What is Dirac: Definition and 896 Discussions

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. L

    Dirac gammology - dimension of the algebra

    Dirac matrices satisfy the relations: \gamma^\mu\gamma^\nu+\gamma^\nu\gamma^\mu=2g^{\mu\nu} I would like to understand why the dimension of this algebra in 3+1 dimensions is 4. If we're looking for all possible sets {\gamma^0,\gamma^1,\gamma^2,\gamma^3} of 4x4 matrices that satisfy this, how...
  2. S

    Dirac delta function identities

    hi deoes anyone know any online resource for proofs of Dirac delta function identities and confirming which representations are indeed DD functions Thanks a lot.
  3. DrClaude

    Dirac equation in a central field (Schiff)

    Not really a homework problem, but I think it fits better in this section. Homework Statement I'm having a problem with eq. (53.12) in the book Quantum Mechanics by Schiff. In the context of the Dirac equation, we have $$ \hbar^2 k^2 = (\vec{\sigma}' \cdot \vec{L})^2 + 2\hbar (\vec{\sigma}'...
  4. S

    Question about the solutions of the dirac equation

    I am working through Greiner's text on relativistic quantum mechanics and I am confused about what appear to be two somewhat contradictory ways of presenting the solutions of the Dirac equation. In chapter 2, he just treats the equation as a system of coupled differential equations and solves...
  5. R

    Integration test of dirac delta function as a Fourier integral

    Homework Statement Problem: a) Find the Fourier transform of the Dirac delta function: δ(x) b) Transform back to real space, and plot the result, using a varying number of Fourier components (waves). c) test by integration, that the delta function represented by a Fourier integral integrates...
  6. sinaphysics

    A question about Dirac Delta Function

    For proving this equation: \delta (g(x)) = \sum _{ a,\\ g(a)=0,\\ { g }^{ ' }(a)\neq 0 }^{ }{ \frac { \delta (x-a) }{ \left| { g }^{ ' }(a) \right| } } We suppose that g(x)\approx g(a) + (x-a)g^{'}(a) Why for Taylor Expansion we just keep two first case and neglect others...
  7. M

    Simplifying Operator and Dirac Algebra for Kets

    Hi Guys, I am facing a problem playing around with some operators and Kets, would like some help! I have \langle \Psi | A+A^\dagger | \Psi \rangle .A Could someone simplify it? Especially is there a way to change the last operator A into A^\dagger? The way I thought about this is...
  8. D

    Any quick help with rearranging schrodinger equation in dirac notation

    I'm looking through my lecture notes, (studying relativistic corrections/perturbation theory using hydrogen), and I seem to have a mind block with one of the equations (the last one from the 3 in the middle). I know that the kinetic energy and coulomb potential has been subbed in for the...
  9. P

    Function whose Fourier transform is Dirac delta

    Is there a time domain function whose Fourier transform is the Dirac delta with no harmonics? I.e. a single frequency impulse
  10. A

    The need for the Dirac delta function

    So part of the idea presented in my book is that: div(r/r3)=0 everywhere, but looking at this vector field it should not be expected. We would expect some divergence at the origin and zero divergence everywhere else. However I don't understand why we would expect it to be zero everywhere but...
  11. N

    How to Solve the Dirac Equation for a Two-Particle System?

    Hello I am trying to solve the dirac equation. I want to solve the dirac eq say for 2 particle system. therefore i request you to please suggest me the book or some material. Thank you
  12. anorlunda

    Dirac on Spreading Wave Packets

    My layman's intuition tells me that wave packets normally spread out in space and disperse, except in special circumstances. Photons don't behave like that. In The Principles of Quantum Mechanics, pp 124-125, Dirac discusses the equations of motions of a photon wave packet. He says...
  13. J

    Casual talk. Constrained Hamilton systems. Dirac brackets.

