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. pellman

    Dividing both sides by a Dirac delta function - ok?

    Suppose I wind up with the relation f(x)\delta (x-x')=g(x)\delta (x-x') true for all x'. Can I safely conclude that f(x) = g(x) (for all x)? Or am I overlooking something? this is a little too close to dividing both sides by zero for comfort.
  2. S

    Signals - Integration of Heavyside Step & Dirac Delta Functions

    Homework Statement \int_{-\infty}^{\infty}{u(t)e^{-t}(\delta(t+1)+\delta(t-1))dt Homework Equations \int_{-\infty}^{t}{u(t)dt = \left\{\begin{array}{cc}0,&\mbox{ if } t< 0\\t, & \mbox{ if } t>0\end{array}\right. \int_{-\infty}^{\infty}{f(t)\delta(t-a)dt} = f(a) The...
  3. F

    Problem with dirac convulation and power of a signal

    Homework Statement 1. i need to obtain the result of x[n] * x[n] (convolution) where x[n] = δ[n] + δ[n-1] 2. I need to obtain the power of the signal x(t) = 4 cos (ω0t) + 2 sin (ω0t) + 2cos(4ω0t) for R = 1 k Ω Homework Equations 1.Who do you convolute 2 diracs ? 2. what is the correct...
  4. J

    Intrinsic angular momentum of Dirac field

    (I'm sorry about my pool English..) I have a question about some exercise for intrinsic angular momentum part of quantized Dirac field. S_3 = \frac{1}{2}\int d^3 x :\Psi^\dagger \Sigma_3 \Psi : \Psi = \int \frac{d^3 k}{\left ( 2\pi \right )^3} \frac{m}{k_0} \left ( b_\alpha \left (...
  5. V

    Using Dirac Delta Function to Determine Point Mass Density

    I'm curious about the use of the Dirac Delta function. I am familiar with the function itself, but have never really seen in used in actual problems. The only problems I've worked with the function are those specifically about the function (ie. Evaluate the Dirac Delta function at x=3). My...
  6. A

    Where can I find the proof of Dirac's function properties?

    Where can i find the proof of dirac's function properties?
  7. P

    Is this Dirac Ket Bra correct?

    A B are two-body and one-body operators respectively. Is the following equation correct? If so, Would you give me the proof in real space? \sum\limits_{ijklm}\langle ij|A|km \rangle \langle m |B |l\rangle= \sum\limits_{ijkl}\langle ij|A B |k l\rangle
  8. T

    Probability current of dirac equation with vector potential

    Homework Statement Given the probability/energyprobability current of the dirac equation j^\mu=\Psi^{+}\gamma^{0}\gamma^{\mu}\Psi with continuity equation \partial_\mu j^\mu = 0 I need to find the current when there is an additional vector potential, introduced via minimal substitution...
  9. K

    Dirac Delta Function: Application & Uses

    how do we apply dirac delta function?when do we apply?
  10. J

    Dirac Delta in polar coordinates

    Homework Statement Hi, I would like to know what is the right way to write continuous deltas standing in a circle of radius a? Homework Equations The Attempt at a Solution I am not sure weather it's δ(r-a) or is it δ(r-a)/|r-a| Thank you
  11. D

    Integrating derivate of Dirac: Where is my fault?

    Hi, I want to do the following calculation: c_{m,n} = \int_{-\infty}^{\infty} t^m \phi(t-n)\,dt I know three things: I know the values of c_{m,n} for m={0,1} and the first 4 for m={2,3} I know that my \phi is symmetric, i.e. \phi(t) = \phi(-t) The Fourier transform of \phi(t)...
  12. B

    Calculating the Transpose of Adjoint of Dirac Spinor

    Homework Statement I want to compute the transpose of the adjoint of a Dirac spinor.Homework Equations My reasoning, based on learning Griffiths notation in “Intro to Elementary Particles”, p. 236, [7.58]: {\bar u^T} = {({u^\dag }{\gamma _0})^T} = {\gamma _0}^T{u^\dag }^T<mathop> =...
  13. J

    The Strangest Man: A Biography of Paul Dirac

    Good book, The Strangest Man by Graham Farmelo a biography of Paul Dirac man into antimatter, not just physics but also generally how things were in the 1900`s including the wars and politics
  14. D

