A Portal Special Presentation- Geometric Unity: A First Look: Difference between revisions
A Portal Special Presentation- Geometric Unity: A First Look (edit)
Revision as of 03:49, 11 April 2020
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===== Choosing All Metrics ===== | ===== Choosing All Metrics ===== | ||
<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>[01:10:36] 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, 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. | ||