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. GIM

    Change of the order of integration including Dirac delta

    Can somebody help me? I am studying Faddeev-Popov trick, following the Peskin and Schroeder's QFT book, but I can't understand one thing. After they inserted the Faddeev-Popov identity, $$I = \int {{\cal D}\alpha \left( x \right)\delta \left( {G\left( {{A^\alpha }} \right)} \right)\det \left(...
  2. Traruh Synred

    A Clifford Algebra and generalizing Dirac equaution

    http://arxiv.org/abs/1001.2485 --- The above paper is about a possible two-time formulation of physics. It is by serious people. To understand it I'm trying to generalized the Dirac eqn. to 3+2 dimensions with signature (++---) I found the following (now closed post) useful...
  3. ShayanJ

    A Non-negativity of the eigenvalues of the Dirac operator

    How can I prove that the eigenvalues of the operator ## i\gamma^\mu \partial_\mu ## are non-negative? I've tried using the ansatz ## \psi=u(p) e^{ip_\nu x^\nu} ## but it didn't help. I've also tried playing with the equation using the properties of gamma matrices but that doesn't seem to lead...
  4. S

    I Fourier transform of Dirac delta

    In lectures, I have learned that F(k)= \int_{-\infty}^{\infty} e^{-ikx}f(x)dx where F(k) is the Fourier transform of f(x) and the inverse Fourier transform is f(x)= \frac{1}{2\pi}\int_{-\infty}^{\infty} e^{ikx}f(k)dk . But on the same chapter in the lecture notes, there is an example solving...
  5. X

    Question about the Dirac Delta Function

    Homework Statement Find the Fourier spectrum of the following equation Homework Equations ##F(\omega)=\pi[\delta(\omega - \omega _0)+\delta(\omega +\omega_0)]## The Attempt at a Solution Would the Fourier spectrum just be two spikes at ##+\omega _0## and ##-\omega _0## which go up to infinity?
  6. Kevin McHugh

    I Question regarding the Dirac delta function

    Given the definition: δ(x) = 0 for all x ≠ 0 ∞ for x = 0 ∫-∞∞δ(x)dx = 1 I don't understand how the integral can equal unity. The integral from -∞ to zero is zero, and the integral from 0 to ∞...
  7. ShayanJ

    A Angular momentum of Dirac particle

    I'm reading Sakurai's "Advanced Quantum Mechanics" (which is different from his "Modern Quantum Mechanics"). In chapter 3, which is about the Relativistic Quantum Mechanics of spin 1/2 particles, after discussing the covariance of the Dirac equation, he goes on to give some examples to clarify...
  8. M

    Dirac Trace Algebra: Which Gamma Matrices Matter?

    Homework Statement This isn't a homework problem; it's just something I'm working on and I'm a little confused as to how to go about dealing with what I have. I have several traces of Dirac's gamma matrices, and I know that the trace of an odd number of gamma matrices is zero. So my first...
  9. Nasbah BM

    I Why we use Dirac delta function? (in 1 Dimension & 3 Dimesions)

    I want to understand why and where exactly we use dirac delta function? what is its exact use?
  10. R

    I General Solution of Dirac Delta Potential Well

    We know that the solutions of time-independent Dirac delta potential well contain bound and scattering states: $$\psi_b(x)=\frac{\sqrt{mu}}{\hbar}e^{-\frac{mu|x|}{\hbar^2}}\text{ with energy }E_b=-\frac{mu^2}{2\hbar^2}$$ and $$ \psi_k(x)= \begin{cases} A(e^{ikx}+\frac{i\beta}{1-i\beta}e^{-ikx})...
  11. kq6up

    I Help With Black Board EQ's in a P.A.M. Dirac Lecture

    My professor assigned us to watch the Dirac videos on Youtube: The video is extremely poor quality. Dirac does speak the equations as he is writing them, so I have been able to catch many of them. I am wondering if a team effort at trying to decipher these would be a worthy effort for all...
  12. R

    Dirac Delta Function in Differential Equation

    Homework Statement Find the solution to: $$\frac{d^2}{dt^2} x + \omega^2 x = \delta (t)$$ Given the initial condition that ##x=0## for ##t<0##. First find the general solution to ##t>0## and ##t<0##. Homework Equations The Attempt at a Solution This looks like a non-homogeneous second...
  13. DiracPool

