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1. I Constraints on Metric Tensor

Aside from being symmetric, are there any other mathematical constraints on the metric?
2. A Can you numerically calculate the stress-energy tensor from the metric?

Great thanks will have a look at Carrol. I'm specifically interested in metrics of closed spaces where boundary points are identified, like a cylinder or tourus. Any extra complications you think ill run into because of strange boundary conditions?
3. A Can you numerically calculate the stress-energy tensor from the metric?

About 10 years ago I worked on a project where I took a mater distribution and numerically solved for spatial curvature. Can this be done in the opposite direction? Can anybody point me to a resource that would allow me to calculate matter distributions when the metric is specified? What are...
4. I Deriving the spherical volume element

Thanks for the help! Using a wedge between the terms in my original expression got me to the answer!

20. Independence of Position and Velocity in Lagrangian Mechanics

In Lagrangian mechanics, both q(t) and dq/dt are treated as independent parameters. Similarly, in Hamiltonian mechanics q and p are treated as independent. How is this justified, considering you can derive the generalized velocity from the q(t) by just taking a time derivative. Does it have...
21. Yang Mills & Fiber Bundles Resource

Nobody else seems to have anything in mind. Would appreciate hearing what you have used!
22. Yang Mills & Fiber Bundles Resource

Hi everyone, Does anyone know of a good intuitive resource for learning Yang-Mills theory and Fiber Bundles? Ultimately my goal is to gain a geometric understanding of gauge theory generally. I have been studying differential forms and exterior calculus. Thanks!
23. Unruh Effect for Standard Model Fields

I have seen the derivation for Unruh radiation for a massless, non-interacting scalar field (Carroll). Are there interesting differences that arise for more realistic standard model cases. For example, what does QCD look like for an accelerating observer? Any papers that detail this would be...
24. I Christoffel Symbol vs. Vector Potential

Can you think of the field as living in a product space of the Minkowski and abstract spaces? Do you know of any reference that explains general yang mills theories geometrically in this way?
25. I Christoffel Symbol vs. Vector Potential

As far as I can tell, in GR, the Chirstoffel symbol in the expression of the Connection is analogous to the vector potential, A, in the definition of the Covariant Derivative. The Chirstoffel symbol compensates for changes in curvature and helps define what it means for a tensor to remain...
26. A Does an infinitesimal generator of acceleration exist?

I am trying to determine what types of field theories have a Lagrangian that is symmetric under an Infinitesimal acceleration coordinate transformations. Does an infinitesimal generator of acceleration exist? How could I go about constructing this matrix?
27. I Heisenberg Picture

Can anybody give a natural interpretation of operators and states in the Heisenberg Picture? When I imagine particles flying through space, it seems that the properties of the particles are changing, rather than the position property itself. Is there any way I should be thinking about these...
28. A Derivation of Black Hole Entropy

Thanks guys these links are great!
29. A Derivation of Black Hole Entropy

I am looking to walk trough hawking and beckenstien's arguments for the proportionality of bh entropy to surface area to better understand black hole entropy. Does anybody know where I can find this calculation? I have taken relativity and qft so I am comfortable with this level of difficulty.
30. Beckenstein Hawking Entropy

Does anybody know where I can find a walkthrough of the derivation of Black hole entropy the way hawking did it? (I'm not worried about deriving from string theory or lqg) I'm looking to follow along to understand the assumptions in the derivation.