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| Tags: christoffel, instead, riemann |
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#1
July 17th 04
posted to sci.physics,sci.physics.relativity
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Christoffel instead of Riemann
Doug Sweetser wrote in message ...
Since you cast your pearl before swine, may I ask two too simple questions... A^mu_;nu = A^mu_,nu + L^w mu_nu A_w =~ A^mu_,nu What is the difference between a semicolon and a comma here? R^a_bcd = L^a_bd,c - L^a_bc,d + L^a_uc L^c_bd - L^a_ud L^u_bc 8.44 What is L? 
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#2
July 17th 04
posted to sci.physics,sci.physics.relativity
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Christoffel instead of Riemann
"Edward Green" wrote in message m... Doug Sweetser wrote in message ... Since you cast your pearl before swine, may I ask two too simple questions... A^mu_;nu = A^mu_,nu + L^w mu_nu A_w =~ A^mu_,nu What is the difference between a semicolon and a comma here? Comma is partial derivative http://mathworld.wolfram.com/CommaDerivative.html Semicolon is covariant derivative http://mathworld.wolfram.com/CovariantDerivative.html R^a_bcd = L^a_bd,c - L^a_bc,d + L^a_uc L^c_bd - L^a_ud L^u_bc 8.44 What is L? L is the horizontally mirrored ASCII-version of the capital Gamma (Christoffel symbol of the second kind). See http://mathworld.wolfram.com/Christo...econdKind.html The above equation is equation (5) on http://mathworld.wolfram.com/RiemannTensor.html Edward, just puzzled and wondering a bit... are you by any chance the Ed Green of http://math.ucr.edu/home/baez/gr/oz7.html ? Dirk Vdm
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#3
July 18th 04
posted to sci.physics,sci.physics.relativity
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Christoffel instead of Riemann
"Dirk Van de moortel" wrote in message ...
"Edward Green" wrote in message m... Doug Sweetser wrote in message ... Since you cast your pearl before swine, may I ask two too simple questions... A^mu_;nu = A^mu_,nu + L^w mu_nu A_w =~ A^mu_,nu What is the difference between a semicolon and a comma here? Comma is partial derivative http://mathworld.wolfram.com/CommaDerivative.html Semicolon is covariant derivative http://mathworld.wolfram.com/CovariantDerivative.html R^a_bcd = L^a_bd,c - L^a_bc,d + L^a_uc L^c_bd - L^a_ud L^u_bc 8.44 What is L? L is the horizontally mirrored ASCII-version of the capital Gamma (Christoffel symbol of the second kind). See http://mathworld.wolfram.com/Christo...econdKind.html The above equation is equation (5) on http://mathworld.wolfram.com/RiemannTensor.html Thank you, thank you, thank you. Edward, just puzzled and wondering a bit... are you by any chance the Ed Green of http://math.ucr.edu/home/baez/gr/oz7.html ? Yes; or at least I am the individual upon whom that Ed Green's exploits were based, however loosely. As you can see, I've made great progress in GR since those days when I dabbled with JB, since I'm still asking about the meaning of standard symbols. ;-)
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#4
July 18th 04
posted to sci.physics,sci.physics.relativity
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Christoffel instead of Riemann
"Edward Green" wrote in message om... "Dirk Van de moortel" wrote in message ... "Edward Green" wrote in message m... Doug Sweetser wrote in message ... Since you cast your pearl before swine, may I ask two too simple questions... A^mu_;nu = A^mu_,nu + L^w mu_nu A_w =~ A^mu_,nu What is the difference between a semicolon and a comma here? Comma is partial derivative http://mathworld.wolfram.com/CommaDerivative.html Semicolon is covariant derivative http://mathworld.wolfram.com/CovariantDerivative.html R^a_bcd = L^a_bd,c - L^a_bc,d + L^a_uc L^c_bd - L^a_ud L^u_bc 8.44 What is L? L is the horizontally mirrored ASCII-version of the capital Gamma (Christoffel symbol of the second kind). See http://mathworld.wolfram.com/Christo...econdKind.html The above equation is equation (5) on http://mathworld.wolfram.com/RiemannTensor.html Thank you, thank you, thank you. Edward, just puzzled and wondering a bit... are you by any chance the Ed Green of http://math.ucr.edu/home/baez/gr/oz7.html ? Yes; or at least I am the individual upon whom that Ed Green's exploits were based, however loosely. It's been a while now... I really enjoyed these exploits and I had been wondering about the cast. As you can see, I've made great progress in GR since those days when I dabbled with JB, since I'm still asking about the meaning of standard symbols. ;-) Well, actually this isn't GR but merely differential geometry, not the most accessible backroom of mathematics indeed :-) Dirk Vdm
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