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. S

    I Expectation for the Harmonic Oscillator ( using dirac)

    I've been trying to form a proof using , using majorly dirac notation.There has been claims that its much better to use in QM. The question i wanted to generally show that the expected value is Zero for all odd energy levels.I believe i have solved the question but I am a bit Iffy about a step...
  2. S

    B Conjugation , involving operators in Dirac Notation.

    In a PDF i was looking through i came about a question for the operator P = |a><b| find Px(adjoint) the adjoint was defined as <v|Px|u> = (<u|P|v>)* where u and v can be any bra and ket now for the question: (<u|a><b|v>)* = <v|Px|u> this is the confusing step , i thought conjugated simply...
  3. C

    I Spin conservation in the Dirac equation

    Here I am considering the one particle free Dirac equation. As is known the spin operator does not commute with the Hamiltonian. However, the solutions to the Dirac equation have a constant spinor term and only an overall phase factor which depends on time. So as the solution evolves in time...
  4. Telemachus

    Correct numerical modeling of the 3D Dirac Delta function

    Hi. I was trying to test a code for the diffusion equation, using the analytical solution for infinite media, with a Dirac delta source term: ##q(\mathbf{r},t)=\delta (\mathbf{r}) \delta (t)##. The code is not giving the analytical solution, and there might be several reasons why this is so...
  5. S

    I Dirac Notation: Bra & Ket Conjugation Rules

    hey guys just a quick question , within the Dirac notation I we have bras and kets.Is it allowable to simply hermitianly conjugate everything , e.g: <w|c> = <b|c> - <d|c> Can we then: <c|w> = <c|b> -<c|d> Or is there some subtly hidden rule.
  6. It's me

    Dirac hydrogen atom vs spin symmetry

    Homework Statement Exact spin symmetry in the Dirac equation occurs when there is both a scalar and a vector potential, and they are equal to each other. What physical effect is absent in this case, that does exist in the Dirac solution for the hydrogen atom (vector potential = Coulomb and...
  7. F

    I Two particles Dirac type equation question

    I was reading this paper https://arxiv.org/pdf/0805.4725.pdf It seems that the potential between the particles can be assumed of different forms, shouldn't the potential be a solution of the problem. Thanks
  8. E

    I How Does the Dirac Equation Utilize Component Functions in Its Derivation?

    In https://quantummechanics.ucsd.edu/ph130a/130_notes/node45.html after "Instead of an equation which is second order in the time derivative, we can make a first order equation, like the Schrödinger equation, by extending this equation to four components." it is evident that the solution is...
  9. B

    I Spin Angular Momentum Dirac Equation

    In the Dirac equation, the wave-function is broken into four wave-functions in four entries in a column of a matrix. Since there are four separate versions of the wave-function, does each version have the spin angular momentum of h-bar/2? This seems overly simplistic. How does spin angular...
  10. F

    I Is the Dirac free equation actually free

    I mean the equation shows the particle could have any momentum, how did that came about. If it is truly free it should have only an energy of mc^2, shouldn't it.
  11. J

    I Causal Fermion System and revival of Dirac Sea

    If the Higgs Field could exist with constant 246GeV across all of space. How come the Dirac Sea couldn't exist? If the Universe can easily accommodate Higgs Field.. why not Dirac Sea for all particles. Also how does the Dirac Sea of bosons work? Like W+, W-? Any idea? I was asking about the...
  12. neilparker62

    I Simplify the Dirac Energy Equation?

