Dirac Definition and 900 Threads

Paul Adrien Maurice Dirac (; 8 August 1902 – 20 October 1984) was an English theoretical physicist who is regarded as one of the most significant physicists of the 20th century.Dirac made fundamental contributions to the early development of both quantum mechanics and quantum electrodynamics. Among other discoveries, he formulated the Dirac equation which describes the behaviour of fermions and predicted the existence of antimatter. Dirac shared the 1933 Nobel Prize in Physics with Erwin Schrödinger "for the discovery of new productive forms of atomic theory". He also made significant contributions to the reconciliation of general relativity with quantum mechanics.
Dirac was regarded by his friends and colleagues as unusual in character. In a 1926 letter to Paul Ehrenfest, Albert Einstein wrote of Dirac, "I have trouble with Dirac. This balancing on the dizzying path between genius and madness is awful." In another letter he wrote, "I don't understand Dirac at all (Compton effect)."He was the Lucasian Professor of Mathematics at the University of Cambridge, was a member of the Center for Theoretical Studies, University of Miami, and spent the last decade of his life at Florida State University.

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  1. F

    Exploring the Delta Dirac Function: What Happens if We Have Two?

    This isn't really homework, I'm just curious. So I'm dealing with the delta dirac function, and I was just wondering what would happen if we had two functions. So the sampling property, \int_{-\infty}^{\infty} f(t)\delta(t-a)\,\,dt = f(a) Now what if we had: \int_{-\infty}^{\infty}...
  2. pellman

    Dirac Lagrangian not invariant under rotations?

    First, I need to be able to do equations in my post but it has been a long time since I posted here. Someone please point me to a resource that gives the how-to. If you make a infinitesimal rotation of the free-field Lagrangian for the Dirac equation, you get an extra term because the Dirac...
  3. S

    Help About charge conjugation of Dirac spinor

    The following formula appears in P J Mulders's lecture notes http://www.nat.vu.nl/~mulders/QFT-0E.pdf {\cal C}~b(k,\lambda)~{\cal C}^{-1}~=~d(k,{\bar \lambda}) (8.18) where {\cal C} is charge conjugation operator. \lambda is helicity. I don't know why there is {\bar {\lambda}} on the...
  4. naima

    Can the Dirac Distribution be Proven Using Integrals?

    bonjour from france, I thought that sum of dirac(x - xi)/g'(xi), where the xi verify g(xi) = 0, was a definition for dirac(g(x)). It was proposed, as an exercise, to prove the equality of the 2 terms. can one help me thanks ps : can i write this in latex?
  5. George Jones

    Solve 0=1 with Dirac's Equation

    Dirac Proves 0 = 1 Suppose A is an observable, i.e., a self-adjoint operator, with real eigenvalue a and normalized eigenket \left| a \right>. In other words, A \left| a \right> = a \left| a \right>, \hspace{.5 in} \left< a | a \right> = 1. Suppose further that A and B are canonically...
  6. F

    Delta Dirac - Question on my final

    Delta Dirac - Question on my final :( :mad: Man I just had this final, and I didn't study the delta function enough. I totally bombed this question. I think I did ok on the rest of it... but I messed up bad on this question. I want to know the answer though. Solve the heat equation: u_t =...
  7. G

    What are the Dirac matrices used for in the Klein-Gordon equation?

    I'm trying to linearize Klein-Gordon equation, following Dirac's nobel lecture: (E^2 - (pc)^2 - (mc^2)^2) \psi = 0 (E + \alpha pc + \beta mc^2) (E + \alpha pc - \beta mc^2) \psi = 0 Expanding the equations yields: -\alpha and \beta commutes with E and p -\alpha^2 = \beta^2 = 1 -\alpha...
  8. L

    3-D Dirac Delta Fnc (DDF) Evaluated

    Hi, After reading DJGriffiths sections on the DDF I have a question about evaluating it in regards Prob. 1.46 (a), to wit: "Write an expression for the electric charge density \rho(\vec{r}) of a point charge q at \vec{r}'. Make sure that the volume integral of \rho equals q." This is easily...
  9. R

    On the Dirac equation in a gravitation field

    Let's discuss the Dirac equation in a gravitation field. I suggest to begin with the following article: http://arxiv.org/abs/math.DG/0603367" It is rather simple. Your comments would be helpful for me.
  10. P

    One-particle Dirac and KG equations

    So there's something I don't quite understand. The density in the KG equation stands for charge density. Here are several questions: 1. For a KG particle, how do I (if it all) find the position probabilty density? 2. For a Dirac particle, what does the (now positive definite) density...
  11. M