    Prove Idntity - Dirac Delta - Distributions

    Homework Statement The Identity to prove: Homework Equations Using Integration by parts The Attempt at a Solution I couldn't produce the denominator.
  15. A

    Ramp function, Dirac delta function and distributions

    r(x) = x if x \geq 0 and r(x) = 0 if x<0 I have to show that: 1-\[ \int_{- \infty}^{+ \infty} r(x) \varphi ''(x) dx = \varphi(0) \] And 2- that the second derivative of r is the Dirac delta. And I managed to do this by integrating by parts. Howver, I don't get why I can't just write: \[...
  16. I

    Gamma 5 Dirac Matrice: Understanding Pseudo-Scalar

    Hi, i wonder somethin' when I see that definition of the matrice: \gamma^5=\gamma^0\gamma^1\gamma^2\gamma^3 I don't see why it is a pseudo-scalar.
  17. P

    Exploring Dirac Matrices in the Context of the Dirac Equation

    I wonder if I can chose any 4x4 matrices \gamma^\mu which fullfil anticommutationn relations \{\gamma^\mu,\gamma^\nu \}=2g^{\mu\nu} as a matricies in Dirac equation: i \gamma^\mu \partial_\mu \psi= m \psi . What changes in the theory if I chose different matricies? (of course I have to...
  18. P

    Dirac equation for proton/neutron

    Is it possible to incorporate into Dirac equation for proton the possibility of its transformation into neutron (isospin freedom)?
  19. P

    Dirac equation in curvilinear coordinates

    I wonder how Dirac equation transform under change of coordinates (in flat spacetime). Should I simply express partial derivaties of one coordinates in another or it is necessary to transform Dirac matrices as well?
  20. C

    Interfering Photons: How Paul Dirac Explained the Double Slit Experiment

    If photon's cannot couple with other photons , then when we shoot photons through a double slit and we get an interference pattern , How are the photons interfering with the other photons , and if there is no such thing as half photon like the photon is either absorbed or it is not ...
  21. E

    Dirac equation & Dirac matrices

    Hi! I was taught that the dirac matrices are AT LEAST 4x4 matrices, so that means that I can find also matrices of higher dimensions. The question is: what do these higher-dimension-matrices represent? Are they just mathematical stuff or have they got a physical meaning? I ask that because in...
  22. L

    Shankar CH1 Derivative of Dirac delta

    Hi, On p67 of shankar Principles of QM, he considers the delta functions derivative. He says: \int \delta'(x-x')f(x')dx'= \int \frac{d\delta(x-x')}{dx}f(x')dx'= \frac{d}{dx}\int \delta(x-x') f(x')dx'=\frac{df(x)}{dx} I don't understand how the second equality follows, how can the...
  23. A

    Proving the Discontinuity of the Dirac Function

    Dirac function :( Hello everyone... I have some triple with my PDEs course especially with the Dirac function. How can I prove it is discontinuous function? I do not know where can I start... Could somebody help me, please.
  24. L

    Is the Inner Product for Dirac Spinors Antisymmetric?

    Homework Statement Show that \psi (\gamma^a\phi)=-(\gamma^a\phi)\psi Homework Equations Maybe \{\gamma^a, \gamma^b\}=\gamma^a\gamma^b+\gamma^b\gamma^a=2\eta^{ab}I Perhaps also: (\gamma^0)^{\dag}=\gamma^0 and (\gamma^i)^{\dag}=-(\gamma^i) The Attempt at a Solution The gammas are...
  25. S

    Definition of time-ordered product for Dirac spinors

    I guess the answer to this question actually should be pretty obvious, but I still have problems getting it right though. I wonder about the definition of the time ordered product for a pair of Dirac spinors. In all the books I've read it simply says: T\left\{\psi(x)\bar{\psi}(x')\right\} =...
  26. A

    Delta Dirac: $\phi=-\pi+\epsilon$

    if \phi is a angular coordinate , between (-\pi,\pi) ¿how much is \delta(\phi-\pi) with \phi=-\pi+\epsilon?
  27. R

    Dirac equation for many particles system

    Can Dirac equation be used for many particles (fermions) system (i.e. a nucleus with many electrons)? And in this case how do you incorporate the anti-symmetry nature of the wavefunctions? Obviously Slater determined will complicate the equation to a point where it’s almost impossible to solve...
  28. F

