This post is too skeletal to respond meaningfully to and doesn't really spell out how the dots would be connected.kodama said:TL;DR Summary: if LQG is wrong
if LQG is wrong
what about BRST quantization of Ashtekar variables?
is that more ambitious than LQGmethods ?
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.ohwilleke said: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?
mitchell porter said: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.
do you think BRST quantization of Ashtekar variables is better than LQG? what about the semiclassical limit ?mitchell porter said: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
https://www.physicsforums.com/threa...ndamental-space-and-time.954446/#post-6053146ohwilleke said: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?
BRST quantization is a method used in theoretical physics to quantize systems with gauge symmetries. It introduces ghost fields and a BRST charge, which encodes the gauge symmetry, to systematically handle constraints and maintain consistency in the quantization process.
Ashtekar variables are a reformulation of the variables used in general relativity, where the metric and connection are replaced by a new set of variables that simplify the equations of general relativity, particularly in the context of canonical quantum gravity. They consist of a densitized triad and a connection, making the theory resemble a gauge theory.
BRST quantization is important for Ashtekar variables because it provides a systematic way to handle the gauge symmetries inherent in general relativity when reformulated using these variables. By introducing ghost fields and the BRST charge, one can ensure that the quantization respects the gauge invariance and deals with the constraints appropriately.
In the context of Ashtekar variables, the BRST charge is constructed to encode the gauge symmetries of the theory. It acts on the physical states and fields, ensuring that the physical states are invariant under gauge transformations. The BRST charge generates transformations that involve the ghost fields and the original gauge fields, maintaining the consistency of the gauge symmetry at the quantum level.
The main challenges in applying BRST quantization to Ashtekar variables include handling the complex structure of the constraints in general relativity, ensuring the correct implementation of the BRST symmetry, and dealing with the non-trivial topology of the space of connections. Additionally, constructing a suitable Hilbert space for the physical states and managing the interplay between the ghost fields and the original variables can be technically demanding.