    Casual talk. Constrained Hamilton systems. Dirac-Poisson brackets. Casual talk. Constrained Hamilton systems. Dirac-Poisson brackets. Hi guys, I think I have finally succeeded in understanding the ideas which Dirac explained in the two first chapters of his book "Lectures on Quantum...
  14. Matterwave

    Exploring the Nature of Neutrinos: Dirac vs Majorana

    Hi, I recently attended several lectures on the topic of neutrino astrophysics. I wanted to verify some of the fact that I gleaned for them, specifically about the Dirac vs Majorana nature of neutrinos. 1) The most basic fact first. If a neutrino is Dirac in nature, then it has 3 flavors...
  15. A

    Derivative of the Step Function: Exploring the Delta Distribution

    How can I find the derivative of a step function?
  16. W

    Is There an Error in the Third Dirac Current Equation?

    I'm having a problem writing the third Dirac current eq. $$1 = \int ψ^t \gamma^0 \gamma^2 ψ$$ which should come out as $$1 = \int i ψ^0 ψ^3 - i ψ^1 ψ^2 + i ψ^2 ψ^1 - i ψ^3 ψ^0$$ By inspection the first and last terms add to zero and the second and third terms add to zero, so the integral...
  17. anorlunda

    Can I delete a thread on Lef In Dirac's Principles of Quantum Mechanics?

    On page 86 of The Principles of Quantum Mechanics, Dirac left me in his dust. I quote: [u_{1},v_{1}](u_{2}v_{2}-v_{2}u_{2})=
  18. C

    The application of of Fermi Dirac statistics in the white dwarf

    hi guys, I wonder if I have fully understood the Fermi Dirac statistics properly, but I have a question on it regarding its application in the white dwarf research. I read the Fermi energy is applicable for T=0, now if the core of a white dwarf is too hot then how can we apply the Fermi Dirac...
  19. G

    Good introduction for dirac notation

    Hi guys, I m reading some theoretical physics paper that requires knowledge of dirac notation if someone could point me out to a good tutorial on it I come from a math background but I am studying this paper with my supervisor.
  20. S

    Solution of differential equation with Dirac Delta

    Is it possible to solve a differential equation of the following form? $$\partial_x^2y + \delta(x) \partial_x y + y= 0$$ where ##\delta(x)## is the dirac delta function. I need the solution for periodic boundary conditions from ##-\pi## to ##\pi##. I've realized that I can solve this for some...
  21. L

    Dirac delta function. Integral

    How to calculate ##\int^{\infty}_{-\infty}\frac{\delta(x-x')}{x-x'}dx'## What is a value of this integral? In some youtube video I find that it is equall to zero. Odd function in symmetric boundaries.
  22. D

    Cannot make sense of a derivation step involving dirac delta

    I am self studying the 17th Chapter of "Mathematical Methods for Physics and Engineering", Riley, Hobson, Bence, 3rd Edition. It is about eigenfunction methods for the solution of linear ODEs. Homework Statement On page 563, it states: "As noted earlier, the eigenfunctions of a...
  23. I

    Dirac notation Schwarz Inequality Proof

    Homework Statement This isn't really a problem so much as me not being able to see how a proof has proceeded. I've only just today learned about Dirac notation so I'm not too good at actually working with it. The proof in the book is: |Z> = |V> - <W|V>/|W|^2|W> <Z|Z> = <V - ( <W|V>/|W|^2 ) W|...
  24. pellman

    Heisenberg equation of motion for the Dirac field?

    I would expect that the Heisenberg equation of motion for the Dirac field would yield the Dirac equation. Indeed, these lecture notes claim it as a fact in eq 7.7 but without proof. My trouble is that I know the anti-commutation rules for the Dirac field but I don't know how to calculate the...
  25. P

    Dirac Spinor Transformation (Ryder)

    Homework Statement This complies when I type it in my Latex editor, but not on here. If you could either let me know how to fix that or copy and paste what I have into your own editor to help, that'd be great. Thanks! While Ryder is setting up to derive a transformation rule for Dirac...
  26. LarryS

    Spin vs Dirac Equation: Understanding Physical Spin

    I believe I understand the mathematical derivation of the Dirac equation. I understand how the four 4X4 matrices, and their relation to the 2X2 Pauli Matrices, arise from that derivation. I understand that the 3 spin observables for Fermions are ALSO represented by the 3 Pauli Matrices...
  27. T

    Index Notation & Dirac Notation

    Quantum Mechanics using Index notation. Is it possible to do it? I really don't get the Dirac Notation, and every-time I encounter it, I either avoid the subject, or consult someone who can read it. There doesn't seem to be any worthy explanation about it, and whenever I ask what is the Hilbert...
  28. D

    How can I derive the Dirac equation from Lagrangian?

