Recent content by Pietjuh

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    Baryon singlet representation for SU(3) flavour symmetry

    Hi there! As most people already might know, we can decompose the 27 dimensional representation for the baryons under SU(3) flavour symmetry as 27 = 10 + 8 + 8 + 1. I can find a lot of information about the particles that lie in the decuplet and in the octet, but nothing about which particle...
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    Parallel transport on the sphere

    Homework Statement Consider a closed curve on a sphere. A tangent vector is parallel transported around the curve. Show that the vector is rotated by an angle which is proportional to the solid angle subtended by the area enclosed in the curve. The Attempt at a Solution First, I parametrize...
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    How can I prove this binomial identity?

    Homework Statement Prove that the following binomial identity holds: {n+k-1 \choose k} = \sum_{i=1}^k {k-1\choose i-1}{n\choose i} The Attempt at a Solution One of the methods I've tried is to use induction on the variable n, but while trying this I got stuk on rewriting the...
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    Programs How long does it take to finish a phd

    Here in the netherlands it's a bit different than in the US. The bachelor degree takes three years. After that you'll do a two year masters degree which consists of one full year of lectures and a one year research project. Everyone who has obtained a bachelor's degree can do a masters degree...
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    Proving Boundedness of Symmetric Operator on Hilbert Space

    Homework Statement Let A be a linear operator on a Hilbert space X. Suppose that D(A) = X, and that (Ax, y) = (x, Ay) for all x, y in H. Show that A is bounded. The Attempt at a Solution I've tried to prove it by using the fact that if A is continuous at a point x implies that A is...
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    From Simple Groups to Quantum Field Theory

    This is all very nice, but what is your point in writing all these things down? This is all very basic stuff, which you can find in all the textbooks, and they do a good job in explaining it.
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    Proving function is improper riemann integrable

    Homework Statement let f:[0,oo) -> R be given by f(x) = sin(x) / x for x>0 and f(0) = c. Prove that f is improper riemann integrable without computing the integral explicitly The Attempt at a Solution I've attempted to find a upperbound for f(x) such that the integral does not diverge...
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    Proving the Existence of a Measure for a Measurable Function

    I'm still not entirely convinced by your argument, especially this sentence: "The measure of any set A, is then just the integral of f over A" I understand that the measure of a set is just the integral of the indicator function. But I still don't understand why it's trivially true that if...
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    Proving the Existence of a Measure for a Measurable Function

    Yes I have to show that 1. the measure of the empty set is zero, and 2. that the measure of a countable union of measureable sets is the sum of the measures of the individual measurable sets. So in this case I need to show that the integral over a domain that is a countable union of...
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    Proving the Existence of a Measure for a Measurable Function

    1. The problem statement Let (X,M,\mu) be a measure space and let f:X \to [0,\infty] be a measurable function. Now define for E\in M the following function: \mu_f (E) = \int_E fd\mu Show that \mu_f is a measure on M. The Attempt at a Solution I will skip the part where I have to show that...
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    Algebraic Quantum Gravity (Thiemann and Giesel)

    The C*-algebra has a lot to do with functional analysis because we can concretely define it as a complex algebra of linear operators on a Hilbert space and which satisfies the following two properties: - It is closed in the norm topology of operators - it is closed under the operation which...
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    Why Must the Parameter p be an Integer in U(1) Representations?

    Let me clarfiy my derivation of the Lie algebra of U(1). Let exp(i theta) be an arbitrary element of U(1). Then the Lie algebra is the tangent space at the identity element, so u(1) is spanned by the basis vector i. This means that u(1) = { ai | a in R }.
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    Why Must the Parameter p be an Integer in U(1) Representations?

    Hello, perhaps this is the most dumb question ever, but I don't see why it holds. I'm looking at the irreducible representations of the Lie group U(1). To find them I considered the irreps of the lie algebra u(1). These irreps are obviously 1 dimensional and are given by f(a i ) = p a i for...
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    Meson build up from a quark-antiquark pair

    I have some questions about mesons. I don't really understand why they are build up from a quark-antiquark pair. I know from the theory that one can classify the mesons by considering the tensor product of the fundamental representation [3] and the representation [3'] (the prime for denoting...
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    How do I solve this Spectral Lines Question?

    You know that the resolving power is given by R = \frac{\lambda}{\Delta\lambda}. But we also have the diffraction law which states a\sin{\theta} = m(\lambda + d\lambda) so R = m N where m is the order of the diffraction and N the total number of slits in the grating. So what you want to do is to...
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