Hello,
I am trying to figure out how to best decompose a vector into a best fit linear superposition of other, given vectors.
For instance is there a way of finding the best linear sum of:
(3,5,7,0,1)
(0,0,4,5,7)
(8,9,2,0,4)
That most closely gives you (1,2,3,4,5)
My problem contains...
Hello,
I am reading through some GR lecture notes and have come across the following:
"A spacetime is static if there exists a coordinate chart where:
∂0gμν = 0
g0i = 0
This spacetime admits a Timelike Killing vector X that satisfies:
X[α∇βXγ] = 0 "
How do I go about proving that this...
Hello,
Does anyone know if there is a solutions manual or any other source of solutions for the book Quantum and Statistical Field theory by Le Bellac?
Thanks!
Hello. I am doing some reading on QED and am getting a bit confused on the different conventions used. In Matthew Schwartz's book we have the Lagrangian given as:
LQED = -¼ FμνFμν + iψ*γμ(∂μ + ieAμ)ψ - V(ψ*ψ)
And the path integral factor is exp(iS).
In another text, however, I see the QED...
Homework Statement
Hi. I am trying to solve a problem on renormalisation group flow and have come across the following coupled equations that I need to solve:
Λ ∂g/∂Λ = b.m
Λ ∂m/∂Λ = -2.m + a.g
Where a and b are just constants. I need to find g(Λ) and m(Λ).
Homework Equations
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I...
Homework Statement
I'm trying to figure out this question:
"Show that the 10-dimensional representation R3,0 of A2 corresponds to a reducible representation of the LC[SU(2)] subalgebra corresponding to any root. Find the irreducible components of this representation. Does the answer depend on...
Hello,
So I was asked this question the other day and don't really know how to go about it:
"Define a random process by:
Xn+1 = Xn+1 with probability 1/2
Xn+1 = 1/Xn with probability 1/2
Given that X0= 100, find the expectation of X10 "
I've only ever really met random processes...
Hello,
I am working through Hughston and Tod "An introduction to General Relativity" and have gotten stuck on their exercise [7.7] which asks to prove the following non- linear wave equation for the Riemann tensor in an empty space:
∇e∇eRabcd = 2Raedf Rbecf − 2Raecf Rbedf − Rabef Rcdef
I have...
Hi,
I am working through a textbook on general relativity and have come across the statement:
"A general (2 0) tensor K, in n dimensions, cannot be written as a direct product of two vectors, A and B, but can be expressed as a sum of many direct products."
Can someone explain to me how this...
Hi. I've been struggling with a formulation of the twin paradox in the Kerr metric.
Imagine there are two twins at some radius in a Kerr metric. One performs equatorial circular motion whilst the other performs polar circular motion. They separate from one another and the parameters of the...
I was just wondering how you would go about calculating the proper time for an observer following a freely falling elliptical orbit in a Schwarzschild metric.
I am happy with how to calculate the proper time for a circular orbit and was wondering whether if you had two observers start and end...
Say you have two masses in an otherwise empty space and you can approximate the metric near each mass as a Schwarzschild (or whatever). Is there a way of combining or 'stitching together' these two metrics to give the overall metric of all spacetime?
I'm just interested to know how a test...
Whenever the twin paradox in GR seems to be discussed, it always seems to be done in the presence of a large mass such that the twins can be considered as test particles moving in some metric.
I was wondering whether the same problem could be generalised and be proposed in completely empty...