    In the above equation for Dirac energy, is it trivial to note that given: Principal quantum number n Orbital angular momentum quantum number l(max) = n - 1 Total angular momentum quantum number j = l + 1/2 = n - 1/2 Then nr = n - j - 1/2 = n - (n - 1/2) - 1/2 = 0 and the energy expression...
  13. DoobleD

    I Fourier series of Dirac comb, complex VS real approaches

    Hello, I tried to compute the Fourier series coefficients for the Dirac comb function. I did it using both the "complex" formula and the "real" formula for the Fourier series, and I got : - complex formula : Cn = 1/T - real formula : a0 = 1/T, an = 2/T, bn = 0 This seems to be valid since it...
  14. neilparker62

    I Use the Dirac Equation to calculate transition frequencies in Hydrogen

    I would just like to understand how to use the above Dirac energy equation to calculate (for example) the 1s-2s transition frequency in hydgrogen. Does one substitute n=1, j=0 for 1s energy level and n=2, j=0 for 2s energy level ? From previous reading I understand the mass referred to in the...
  15. Gene Naden

    Positive and negative plane wave solutions of Dirac equation

    I continue to be occupied with the first chapter of Lessons on Particle Physics by Luis Anchordoqui and Francis Halzen. The link is https://arxiv.org/PS_cache/arxiv/pdf/0906/0906.1271v2.pdf. I am on page 24, where they derive equations 1.5.67, which are: ##(\gamma^\mu p_\mu-m)u(p)=0## and...
  16. Gene Naden

    A Invariance of Dirac Lagrangian

    I am working through the first chapter of Lessons on Particle Physics by Luis Anchordoqui and Francis Halzen. The link is https://arxiv.org/PS_cache/arxiv/pdf/0906/0906.1271v2.pdf I am on page 22. Equation 1.5.61: ##L_{Dirac}=\psi \bar ( i\gamma^\mu \partial_\mu-m)\psi## where ##\psi bar =...
  17. Gene Naden

    A Transformation of solutions of the Dirac equation

    I am working through "Lessons on Particle Physics." The link is https://arxiv.org/PS_cache/arxiv/pdf/0906/0906.1271v2.pdf. I am on page 21, equation (1.5.50), which is ##S(\Lambda)=1-\frac{i}{2}\omega_{\mu\nu}\Sigma^{\mu\nu}##. I would like some motivation for this equation. I wonder what the...
  18. S

    I Understanding the Parity Operator in Dirac Field Theory

    Hello! I am a bit confused about matrices dimensions in the second quantization of the Dirac field. The book I am using is "An Introduction to Quantum Field Theory" by Peskin and Schroder and I will focus in this question mainly on the Parity operator which is section 3.6. The field operator...
  19. Gene Naden

    A Transformation of Dirac spinors

    So I am working through Lessons in Particle Physics by Luis Anchordoqui and Francis Halzen, the link is https://arxiv.org/PS_cache/arxiv/pdf/0906/0906.1271v2.pdf I am in the discussion of the Dirac equation, on page 21, trying to go from equation 1.5.49 to 1.5.51. And I get stuck. Equation...
  20. D

    I Show that the integral of the Dirac delta function is equal to 1

    Hi, I am reading the Quantum Mechanics, 2nd edition by Bransden and Joachain. On page 777, the book gives an example of Dirac delta function. $\delta_\epsilon (x) = \frac{\epsilon}{\pi(x^2 + \epsilon^2)}$ I am wondering how I can show $\lim_{x\to 0+} \int_{a}^{b} \delta_\epsilon (x) dx$...
  21. L

    Exploring Dirac Hamiltonian with Matrices

    Homework Statement Matrices ##\alpha_k=\gamma^0 \gamma^k##, ##\beta=\gamma^0## and ##\alpha_5=\alpha_1\alpha_2\alpha_3 \beta##. If we know that for Dirac Hamiltonian H_D\psi(x)=E \psi(x) then show that \alpha_5 \psi(x)=-E \psi(x) Homework EquationsThe Attempt at a Solution I tried to...
  22. J

    I How Does Dirac Notation Simplify Quantum Mechanics for Harmonic Oscillators?

