A Portal Special Presentation- Geometric Unity: A First Look: Difference between revisions
A Portal Special Presentation- Geometric Unity: A First Look (edit)
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<p>[01:10:23] Let's get started. We take $$X^4$$, we need metrics. We have none. We're not allowed to choose one. So we do the standard trick is we choose them all. | <p>[01:10:23] Let's get started. We take $$X^4$$, we need metrics. We have none. We're not allowed to choose one. So we do the standard trick is we choose them all. | ||
<p>[01:10:36] So we allow $$U^14$$ to equal the space of metrics on $$X^4$$ | <p>[01:10:36] So we allow $$U^14$$ to equal the space of metrics on $$X^4$$ pointwise. Therefore, if we propagate on top of this, let me call this the projection operator. If we propagate on $$U^14$$ we are in some sense following a Feynman like idea of propagating over the space of all metrics, but not at a field level. | ||
<p>[01:10:58] At a | <p>[01:10:58] At a pointwise tensorial level. | ||
<p>[01:11:03] Is there a metric on $$U^14$$? Well, we both want one and don't want one. If we had a metric from the space of all metrics, we could define fermions, but we would also lock out any ability to do dynamics. We want some choice over what this metric is, but we don't want full choice because we want enough to be able to define the matter fields to begin with. | <p>[01:11:03] Is there a metric on $$U^14$$? Well, we both want one and don't want one. If we had a metric from the space of all metrics, we could define fermions, but we would also lock out any ability to do dynamics. We want some choice over what this metric is, but we don't want full choice because we want enough to be able to define the matter fields to begin with. | ||