    Integration of Dirac delta w/ different dimensionalities

    Hi! The Dirac delta satisfies \int dx f(x) \delta(x-a) = f(a) But how about \int d^3x f(x) \delta^{(4)}(x-a) Here, x and a are four-momenta, and the integral is over the regular 3-dim momentum. How does the delta behave here?
  29. P

    Fermi Dirac distribution function

    I have a question that is puzzling me as always...The Fermi-Dirac distribution function is (at T=0): f\epsilon=\frac{1}{e^{\beta(\epsilon-\epsilon_{F})}+1} and we know that we can subsitute f\epsilon by 1 for \epsilon< \epsilon_{F} and 0 otherwise. However what is f(-\epsilon)? The answer is...
  30. R

    Solution for Dirac equation with zero mass.

    The dirac equation for massless particles can be decoupled into separate equations for left and right handed parts. i \tilde{\sigma}^\mu\partial_\mu \psi_R= 0 and i \sigma^\mu\partial_\mu \psi_L= 0. Now we can have four solutions for each of the above equations. For the equation i...
  31. N

    Fourier transform and convolution, dirac function

    Hi everyone, I uploaded a solution about Fourier transform. At the solution of this problem, it states that make convolution. But i tried to do convolution but my result is not same with this result. When you do the convolution with 2.10 and 2.11, is the result 2.13 correct ? How is it done ...
  32. C

    Derivative of dirac delta function

    Homework Statement show x\frac{d}{dx}\delta(x)=-\delta)(x) using the gaussian delta sequence (\delta_n) and treating \delta(x) and its derivative as in eq. 1.151. Homework Equations the gaussian delta sequence given in the book is \delta_n=\frac{n}{\sqrt{\pi}}e^{-n^2x^2} and eq...
  33. D

    Finding mass with dirac delta function

    Homework Statement Distribution of matter is given in cylindrical coordinates: \rho(\vec{r})=\frac{1}{\rho}\delta(\rho^2-10\rho+9)\delta\left(\frac{z^2-a^2}{z^2+a^2}\right)\delta(\cot(\phi)) where a>0 is a constant. Find the complete mass of the object. Homework Equations The...
  34. E

    Dirac Delta Function: Definition &amp; Samples

    Hello, Dirac Delta Function is defined as the function that its amplitude is zero everywhere except at zero where its amplitude is infinitely large such that the area under the curve is unity. Sometimes it is used to describe a function consists of a sequence of samples such as...
  35. maverick280857

    How Does the Charge Conjugate Dirac Field Transform in Quantum Field Theory?

    Hi, I'm trying to work my way through Halzen and Martin's section 5.4. I'd appreciate if someone could answer the following question: How does j^{\mu}_{C} = -e\psi^{T}(\gamma^{\mu})^{T}\overline{\psi}^{T} become j^{\mu}_{C} = -(-)e\overline{\psi}\gamma^{\mu}\psi ? Is there some...
  36. D

    Dirac Delta Scaling: Solving the Integral Equation

    Using the defining property of the dirac delta function, \int{dx f(x) \delta(x-c)} show that \delta(ax)=\frac{1}{|a|}\delta(x) I think all I need to do is make the right u substitutions and it will come out right, but I can't think of how to make the substitutions...after a long time working...
  37. K

    Dirac delta function as the limit of a seqquence

    Dirac delta function as the limit of a sequence Hi.. If I have a sequence which in some limit tends to infinity for x=0 and goes to zero for x\neq0, then can I call the limit as a dirac delta function? If not, what are the additional constraints to be satisfied?
  38. maverick280857

    How to Derive Pauli's Equation from Dirac's Equation in a Weak Field?