    Dirac Delta Function: Scaling and Shifting

    Just have a question about the dirac delta function. I understand how you would write it if you want to shift it but how would you scale it assuming we are using discrete time. Would you write 2*diracdelta[n] or diracdelta[2n]. Also, would that increase it or reduce it by 2 meaning that...
  12. Cincinnatus

    Exploring the Mystery of the Dirac Delta Function

    I've recently come across this function in one of my science classes and am wondering were this identity comes from: \displaystyle{\int{\delta(t-\tau)f(\tau)d\tau}=f(t)} Where \delta(t) is the dirac delta function and f(t) is any (continuous?) function.
  13. A

    Proving Dirac Delta Function Does Not Exist

    How can I prove that no continuous function exists that satisfies the property of the dirac delta function? I thought it should be pretty easy, but it's actually giving me quite a hard time! I know that the integral of such a function must be 1, and that it must also be even (symmetric about the...
  14. F

    Fourier tr. of dirac delta in minkowski space

    Hey everyone, a quick question: what is the Fourier space representation of the dirac delta function in minkowski space? It should be some integral over e^{ikx} (with some normalization with 2*pi's). I'm curious if the "kx" is a dot product in the minkowski or euclidean sense, and how one...
  15. P

    Properties of the dirac delta function

    I'm trying to show that \int \delta \prime(x-x')f(x') dx = f\prime(x) can I differentiate delta with respect to x' instead (giving me a minus sign), and then integrate by parts and note that the delta function is zero at the boundaries? this will give me an integral involving f' and delta...
  16. G

    How Do Gamma Dirac Matrices Factor into Neutron Beta Decay Calculations?

    Hello, This problem is related to the beta decay of a neutron in a proton an electron and a anti-neutrino. I need to prove that, in the limit where the mass of the neutron and the proton goes to infinity, m_P, m_N \to \infty, we have \bar{u}\gamma^\mu(1-\alpha \gamma_5)(\gamma^\alpha k_\alpha...
  17. G

    Dirac Contraction: Evaluating Propagators at Same Point

    I don't have pstricks...so I am going to use words. \text{contraction}\{ \overline{\psi}(x_1) \psi(x_1) \} My question: Propogators are usually dealing with different points...but what is the contraction of two quantities evaluated at the same point. Thanks.
  18. C

    Fermi Dirac (FD) and Maxwell Boltzmann (MB)

    I have a homework problem that asks me to interpret the two curves for when the Fermi level (Ef) is 0.25 eV. I ploted the two graphs and both of them look nothing alike when E < Ef. But both plots predict a probability of essentially zero when E > Ef. I was wondering why is there such a large...
  19. R

    Derivative of an integral containing a Dirac delta

    If I had a function g(x) defined by g(x) = \int_{-\infty}^{\infty} f(x) \delta(x) dx where \delta(x) is the dirac delta function, what would dg(x)/dx be? The fundamental theorem of calculus requires that f(x) \delta(x) needs to be a continuous and differentiable function before I can...
  20. L

    Coulomb's Low And Dirac Delta Functio

    I want to prove coulomb's low for a single charge point from the general form of coulomb's low: E→=1/(4∏€) ∫∫∫ ρv(ŕ) * (r→- ŕ→)/│(r→- ŕ→)│^3 dŕ using Dirac Delta function where r→ is the field point vector ŕ→ is the source point vector ρv(ŕ) is the volume charge density I really don't...
  21. E

    Integrals and dirac delta function

    hello again, i have an integral to solve and not sure how to approach this: \int f(q+T)\delta (t-q)dq and the boundaries of integral are -inf +inf couldn't figure it out with latex. what I know about this is that if delta function is integrated like this, it would be just the value of...
  22. CarlB

    Dirac equation from random walk

    I was unaware that one could obtain the Dirac equation as a result of a random walk. I believe that this has been done by other researchers, but I found it by Ord's papers: http://arxiv.org/find/quant-ph/1/au:+Ord_G/0/1/0/all/0/1 Anyone else find these interesting? My interest is due to...
  23. S

    What is the value of the integral of a Dirac Delta function from 0 to infinity?

    just curiosity, if you integrate dirac-delta from exactly zero to infinity, will you get one or a-half? since it is symmetrical about zero, i think it is a half. is it? i mean: \int_{0}^{\infty} \delta(x) dx=\frac{1}{2} or is it 1? thanks.
  24. S

