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Stephen Hawking

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... Formulation of QFT – Path Integrals  Amplitude to propagate from state A to B in time T governed by exp[-i H T], specifically the matrix element between A and B  Path integral breaks down the propagation into infinitesimal elements between complete sets of states  Feynman diagrams handy for keep ...
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... Ψ should be single valued, continuous as a function of Θ and Φ: the wave meets itself as Θ and Φ cycle around the origin ← with quantum numbers ...
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... case of stock markets with price limit rule: the rate of return in a trading day can not exceed a fixed limit ±q% (for example, in most Chinese stock markets q = 10). By choosing 1% as a ‘quantum’ for the rate of return, the set of all the possible values of R is L = {−q, −q+1, ... , q−1, q}. 2. A F ...
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... 3. Suppose at time t=0, the position space wavefunction for a particle is not given explicitly but its momentum space wavefunction is given. Is it possible to determine the uncertainty in the position of the particle at time t=0 without knowing the Hamiltonian of the system? Explain. ...
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... it has not been possible to combine general relativity with quantum mechanics to form a satisfactory theory of quantum gravity. One of the problems, among others, is that general relativity does not fit the present paradigm for a fundamental theory; that of a renormalizable quantum field theory. Alt ...
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... We can see that ideal Hydro can be satisfied only if f=feq , on the other hand the underlying hypothesis of Hydro is that the mean free path is so small that the f(x,p)is always at equilibrium during the evolution. Similarly ∂T , for f≠feq and one can do the expansion in terms of transport ...
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Path integral formulation

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