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  1. J

    The integral does not converge...

    I am asked to compute ##[\phi(x), \phi^\dagger(y)]## , with ##\phi = \int \frac{dp^3}{(2\pi)^3}e^{-ipx}\hat{a}(\vec{p})## and with z=x-y a spacelike vector. And show that this commutator does not vanish, which means that for this non-relativsitic field i.e. with ##p^0 = \frac{\vec{p}^2}{2m}##...
  2. J

    Linear momentum of the Klein Gordon field

    The correct answer is: #P = \int \frac{dp^3}{(2\pi)^3}\frac{1}{2E_{\vec{p}} \big(a a^{\dagger} + a^{\dagger}a\big)# But I get terms which are proportional to ##aa## and ##a^{\dagger}a^{\dagger}## I hereunder display the procedure I followed: First: ##\phi = \int...
  3. J

    A Concept of wavefunction and particle within Quantum Field Theory

    -1st: Could someone give me some insight on what a ket-state refers to when dealing with a field? To my understand it tells us the probability amplitude of having each excitation at any spacetime point, but I don't know if this is accurate. Also, we solve the free field equation not for this...
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    A Why we can perform normal ordering?

    As explained in the summary, it seems that the commutators of some operators (creation and anihilation) can be ignored when quantising the hamiltonian of the Klein Gordon Field. I wonder why we are allowed to do such a thing. Is that possible because we are solely within a semiquantum...
  5. J

    I Bipartite quantum negativity

    Let as consider a system ##H = A\otimes B## I've been said that quantum negativity, i.e. taking the partial transpose w.r.t A or B and summing the magnitude of the negative eigenvalues obtained, is a measure of how entangled are the parties A and B. First question: Why is it that we do not...
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    I Restricted Boltzmann machine uniqueness

    I am dealing with restricted boltzmann machines to model distributuins in my final degree project and some question has come to my mind. A restricted boltzmann machine with v visible binary neurons and h hidden neurons models a distribution in the following manner: ## f_i= e^{ \sum_k b[k]...
  7. J

    I Quantum negativity

    When I computes the negativity (with the partial transpose) of the density matrix corresponding to the GHZ I obtain zero, no matter what is the partition I choose. I've read somewhere that this is because GHZ's distillable entanglement is zero, which I don't really understand because I haven't...
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    I Geodesics parametrization

    Let us consider a sphere of a unit radius . Therefore, by choosing the canonical spherical coordinates ##\theta## and ##\phi## we have, for the differential lenght element: $$dl = \sqrt{\dot{\theta}^2+sin^2(\theta)\dot{\phi}^2} $$ In order to find the geodesic we need to extremize the...
  9. J

    I Commutation between covariant derivative and metric

    First, we shall mention that it is known that the covariant derivative of the metric vanishes, i.e ##\nabla_i g_{mn} = 0##. Now I want tro prove the following: $$ \nabla_i A_k = g_{kn}\nabla_i A^n$$ The demonstration I encounter takes advantage of the Leibniz rule: $$ \nabla_i A_k = \nabla_i...
  10. J

    I Metric transformation between inertial frames

    The metric tensor in an inertial frame is ## \eta = diag(-1, 1)##. Where I amb dealing with only 1-D space. The metric tranformation rule after a crtain coordinate chane is the following: $$ g_{\mu \nu} = \frac{\partial x^\alpha}{\partial x'^{\mu }} \frac{\partial x^\beta}{\partial x'\nu }...
  11. J

    I Is the surface of a sphere locally flat?

    Given a certain manifold in ##R^3## I've been told that at every location ##p## it is possible to encounter a reference frame from which the metric is the euclidean at zero order from that point and its first correction is of second order. This, nevertheless does not match with the following...
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    I Parallel transport general relativity

    Suppose you have a tensor quantity called "B" referenced in a certain locally inertial frame (with four Minkowski components for instance). As far as I know, a parallel transportation of this quantity from a certain point "p" to another point "q" consists in expressing it in terms of the...
  13. J

    A Quantum tomography: Where does the magic happen?

    My question is: How does this happen? Less measurements than 4^n-1 means that literally we don't have enough information to label the state. How can the neural network overcome this lack of information?
  14. J

    Restricted Boltzmann machine understanding

    Suppose you have an experiment of 2 possible outcomes 0 and 1 with probabilities p and 1-p respectively. I've been told in University that Restricted Boltzmann machines (RBM) can be used to infer probability distributions so I guess that one could built a RBM in order to infer p in the example...
  15. J

    A Restricted Boltzmann machine for Quantum state tomography

    I'm struggling with my Final Degree Project. I would like to perform a quantum simulation and perform quantum tomography for a single-qubit using a resrticted boltzmann machine. In order to do so I'm trying to follow the recipe in the paper "Neural Network quantum state tomography, Giacomo...
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    I Bose-Einstein condensate diagram

    I have seen many of these diagrams in internet and I fail to figure out what their actual meaning is. Can someone explain what the axes and different colours mean? Also, which is the physical interpretation that can be extracted from them? Thanks in advance :).
  17. J

    Moiré pattern presentation

    No relevant equations.
  18. J

    I Rutherford's experiment doubt

    Here it goes. I'm reading some notes on the Rutherford (gold foil) experiment and they first state what one should expect if the atom model was like the one described by Thomson (plumb pudding model). In order to somehow predict what the deviation should be when throwing alpha particles towards...
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    I Interaction Picture Doubts

    When working on the interaction picture you can show that in a certain rotating frame the Hamiltonian of a 2-level system (for example) becomes uncoupled. This implies that in such frame there are no Rabi oscillations or other dynamical phenomena, this seems weird to me and I would like to know...
  20. J

    Addition of Harmonics in a string wave

    In basic optics, we are given the general solution of the wave equation (massless string of length L) as a linear combination of normal modes, that need to have some of the permitted frequencies due to boundary conditions. In laboratory, we observed that phenomenon. We generated a wave in a...
  21. J

    Fourier transform fallacy? (Optics)

    Here it goes. I have been taught that a finite pulse of light does not have a single frequency. By finite pulse I was given an example of a source of light that has been emitted during a finite amount of time and, consequently, covers a finite region of space. Then I was taught that you can...
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