both have the property, that mathematically different field configurations can be physically equivalent, because of a symmetry (gauge symmetry, general covariance). So when you do a quantum sum over histories, there is a problem of avoiding redundancy - you don't want the same physical state to be counted multiple times.

One way to avoid this is to single out just one mathematical form of each physical state, by imposing an extra condition (a simple example is Coulomb gauge); this is a form of "gauge-fixing". BRST works differently; it adds some fictitious extra fields called ghost fields, which basically compensate for the overcounting, in the amended sum over histories. Once the ghost fields are added, the gauge symmetry is broken, but there's a new "BRST symmetry" which assists calculation.

A BRST symmetry for Ashtekar variables was worked out almost immediately back in the 1980s, but that's only one step in carrying out the full process of making a quantum theory. I dug through the paper's 50 citations; the most advanced follow-up I found was a 1998 paper from Russia, in which the authors start with the "Hilbert-Palatini" action for general relativity, then change the variables to Ashtekar's new variables, and see what that does to the Hilbert-Palatini formulas. I couldn't find a good follow-up to the 1998 paper, but they highligh as their most interesting conclusion, that the BRST path integral for Ashtekar variables is a contour integral. This is also the case with most formulae in twistor theory, so it's consistent with what people keep saying, that the Ashtekar variables have something in common with the twistor perspective.

 

[kodama]

the BRST path integral for Ashtekar variables is a contour integral. This is also the case with most formulae in twistor theory, so it's consistent with what people keep saying, that the Ashtekar variables have something in common with the twistor perspective.

are Ashtekar variables and twistor theory closely related field

 

[kodama]

A BRST symmetry for Ashtekar variables was worked out almost immediately back in the 1980s, but that's only one step in carrying out the full process of making a quantum theory. I dug through the paper's 50 citations; the most advanced follow-up

do you think BRST quantization of Ashtekar variables is better than LQG? what about the semiclassical limit ?

 

[kodama]

This post is too skeletal to respond meaningfully to and doesn't really spell out how the dots would be connected.

What about LQG would be wrong? Do Ashetkar variables make any sense outside LQG type theories? What would BRST quantization of Ashtekar variables even amount to?

Is there any literature going down this road or is this just your out of the blue flight of fancy?

https://www.physicsforums.com/threa...ndamental-space-and-time.954446/#post-6053146

https://physics.stackexchange.com/q...lly-not-listed-as-a-theory-of-e/360010#360010