    Swan song interview with Paul Dirac

    I wasn't sure what section to post this in as there's several things going on here. We got quantum mechanics, we got special and general relativity, and we got Friedrich Hund who, as far as I can tell, could be the inspiration for Dr. Strangelove... If you want the full 20 minute interview...
  14. Rococo

    Calculating <ψ(t)|x|ψ(t)> in a Harmonic Oscillator Potential

    Homework Statement A particle in a harmonic oscillator potential in the following state after a time t: ## | ψ(t) > = \frac{1}{\sqrt{2}} [e^{(-iE_0 t/\hbar)} |ψ_0> + e^{(-iE_1 t/\hbar)} |ψ_1> ] ## I want to write an expression for ## <ψ(t)| \hat{x} | ψ(t) > ##. Homework Equations The...
  15. ZKhawla

    Dirac derivative and signal energy distribution

    Hi, I'm writing a mathematical expression of energy distribution of a signal, and in the formula I’ve found first and second derivative of delta function. I have to analyze my result but couldn’t found how to read these two derivative from an energy point of view. And how can we see further...
  16. A

    Bessel functions and the dirac delta

    Homework Statement Find the scalar product of diracs delta function ##\delta(\bar{x})## and the bessel function ##J_0## in polar coordinates. I need to do this since I want the orthogonal projection of some function onto the Bessel function and this is a key step towards that solution. I only...
  17. omidaut

    Representation of Dirac Spinors

    Hi there, I have a question with its answer, but, still I don't understand it. Can anybody help me in explaining it? Thanks.
  18. J

    A Separating the Dirac Delta function in spherical coordinates

    The following integral arises in the calculation of the new density of a non-uniform elastic medium under stress: ∫dx ρ(r,θ)δ(x+u(x)-x') where ρ is a known mass density and u = ru_r+θu_θ a known vector function of spherical coordinates (r,θ) (no azimuthal dependence). How should the Dirac...
  19. Clarky48

    Dirac notation - expectation value of kinetic energy

    It's my first post so big thanks in advance :) 1. Homework Statement So the question states "By interpreting <pxΨ|pxΨ> in terms of an integral over x, express <Ekin> in terms of an integral involving |∂Ψ/∂x|. Confirm explicitly that your answer cannot be negative in value." ##The 'px's should...
  20. DiracPool

    Momentum-free spinors and the Dirac equation

    We can create a Dirac equation with no potential energy and zero momentum and still get spin? Is this correct? How do the Pauli spin matrices apply here? On the surface, the Dirac equation seems fairly straightforward, but when you dig even a little deeper, it's starts to become unwieldy...
  21. chi_rho

    Delta Function Identity in Modern Electrodynamics, Zangwill

    I am currently reading Modern Electrodynamics by Andrew Zangwill and came across a section listing some delta function identities (Section 1.5.5 page 15 equation 1.122 for those interested), and there is one identity that really confused me. He states: \begin{align*} \frac{\partial}{\partial...
  22. KostasV

    Delta function and dirac notation

    Hello there ! I found this discussion http://physics.stackexchange.com/questions/155304/how-do-we-normalize-a-delta-function-position-space-wave-function about dirac notation and delta function . The one that answers to the problem says that ##<a|a>=1## and ##<a|-a>=0## . As far as i know: 1)...
  23. j3dwards

    Average of function (using dirac delta function)

    Homework Statement Compute the average value of the function: f(x) = δ(x-1)*16x2sin(πx/2)*eiπx/(1+x)(2-x) over the interval x ∈ [0, 8]. Note that δ(x) is the Dirac δ-function, and exp(iπ) = −1. Homework Equations ∫ dx δ(x-y) f(x) = f(y) The Attempt at a Solution Average of f(x) = 1/8 ∫from...
  24. ognik

    MHB Find Fourier series of Dirac delta function

    Hi - firstly should I be concerned that the dirac function is NOT periodic? Either way the problem says expand $\delta(x-t)$ as a Fourier series... I tried $\delta(x-t) = 1, x=t; \delta(x-t) =0, x \ne t , -\pi \le t \le \pi$ ... ('1' still delivers the value of a multiplied function at t)...
  25. C