    Hi, I'm trying to get to Pauli's equation from Dirac's equation in the weak field regime. Specifically, if I substitute \psi = \left(\begin{array}{cc}\chi \\ \varphi \end{array}\right) into the Dirac equation, I get two coupled equations i\frac{\partial\chi}{\partial t} =...
  39. E

    Evaluating Dirac Delta Integrals: Homework Statement

    Homework Statement Evaluate the following integrals: \int^{+\infty}_{-\infty}\delta[f(x)]dx and \int^{+\infty}_{-\infty}\delta[f(x)]g(x)dx Homework Equations \int^{+\infty}_{-\infty}\delta(x)dx=1 \int^{+\infty}_{-\infty}\delta(x)f(x)dx=f(0) \int^{+\infty}_{-\infty}\delta(x-a)f(x)dx=f(a)The...
  40. R

    The harmonic oscillator in terms of path integrals without dirac notation

    Hi, I'm desperately searching for some literature which discusses the harmonic oscillator, preferably simple, in terms of the path integral formulation. I am unfamiliar with dirac notation and want something as simple as possible which gives general results of the harmonic oscillator in terms of...
  41. F

    Does the Dirac measure still exist on a complex domain?

    does the Dirac measure still exist with complex variance? The Dirac delta function can be rigorously defined as a measure. See http://en.wikipedia.org/wiki/Dirac_delta_function#As_a_measure For the gaussian form of the Dirac delta function we have, \[ {\rm{\delta (x - x}}_0 ) =...
  42. F

    Dominate Convergence Theorem for the Dirac delta function

    I'm trying to understand the multiple limit processes involved with the Dirac delta function. Does it matter which process you do first the integral or the delta parameter that approaches zero? The closest theorem I found that addresses the order of taking limits is the Dominate Convergence...
  43. pellman

    Complex integral representation of Dirac delta function?

    We all know that \frac{1}{2\pi}\int{e^{ik(x-x')}dk=\delta(x-x'). i am working a problem which appears to depend on the statement \int e^{z^*(z-w)}dz^*\propto\delta(z-w) Does anyone know if this is valid? \delta(z-w) is defined in the usual way so that...
  44. K

    Derivation of Dirac equation using Lorentz transform

    Hi..I was studying Ryder, Chapter 2[Quantum Field Theory]...he derives the Dirac eq using Lorentz transformations..I found the approach fascinating..but there is one part I do not really understand... Just a few lines before he writes down the Dirac equation, he identifies \varphi_{R}(0) with...
  45. K

    Integration of dirac delta composed of function of integration variable

    Hi all, I'm working through Chandrasekhar's http://prola.aps.org/abstract/RMP/v15/i1/p1_1" and can not understand the steps to progress through Eq. (66) in Chapter 1. The integral is: \prod^{N}_{j=1} \frac{1}{l^{3}_{j}|\rho|}\int^{\infty}_{0} sin(|\rho|r_{j})r_{j}\delta...
  46. P

    Dirac equation for the conjugated field

    This is probably a stupid question, but when I apply the Euler-Lagrange equation to the Lagrangian density of the Dirac field I get for the conjugate field \bar{\psi} (-i \partial_\mu \gamma^{\mu} -m) = 0 (derivative acts to the left). But when I take a hermitian conjugate of the Dirac...
  47. F

    Product of dirac delta distributions

    I'm told that a product of distributions is undefined. See, http://en.wikipedia.org/wiki/Distribution_(mathematics)#Problem_of_multiplication where the Dirac delta function is considered a distribution. Now the Dirac delta function is defined such that, \[ \int_{ - \infty }^{ +...
  48. P

    Program for Traces of Dirac matrices

    Hi all, I want to calculate traces of Dirac matrices with a program like Mathematica. I found the package FeynCalc but it seems to be outdated. It is always producing results like this: 4 (-(DiracCanonical->False) (Factoring->False) (FeynCalcInternal->True) g^(mu nu)...
  49. A

    Understanding the Dirac Delta Potential: Exploring Its Integral Properties

    why in the problem of dirac delta potential, the integral \int^{\epsilon}_{-\epsilon}\phi''(x)dx is equal to \phi'(\epsilon)-\phi'(-\epsilon)? but \int^{\epsilon}_{-\epsilon}\phi(x)dx is equal to 0 if, for example\phi(x)=e^x then \phi(x)''=\phi(x) but, the firts integral is...
  50. G

    Hermitian conjugation and conserved current in the Dirac equation

    Consider the Dirac equation in the ordinary form in terms of a and \beta matrices i\frac{{\partial \psi }} {{\partial t}} = - i\vec a \cdot \vec \nabla \psi + m\beta \psi The matrices are hermitian, \vec a^\dag = \vec a,\beta ^\dag = \beta . Daggers denote hermitian...
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