    How do i derive the Dirac equation from L_{dirac} = \overline{ψ}_α [i(γ^μ)_{αβ} - m]ψ_β ?. I can get it for the \overline{ψ} , but I'm having trouble deriving it for ψ .
  29. ChrisVer

    Dirac Lagr in Hermitian form

    Is there any way to write the Dirac lagrangian to have symmetric derivatives (acting on both sides)? Of course someone can do that by trying to make the Lagrangian completely hermitian by adding the hermitian conjugate, and he'll get the same equations of motion (a 1/2 must exist in that...
  30. P

    Hermitian conjugate of Dirac field bilinear

    In the standard QFT textbook, the Hermitian conjugate of a Dirac field bilinear \bar\psi_1\gamma^\mu \psi_2 is \bar\psi_2\gamma^\mu \psi_1. Here is the question, why there is not an extra minus sign coming from the anti-symmetry of fermion fields?
  31. D

    Entropy of a Fermi dirac ideal gas

    Hello Homework Statement From the expression of the partition function of a fermi dirac ideal gas ln(Z)=αN + ∑ ln(1+exp(-α-βEr)) show that S= k ∑ [ <nr>ln(<nr>)+(1-<nr>)ln(1-<nr>) Homework Equations S=k( lnZ+β<E>) <nr>=-1/β ∂ln(Z)/∂Er <E>=-∂ln(Z)/∂β The Attempt at a Solution I...
  32. K

    Computation about Gaussian and Dirac Delta Function

    I have a Gaussian distribution about t, say, N(t; μ, σ), and a a Dirac Delta Function δ(t). Then how can I compute: N(t; μ, σ) * δ(t > 0) Any clues? Or recommender some materials for me to read? Thanks!
  33. E

    Dirac Delta Function: Is delta(x-y) the Same as delta(y-x)?

    Sorry if the question seems naive but if we have the Dirac delta function delta(x-y) is it the same as delta(y-x)?? Or there are opposite in sign? And why ? Thank you for your time
  34. Matterwave

    Questions on the Dirac equation

    I must admit that I have never had a great familiarity with the Dirac equation. No matter how many times I study it, I get bogged down in the algebra and never seem to get a good understanding of it. So here's a few questions in my mind at the moment. I am referring here to the Dirac equation as...
  35. M

    Dirac ket-bra simplification over here.

    I usually know how to manipulate bras and kets. But I probably found difficulty because of the double summation. How did Sakurai manage to go from the second line to the ird line in the attachment? SECTION 4.4 in Sakurai.
  36. T

    Understanding Dirac notation - Product of ops. is product of matrices

    Homework Statement This makes intuitive sense to me, but I am getting stuck when trying to read the Dirac notation proof. Anyway, the author (Shankar) is just demonstrating that the product of two operators is equal to the product of the matrices representing the factors. Homework Equations...
  37. M

    Transition Rates / Squared Dirac Delta

    I am not understanding something from my textbook. This is related to Fermi's Golden rule. It's about what happens when the matrix element of the perturbation H' ends up being a Dirac delta for chosen normalization. Here is Fermi's Golden rule. \Gamma_{ba} = 2\pi \left|\langle b \mid H'\mid a...
  38. D

    Klein Paradox - Dirac equation with step potentional

    Hi all! I was reading up on the Klein paradox in Itzykson & Zuber's Quantum Field Theory (but I think this is a pretty standard part that's probably present in most QFT textbooks) and on page 62 they have a pretty straight forward solution to the Dirac equation with a step potential. I've...
  39. D

    The Dirac Lagrangian Density: A Brief Overview

    Hi, This is probably a trivial question, but I just wanted to check my understanding. Is the following expression for the Dirac Lagrangian correct...
  40. E

    Dirac Delta/Mean Value Theorem Problem

    Homework Statement Consider the function \delta_{\epsilon}(x) defined by \delta_{\epsilon}(x)=\begin{cases} 0\text{,} & x<-\epsilon\text{,}\\ \frac{3}{4\epsilon^{3}}(\epsilon^{2}-x^{2})\text{,} & \epsilon\leq x\leq\epsilon\text{,}\\ 0\text{,} & \epsilon<x\text{,} \end{cases} (b) Consider a...
  41. M

    What is the use of Dirac delta function in quantum mechanics?

