Recent content by quickAndLucky

  1. Q

    I Constraints on Metric Tensor

    Aside from being symmetric, are there any other mathematical constraints on the metric?
  2. Q

    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. Q

    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. Q

    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!
  5. Q

    I Deriving the spherical volume element

    I’m trying to derive the infinitesimal volume element in spherical coordinates. Obviously there are several ways to do this. The way I was attempting it was to start with the cartesian volume element, dxdydz, and transform it using $$dxdydz = \left (\frac{\partial x}{\partial r}dr +...
  6. Q

    A What is the "real" Feynman propagator?

    So am I correct in the following? There are several KG Green's functions (my first eqn, Advanced, Retarded, Feynman) and the one which we choose is my 2nd equation because it is equivalent to the amplitude of a particle traveling into the future and an antiparticle with negative energy traveling...
  7. Q

    A What is the "real" Feynman propagator?

    Thanks! Watching Tobias Osborne's QFT lectures on youtube and following along with David Tong's lecture notes. Supplementing with Sredniki and Zee.
  8. Q

    I How do we justify "Natural" Units

    I like the examples of temperature and mass measured as energy and get but one of the confusing things with natural units is that the fundamental constants are unitless. Also it is intuitively clear that temperature and energy should be related quantities as they are essentially the macro and...
  9. Q

    I Does the Principle of Least Action Have a Physical Meaning?

    If there were some realistic theories of mechanics that could not be represented using forces then I would argue that forces might not be fundamental. But even if forces weren't fundamental they could still be practical to use in in most cases and definitely worth teaching.
  10. Q

    I Does the Principle of Least Action Have a Physical Meaning?

    Most strongly interacting conformal field theories have no Lagrangian description. If you know the S-Matrix you have completely specified the theory and there isn't a need for a Lagrangian or action. If you can construct realistic field theories without the PLA you might argue that the PLA is...
  11. Q

    A What is the "real" Feynman propagator?

    The logic of the Feynman Propagator is confusing to me. Written in integral form as it is below $$\Delta _ { F } ( x - y ) = \int \frac { d ^ { 4 } p } { ( 2 \pi ) ^ { 4 } } \frac { i } { p ^ { 2 } - m ^ { 2 } } e ^ { - i p \cdot ( x - y ) },$$ there are poles on the real axis. I have seen...
  12. Q

    I How do we justify "Natural" Units

    How is it that when using "natural" units we drop the units themselves. I understand that you can arbitrarily change the magnitude of a parameter by choosing a new unit. For example Oliver R. Smoot is exactly 1 smoot tall. However, in natural units with [c]=[h/(2π)]=1 the "smoot" part is...
  13. Q

    I Derivative of a Variation vs Variation of a Derivative

    Thinking of ##\partial _{\mu}\phi ## as an independent vector field that itself varies seemed to help! Thanks haushofer and samalkhaiat!
  14. Q

    I Derivative of a Variation vs Variation of a Derivative

    I guess my question is "why do variations and derivatives commute?"
  15. Q

    I Derivative of a Variation vs Variation of a Derivative

    When a classical field is varied so that ##\phi ^{'}=\phi +\delta \phi## the spatial partial derivatives of the field is often written $$\partial _{\mu }\phi ^{'}=\partial _{\mu }(\phi +\delta \phi )=\partial _{\mu }\phi +\partial _{\mu }\delta \phi $$. Often times the next step is to switch...
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