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===== Henrique Gomes ===== | ===== Henrique Gomes ===== | ||
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==== Research Interests ==== | ==== Research Interests ==== | ||
- | + | Along with collaborators Tim Koslowski and Sean Gryb of Perimeter Institute (at the time), I developed a very different formulation of general relativity. In truth, it is not only a different formulation, | |
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+ | The formulation of general relativity as ``shape dynamics'' | ||
+ | is less than two years old, and it is early to say where | ||
+ | this program will lead. In the past, however, such reformulations | ||
+ | have often suggested new questions, and led to fruitful new | ||
+ | | ||
+ | to investigate are: | ||
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+ | There are several indications that shape dynamics is well-adapted | ||
+ | to such spaces. | ||
+ | | ||
+ | mean curvature slice in exact de Sitter space); there is a natural | ||
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+ | and the Hamilton-Jacobi equation induces an action for | ||
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+ | Dirac quantization: | ||
+ | | ||
+ | | ||
+ | the latter second order---the Dirac approach to quantization is | ||
+ | much more straighforward in shape dynamics. | ||
+ | of course: the shape dynamics Hamiltonian is nonlocal. | ||
+ | are straightforward systematic approximations that might allow us | ||
+ | to make sense of the dynamics, leading to a new approach to quantum | ||
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+ | One of the successes of String Theory (and the requirement for 10 or 26 dimensions) comes from the cancellation of gauge anomalies. | ||
+ | In Shape Dynamics conformal transformations are gauge symmetries, and there is worry that its quantization will produce such anomalies. | ||
+ | The worry is presently being shown to be validated, but perhaps not complete. Two independent lines of inquiry seem to be pointing towards a similar anomaly cancellation that happens in String Theory, but without the need for extra dimensions. One is an exact renormalization group approach to gravity, a la Reuter, of the extended Linking theory from which Shape Dynamics arises as a gauge-fixing. The other coming from the realization that the proper BRST treatment of Shape Dynamics possesses a hidden invariance, the symmetries behaving in many ways like a supersymmetry (i.e. they form the same algebra). | ||
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+ | Cosmological solutions and perturbations: | ||
+ | In Shape Dynamics, there exists an issue that there are certain obstructions to the constructions of some standard cosmological solutions. Sorting out which solutions are allowed and constructing an adapted Shape Dynamics cosmological solution is yet to be done. | ||
+ | Observing that Shape Dynamics has very simple linear local constraints, | ||
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+ | Different method of finding solutions of initial data: | ||
+ | The usual method of evolving solutions of GR is called "the York method" | ||
==== Contact ==== | ==== Contact ==== | ||
- | Office: | + | Office: |
- | Phone: | + | Phone: |
Email: < | Email: < | ||
[[http://??? | [[http://??? | ||
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