Published:
The way to define an h-cobordism is as follows: if the inclusion maps $\iota_{0}$ and $\iota_{1}$ corresponding to a cobordism $M$ are homotopy equivalences, then $M$ is said to be an h-cobordism. That is, if the inclusion maps $\iota_{0}:N_{0}\hookrightarrow M$ and $\iota_{1}: N_{1}\hookrightarrow M$ are homotopy equivalences, then we say that the cobordism $M$ is an h-cobordism. The h-cobordism theorem is as follows: Read more
Published:
I am somewhat lame with writing things like this, but I think if I get right into it, it would save me from a lot of awkwardness that comes around with trying to explain why you are trying to explain things no one asked – but I bet people ask about von Neumann algebras (a really interesting thing), so I decided to try it this way. Read more
Published:
The way to define an h-cobordism is as follows: if the inclusion maps $\iota_{0}$ and $\iota_{1}$ corresponding to a cobordism $M$ are homotopy equivalences, then $M$ is said to be an h-cobordism. That is, if the inclusion maps $\iota_{0}:N_{0}\hookrightarrow M$ and $\iota_{1}: N_{1}\hookrightarrow M$ are homotopy equivalences, then we say that the cobordism $M$ is an h-cobordism. The h-cobordism theorem is as follows: Read more
Published:
In general, solving something like the Hamiltonian constraint (called the Wheeler-DeWitt equation, which we will abbreviate to “WDW”) in the framework of canonical quantum gravity is hard. Usually, one picks up an additional ansatz that simplifies the situation, such as minisuperspace and so on, although I am not aware of such cases. In a paper called “Hilbert Space of Quantum Gravity in de Sitter Space”, it was shown that the solutions to the WDW equation (while a WDW state also corresponds to the momentum constraint, usually it is more preferrable to consider the explicit study of the Hamiltonian constraint and an implicit study of the momentum constraint, due to certain reasons I will expand on at the end of this post) in de Sitter take up a nice form, which was found by an ansatz, where one starts by saying that at late-time slices (found by setting a conformal factor $\Omega$ such that $\log\int\sqrt{|g|}d^{D}x\to\infty$ corresponds to the factor $\Omega\to+\infty$), the wavefunctional takes up the form [\Psi=e^{i\mathcal{F}}\;,] where $\mathcal{F}$ is a functional that will not be explicitly worked with at the present level. Read more
Published:
The way to define an h-cobordism is as follows: if the inclusion maps $\iota_{0}$ and $\iota_{1}$ corresponding to a cobordism $M$ are homotopy equivalences, then $M$ is said to be an h-cobordism. That is, if the inclusion maps $\iota_{0}:N_{0}\hookrightarrow M$ and $\iota_{1}: N_{1}\hookrightarrow M$ are homotopy equivalences, then we say that the cobordism $M$ is an h-cobordism. The h-cobordism theorem is as follows: Read more
Published:
In general, solving something like the Hamiltonian constraint (called the Wheeler-DeWitt equation, which we will abbreviate to “WDW”) in the framework of canonical quantum gravity is hard. Usually, one picks up an additional ansatz that simplifies the situation, such as minisuperspace and so on, although I am not aware of such cases. In a paper called “Hilbert Space of Quantum Gravity in de Sitter Space”, it was shown that the solutions to the WDW equation (while a WDW state also corresponds to the momentum constraint, usually it is more preferrable to consider the explicit study of the Hamiltonian constraint and an implicit study of the momentum constraint, due to certain reasons I will expand on at the end of this post) in de Sitter take up a nice form, which was found by an ansatz, where one starts by saying that at late-time slices (found by setting a conformal factor $\Omega$ such that $\log\int\sqrt{|g|}d^{D}x\to\infty$ corresponds to the factor $\Omega\to+\infty$), the wavefunctional takes up the form [\Psi=e^{i\mathcal{F}}\;,] where $\mathcal{F}$ is a functional that will not be explicitly worked with at the present level. Read more
Published:
I am somewhat lame with writing things like this, but I think if I get right into it, it would save me from a lot of awkwardness that comes around with trying to explain why you are trying to explain things no one asked – but I bet people ask about von Neumann algebras (a really interesting thing), so I decided to try it this way. Read more
Published:
I am somewhat lame with writing things like this, but I think if I get right into it, it would save me from a lot of awkwardness that comes around with trying to explain why you are trying to explain things no one asked – but I bet people ask about von Neumann algebras (a really interesting thing), so I decided to try it this way. Read more
Published:
This is a sample blog post. Lorem ipsum I can’t remember the rest of lorem ipsum and don’t have an internet connection right now. Testing testing testing this blog post. Blog posts are cool. Read more
Published:
This is a sample blog post. Lorem ipsum I can’t remember the rest of lorem ipsum and don’t have an internet connection right now. Testing testing testing this blog post. Blog posts are cool. Read more
Published:
This is a sample blog post. Lorem ipsum I can’t remember the rest of lorem ipsum and don’t have an internet connection right now. Testing testing testing this blog post. Blog posts are cool. Read more
Published:
In general, solving something like the Hamiltonian constraint (called the Wheeler-DeWitt equation, which we will abbreviate to “WDW”) in the framework of canonical quantum gravity is hard. Usually, one picks up an additional ansatz that simplifies the situation, such as minisuperspace and so on, although I am not aware of such cases. In a paper called “Hilbert Space of Quantum Gravity in de Sitter Space”, it was shown that the solutions to the WDW equation (while a WDW state also corresponds to the momentum constraint, usually it is more preferrable to consider the explicit study of the Hamiltonian constraint and an implicit study of the momentum constraint, due to certain reasons I will expand on at the end of this post) in de Sitter take up a nice form, which was found by an ansatz, where one starts by saying that at late-time slices (found by setting a conformal factor $\Omega$ such that $\log\int\sqrt{|g|}d^{D}x\to\infty$ corresponds to the factor $\Omega\to+\infty$), the wavefunctional takes up the form [\Psi=e^{i\mathcal{F}}\;,] where $\mathcal{F}$ is a functional that will not be explicitly worked with at the present level. Read more