    Dirac equation and path integral

    Hello How to get the propagator for the Dirac equation (1+1) and forth and what about the Feynman's Checkerboard (or Chessboard) model Thanks I need Your help
  25. C

    Understanding Transition btwn Steps of Dirac Delta Function

    Can someone help me understand the transition between these two steps? <x> = \iint \Phi^* (p',t) \delta (p - p') \left( - \frac{\hbar}{i} \frac{\partial}{\partial p} \Phi (p,t) \right) dp' dp = <x> = \int \Phi^* (p,t) \left( - \frac{\hbar}{i} \frac{\partial}{\partial p} \Phi (p,t)...
  26. D

    Help with Dirac Delta Function Problem

    i can't solve there problem, please help me 1) delta(y^2-a^2) = 1/absolute 2a[delta(y-a)+delta(y+a)] 2) f(y)delta(y-a) = f(a)delta(y-a)
  27. E

    Dirac delta function (DE problem) solved

    NOTE: I actually found the correct answer while I was typing this :rolleyes: and since I already had it typed, I figured i would post anyway. mods you can do with it as you please or leave it for reference. thanks Here's the problem: A uniform beam of length L carries a concentrated...
  28. A

    What is the simplest way to understand the Dirac Delta function?

    1. INTRODUCTION Many students become frustrated when they first meet the Dirac Delta function, typically in a course involving electrostatics, or Laplace transforms. As it is commonly presented, the Dirac function seems totally meaningless: Either, it is "defined" as...
  29. S

    Dirac Delta Function: Understanding Laplace & Inverse Laplace Properties

    I have a test in Diff Eq. tommorow and part of the test is inovling the Dirac Delta function. I have no clue as to what it is at all. More specifically its Laplace and Inverse Laplace. If anyone could explain to me what the delta function is and how to use in in diff eq and what are its...
  30. arivero

    Van der Waerden's Derivation of the Dirac Equation

    Sakurai credits B. L. van der Waerden 1932 a pretty derivation of Dirac equation from two-component wave functions. First decompose E^2-p^2=m^2 as (i \hbar {\partial \over \partial x_0} + {\bf \sigma} . i \hbar \nabla) (i \hbar {\partial \over \partial x_0} - {\bf \sigma} . i \hbar...
  31. Reshma

    Explaining Dirac Delta Function: \vec A

    Can someone explain me the Dirac Delta function for the function: \vec A = \frac{\hat r}{r^2}
  32. P

    Question regarding Dirac matrices

    Hey there. In an exercise I was trying to show that every solution of the Dirac equation also solves the Klein-Gordon equation. Now I have two very simple questions: Is \gamma_\nu \gamma^\mu = \gamma^\nu \gamma_\mu ? And is \partial_\nu \partial^\mu = \partial^\nu \partial_\mu ...
  33. F

    Diff Eq and the Dirac Delta(impulse) function.

    Ok, I was given: Solve the following using superposition: \ddot{x}+2\dot{x}+4x=\delta(t) bounded by \dot{x}=0, x(0)=0 I solved the Homo eqn and got the following: x(t)=e^{-t}(\cos (\sqrt{3}t)+\frac{\sqrt{3}}{3}\sin ({\sqrt{3}t)) I also know that : \ddot{x}+2\dot{x}+4x=u(t)...
  34. H

    Is Dirac Notation Standard in QM?

    Hi all, I recently purchased Shankar's Principles of Quantum Mechanics which relies heavily on Dirac's bra-ket notation. I'm just wondering if this is the norm or should I get used to switching between what I'm learning and some other accepted standard notation? Thanks in advance!
  35. J

    LaTeX Latex - how to do Dirac slash notation

    Latex -- how to do Dirac slash notation How do you do Dirac slash notation using LaTeX? For instance, I want to be able to type /\partial = \gamma_i \partial^i /p = \gamma_i p^i /A = \gamma _i A^i with the slashes running through the symbols \partial , p, and A.
  36. A

    Help on QM Problem - Dirac Notation

    Consider the following state vector and Hamiltonian: |\psi (0) \rangle = \frac{1}{5}\left (\begin{array}{cc}3\\0\\4\end{array}\right ) \hat{H} = \left (\begin{array}{ccc}3&0&0\\0&0&5\\0&5&0\end{array}\right ) If we measure energy, what values can we obtain and with what probabilities...
  37. K