    Time dependent three dimensional dirac delta function

    Ok so for equations of spherical wave in fluid the point source is modeled as a body force term which is given by time dependent 3 dimensional dirac delta function f=f(t)δ(x-y) x and y are vectors. so we reach an equation with ∫f(t)δ(x-y)dV(x) over the volume V. In the textbook it then says that...
  26. akk

    A Normalization constant of Fermi Dirac distribution function

    Fermi-Dirac distribution function is given by f(E)=(1)/(Aexp{E/k_{B}T}+1) here A is the normalization constant? How we can get A? E is the energy, k_{B} is the Boltzmann constant and T is the temperature. thank you
  27. N

    Canonical momentum for Dirac adjoint field

    I read that the canonical momentum for Dirac adjoint field is zero. Why is that?
  28. B

    Dirac Delta Function - Fourier Series

    1. Homework Statement Find the Fourier series of ##f(x) = \delta (x) - \delta (x - \frac{1}{2})## , ## - \frac{1}{4} < x < \frac{3}{4}## periodic outside. Homework Equations [/B] ##\int dx \delta (x) f(x) = f(0)## ##\int dx \delta (x - x_0) f(x) = f(x_0)##The Attempt at a Solution...
  29. M

    Finding Band Gaps for Dirac Comb Potential

    Homework Statement Find band gaps for Dirac Comb potential $$V = \sum_n aV_0(x-na) $$ Homework Equations Bloch Theorem $$\psi(x+a) = e^{ika}\psi(x)$$ The Attempt at a Solution I can solve exactly up to $$\cos(k a) = \cos(\kappa a) + \frac{2ma^2V_0}{\hbar^2}\frac{\sin(\kappa a)}{\kappa a} =...
  30. Spinnor

    Dirac equation in 1+1 spacetime, resources

    Trying to get a good understanding of the Dirac equation in 1 space dimension. Looking for resources and stumbled upon another source that should keep me busy over the weekend. Looks to be made as simple as possible while not leaving out the physics. Thanks to Hans for putting it online...
  31. jk22

    Exploring the Dirac Delta Function

    I consider the Dirac delta. In physics the delta squared has an infinite norm : $$\int\delta (x)^2=\infty $$ But if i look at delta being a functional i could write : $$\delta [f]=f (0) $$ hence $$\delta^2 [f]=\delta [\delta [f]]=\delta [\underbrace {f (0)}_{constant function}]=f (0)$$ Thus...
  32. Einstein's Cat

    Learning Quantum Mechanics with Dirac: Understanding Ket Vectors

    I'm attempting to learn the mathematics of quantum mechanics using textbooks such as "The Principles of Quantum Mechanics" by Dirac. I'm uncertain however of how ket vectors work! Say |A> + |B> = |C>, then what does |C> please represent?
  33. A

    The current of a single electron

    I guess my question has multiple parts. Any help in understanding the questions is appreciated. Assume a single electron in free space. The electron starts moving because of some force applied to it. The source of the force could be pretty much anything, let's say a uniform E-field in X...
  34. V

    Delta Dirac 3d Dimensional Analysis

    1. I ´m trying to do the dimensional analysis of the Delta Dirac in 3 Dimensions. [PLAIN]http://[url=http://postimg.org/image/oif09fcd5/] 3. This is my atempt [PLAIN]http://[url=http://postimg.org/image/4qavbtv4p/]
  35. S

    Dirac equation and structure of spacetime

    I've been reading about the Dirac equation, and most authors eventually make some statement to the effect that the fact of spin and antiparticles falling out of the equation reflects a deep connection to the structure of spacetime. Is the implication that the math requires four particle states...
  36. Lylo

    The triple Dirac delta-function well: getting KAPPA

    Homework Statement I will try to be light on the math as I am just now getting into using LaTex, and I don't want things to get too ugly from me not using it. Hello there, I found a thread here on PF concerning a triple delta-function potential well problem, which was a bit informative...
  37. A

    Exploring the Dirac Equation: β,αk,pk, and Ψ(x,t)

    Hello there I have a problem about Dirac equation So I want to know what is matrices β,αk,pk value. And is it right that with Dirac equation we can calculate every particle spin and how we take dervitative of Ψ(x,t) and what is Ψ(x,t) value.
  38. ddd123

    Microcanonical partition function - Dirac delta of operators

    Homework Statement Why is it that the microcanonical partition function is ##W = Tr\{\delta(E - \hat{H})\}##? As in, for example, Mattis page 62? Moreover, what's the meaning of taking the Dirac delta of an operator like ##\hat{H}##? Homework Equations The density of states at fixed energy is...
  39. S