    If you ask me define Dirac delta function, i can easily define it and prove its properties using laplacian or complex analysis method. But still i don't understand what is the use of DIRAC DELTA FUNCTION in quantum mechanics. As i have done some reading Quantum mechanics from Introduction to...
  42. S

    Expectation value for momentum operator using Dirac Notation

    Question and symbols: Consider a state|ε> that is in a quantum superposition of two particle-in-a-box energy eigenstates corresponding to n=2,3, i.e.: |ε> = ,[1/(2^.5)][|2> + |3>], or equivalently: ε(x) = [1/(2^.5)][ψ2(x) + ψ3. Compute the expectation value of momentum: <p> = <ε|\widehat{}p|ε>...
  43. D

    Exponential projection operator in Dirac formalism

    Homework Statement Hey guys. So here's the situation: Consider the Hilbert space H_{\frac{1}{2}}, which is spanned by the orthonormal kets |j,m_{j}> with j=\frac{1}{2}, m_{j}=(\frac{1}{2},-\frac{1}{2}). Let |+> = |\frac{1}{2}, \frac{1}{2}> and |->=|\frac{1}{2},-\frac{1}{2}>. Define the...
  44. E

    Dirac Delta source for vectorial equation

    Hello! By manipulating Maxwell's equation, with the potential vector \mathbf{A} and the Lorentz' gauge, one can obtain the following vector wave equation: ∇^2 \mathbf{A}(\mathbf{r}) + k^2 \mathbf{A}(\mathbf{r}) = -\mu \mathbf{J}(\mathbf{r}) The first step for the solution is to consider a...
  45. X

    Proving that the Dirac Delta is the limit of Gaussians

    Homework Statement I need to prove for arbitrary functions φ(x) that: \lim_{\lambda \to 0} \int_{-\infty}^{\infty} \frac{1}{\sqrt{2 \pi} \lambda} exp\left( \frac{-x^{2}}{2 \lambda^{2}} \right) \varphi(x) dx = \varphi(0), which, in the sense of distributions is basically the delta...
  46. ChrisVer

    Exploring Dirac Spinors: Two-Particle Inputs

    Hello. I would like to ask something that will help me understand a little better how we work with Dirac spinors' inputs... I know that the dirac equation has 4 independent solutions, and for motionless particles, the (spinor) solutions are: u_{+}=(1,0,0,0)^{T} electron +1/2...
  47. F

    Dirac Delta Function Help: Justifying Translation/Sifting Property

    I have been reviewing some details on the Dirac Delta function and I've hit a little bit of a road block with trying to wrap my head around how the Translation/Sifting property of the function is justified. Now according to my text the overall definition is the generalized function with the...
  48. H

    Dirac Expression for Vector Potential of a Magnetic Monopole Problem

    Hi, Homework Statement Consider the vector potential, \vec{A}(\vec{x}), below. The problem is to calculate \vec{A}(\vec{x}) explictly, and show that it has components A_{r}, A_{\theta} and A_{\phi} Homework Equations \vec{A}(\vec{x}) = \frac{g}{4\pi} \int_{-\infty}^{0} \frac{dz'...
  49. N

    Dirac Notation and Hermitian operators

    Homework Statement Using Dirac Notation prove for the Hermitian operator B acting on a state vector |ψ>, which represents a bound particle in a 1-d potential well - that the expectation value is <C^2> = <Cψ|Cψ>. Include each step in your reasoning. Finally use the result to show the...
  50. C

    [Srednicki] Charge Conjugation of Dirac Spinor

    Homework Statement I am reading Srednicki's QFT up to CPT symmetries of Spinors In eq. 40.42 of http://web.physics.ucsb.edu/~mark/ms-qft-DRAFT.pdf I attempted to get the 2nd equation: C^{-1}\bar{\Psi}C=\Psi^{T}C from the first one: C^{-1}\Psi C=\bar{\Psi}^{T}C Homework Equations...
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