    Laplace transform of dirac delta function

    let S be the Unit Step function for a function with a finite jump at t0 we have: (*) L{F'(t)}=s f(s)-F(0)-[F(t0+0)-F(t0-0)]*exp(-s t0)] so: L{S'(t-k)}=s exp(-s k)/s-0-[1-0]*exp(-s k) = 0 & k>0 but S'(t-k)=deltadirac(t-k) and we know that L{deltadirac(t-k)}=exp(-s k) so...
  38. J

    Quantum mechanics in DIRAC notation

    Consider a particle in a harmonic pscillator potential V (x) is given by V = \frac{1}{2}m\omega^2 Also \hat a = n^\frac{1}{2}|n-1>, and \hat a\dagger = (n-1)^\frac{1}{2}|n-1> where \hat a = \frac{\beta}{\sqrt 2}(\hat x + \frac{i\hat p}{m\omega}) \hat a\dagger =...
  39. D

    Finding Momentum Density in Dirac Field

    How can I find the momentum density in the dirac field? Can someone show me, tell me how or give me a reference? Preferably not in relativistically covariant notation; I found this expression for the momentum density G, and want to know where it comes from...
  40. K

    Formal Proof: 4x4 Gamma Matrices in Special Relativity Project

    Hi everyone, From the condition: \gamma_{\mu}\gamma_{\nu}+\gamma_{\nu}\gamma_{\mu} = 2g_{\mu\nu} how does one formally proceed to show that the objects \gamma_{\mu} must be 4x4 matrices? I unfortunately know very little about Clifford algebras, and for this special relativity project...
  41. C

    Angular Momentum vs Hamiltonian in Dirac Field Theory (Canonical)

    I need some suggestions and/or corrections if I understand this correct? My questions are based on the book by Mandl and Shaw. Conserved currents are based on Noethers theorem and directly connected to spacetime and field transformations (rotations, translations, phase, ...). One can...
  42. J

    Quantum Mechanics with DIRAC NOTATION

    These are three quantum mechanics questions that I am having trouble with. a) Calculate <alpha/beta> by converting to standary notation. b) Prove that A is the identity operator where the sum is overa complete set of states. A is given in the attachment labelled by b c) IF the state C...
  43. T

    Where can I find information on solving for new energies using Dirac notation?

    So in my problem set I'm asked to solve for the "new energies of the system" I'm given the initial energies of this system and told a new potential is added. I know all the matrix elements. I solved for H|psi> so where do I go from here for the energies?
  44. E

    Are These Nascent Properties of the Dirac Delta Function Valid?

    Okay...so here's the thing. I have been researching the dirac Delta properties. The sights I've visited, thus far, are moderately helpful. I'm looking to tackle this question I'm about to propose, so for you Brains out there (the truly remarkable :rolleyes:) please don't post a solution...
  45. H

    Dirac Notation Help: Solve H, A, K Problems

    We are working on Dirac notation in my quantum class, and for the most part I see that it is a very easy way to do problems. But I am still getting stuck on how to deal with a few things on my current homework assignment. These come out of chapter 2 in the Cohen-Tannoudji book if you want to...
  46. T

    A naked singularity lies within the Sea of Dirac

    Hello all! I come in peace... sort of. :biggrin: As i was watching the anime Neon Genesis Evangelion, where one of the alien characters had the ability to capture its opponents in a Sea of Dirac, which was claimed to stretch over 800 meters in diameter, but had a thickness of only 3...
  47. MathematicalPhysicist

    The Dirac delta function question

    in the attatch file there is the dd function. what i want to know is: when x doesn't equal 0 the function equals 0 and the inegral is the integral of the number 0 which is any constant therefore i think the integral should be equal 0. can someone show me how this integral equals 1? for...
  48. M

    Exploring the Conservation Laws of the Dirac Field

    I have a question about the Dirac field. If as quantum field theory states , every point in the Universe is filled with "virtual" photons , and if these "virtual" photons in turn give rise to electron-positron pairs , which being components of matter and anti-matter collide and annihilate each...
  49. E

    Mathematica Schroedinger, Klein-Gordon & Dirac Propagators

    Let be the propagators for the Schroedinguer,Klein-Gordon and Dirac?...are they hermitian operators?..are their eigenfunctions ortogonal?...
  50. pellman

    Dirac delta function on the complex plane?

    Supposedly, &int; ez*(z - z0)f(z) dz*dz is proportional to f(z0) much in the same way that (1/2&pi;)&int; eiy(x - x0)f(x) dxdy = &int; &delta;(x - x0)f(x) dx = f(x0) Is this true? Could someone help convince me of it, or point me to a text? I would say that even if true, it...
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