    Charge conjugation matrix and Dirac equation's solutions

    I saw this somewhere but I think it is wrong... I already read Griffiths' "Introduction to Particle Physics" (the 1st edition) from the page 216 to the page 222 (chapter of Quantum Electrodynamics - section "Solution to the Dirac Equation") and I didn't understood why was there the imaginary...
  40. C

    Proving a Dirac delta property

    Homework Statement [/B] Prove that \delta[a(x-x_1)]=\frac{1}{a}\delta(x-x_1) Homework Equations In my attempt I have used \delta(ax)=\frac{1}{a}\delta(x) but I'm not sure I'm allowed to use it in this proof. The Attempt at a Solution Some properties of Dirac delta function are proven using...
  41. Terocamo

    Fourier Transform of Dirac Comb/Impulse Train

    With Dirac Comb is defined as follow: $$III(t)=\sum_{n=-\infty}^\infty\delta(t-nT)$$ Fourier Transform from t domain to frequency domain can be obtained by: $$F(f)=\int_{-\infty}^{\infty}f(t)\cdot e^{-i2\pi ft}dt$$ I wonder why directly apply the above equation does not work for the Dirac Comb...
  42. Terocamo

    Confusion Surrounding Dirac Delta Comb Sampling: Why is δ(0) Infinite?

    I have recently digged up a post in the forum about a confusion arise from definition of Dirac Delta function and I am actually really bothered by it (link to the thread). When people talk about sampling some function f(x) with Dirac Comb, or impulse train, they would be talking about the...
  43. Domenico94

    Response of a system (Control theory)

    Hi everyone. I'm studying for the exam of control theory, and now I'm having an hard time with the response of a system, in particular when we have oscillations. Suppose you have a system, with a transfer function, say, G(S), in the form: G(S) = 1 -------------------...
  44. J

    Dirac Relativistic Wave Equation

    I would like people's opinions on why the negative energy solutions of Dirac's Relativistic Wave equation were simply ignored in 1934 to make things fit. Another related question is with the energy conservation laws as they stand. Why in pair production from a photon at 1.022MeV forming a...
  45. L

    Getting to Grips with Dirac Notation: A Stuck Student's Story

    I've been working through some dirac notation and I'm stuck... Here's where I'm at: I understand that an expectation value: <x> = ∫ ψ* x ψ dx = <ψ|xψ> = <ψ|x|ψ> Also, we can say H|ψ> = E|ψ> where E is an eigenvalue of the operator H and |ψ> represents a state your acting on. I get that you can...
  46. LarryS

    Dirac Equation - Analytic Solution?

    The quantum harmonic oscillator is an analytic solution of the Schrodinger Equation. Does the original Dirac Equation for a free electron also have an analytic solution? Of course a "solution" of the Dirac Equation would consist of 4 functions. Thanks in advance.
  47. S

    How Does Chirality Affect the Dirac Adjoint in Quantum Mechanics?

    I have a question about chirality. When a spinor \psi have plus chirality, namely \gamma_5\psi=+\psi, how can I write this condition for the Dirac adjoint \bar{\psi}=\psi^\dagger i\gamma^0? Let me choose the signature as \eta_{\mu\nu}=\mathrm{diag}(-,+,+,+) and define \gamma_5\equiv...
  48. F

    Understanding Photon Polarization with Dirac's Principles of Quantum Mechanics

    Is this statement correct: ? "The effect of making this observation is to force the photon entirely into the state of parallel or entirely into the state of perpendicular polarization." * I don't see how you can talk about how the polarization of a photon changes if the photon gets absorbed...
  49. AwesomeTrains

    State transformation - Position to momentum space (Dirac)

    Hey everyone! It's my first semester with quantum mechanics and I'm uncertain if my solution of this problem is correct, would be nice if someone could check and let me know :smile: 1. Homework Statement I have to calculate the representation of the state: |\alpha \rangle \equiv exp[-i...
  50. Z

    Exploring Dirac Delta Function: Using to Express 3D Charge Distributions

    Hello community, this is my first post and i start with a question about the famous dirac delta function. I have some question of the use and application of the dirac delta function. My first question is: Using Dirac delta functions in the appropriate coordinates, express the following charge...
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