    I am completely baffled by bit of notation in Quantum Mechanics Concepts and Applications by Zitteli. He is trying to get the differential equation for the ground state of a harmonic oscillator using the algebraic method as opposed to Schrodinger's equation. I suspect he is compressing a lot of...
  23. P

    Calculate the Dirac delta function integral

    https://1drv.ms/w/s!Aip12L2Kz8zghV6Cnr8jPcRTpqTX https://1drv.ms/w/s!Aip12L2Kz8zghV6Cnr8jPcRTpqTX My question is in the above link
  24. 4

    I Solving Dirac Algebra Arithmetic

    I have a question regarding the Dirac notation arithmetic. Below is a measurement of a general 2 qubit state with the measurement operator M=|0><0| ⊗ I , where I is the identity operator. To go from equation (2) to equation (3), I've been converting all the Dirac notation to matrices and column...
  25. W

    I Why this system has a rotational symmetry in Dirac equation?

    why system has a rotational symmetry in dirac equation? is that a general property of all systems?
  26. P

    Dirac delta; fourier representation

    Homework Statement I know that we can write ## \int_{-\infinity}^{\infinity}{e^{ikx}dx}= 2\pi \delta (k) ## But is there an equivalent if the interval which we are considering is finite? i.e. is there any meaning in ##\int_{-0}^{-L}{e^{i(k-a)x}dx} ## is a lies within 0 and L? Homework...
  27. S

    I Question about the Dirac delta function

    Hi, if I have an interval on the x-axis, defined by the parameter L, can this, interval be transformed to a Dirac delta function instead, on the x-axis? Thanks!
  28. I

    I Meaning of Dirac Delta function in Quantum Mechanics

    If I have a general (not a plain wave) state $$|\psi\rangle$$, then in position space : $$\langle \psi|\psi\rangle = \int^{\infty}_{-\infty}\psi^*(x)\psi(x)dx$$ is the total probability (total absolute, assuming the wave function is normalized) So if the above is correct, does that mean...
  29. B

    I The Relation Between Wavefunctions in Dirac Equation

    Can the wave function in four dimensions be expressed as e^i(kx+ky+kz-wt)?
  30. K

    I Dirac quantization of gravity e.g. GR in Ashtekar Variables

    I'd like this issue clarified I understand that a full nonpertubative quantization of a yang mills gauge theory in 4D is unavailable. is Dirac quantization of classical theory of gravity e.g GR rewritten Ashtekar Variables Variables or some variation of the idea, a viable approach to a...
  31. maistral

    A Integral of Dirac function from 0 to a.... value

    Hi. So I'm trying to use Laplace transforms in inverting a particular s-function via the convolution formula. I ended up with this terrifying-looking thing: So distributing, I ended up with: Evaluating the second integral poses no problem for me (although I think the integration will...
  32. Milsomonk

    Commutator of the Dirac Hamiltonian and gamma 5

    Homework Statement Show that in the chiral (massless) limit, Gamma 5 commutes with the Dirac Hamiltonian in the presence of an electromagnetic field. Homework EquationsThe Attempt at a Solution My first question is whether my Dirac Hamiltonian looks correct, I constructed it by separating the...
  33. Milsomonk

    The Dirac equation in Weyl representation

    Homework Statement Compute the antiparticle spinor solutions of the free Dirac equation whilst working in the Weyl representation.Homework Equations Dirac equation $$(\gamma^\mu P_\mu +m)v_{(p)}=0$$ Dirac matrices in the Weyl representation $$ \gamma^\mu= \begin{bmatrix} 0 & \sigma^i \\...
  34. L

    I Lebesgue Integral of Dirac Delta "function"

    Is the "function" R->R f(x) = +oo, if x =0 (*) 0, if x =/= 0 Lebesgue measureable? Does its Lebesgue Integral exist? If yes, how much is it? (*) Certainly we shoud give a convenient meaning to that writing. -- lightarrow
  35. Milsomonk

    I Dirac equation solved in Weyl representation

    Hi guys :) I'm just wondering if anyone knows of a book that has the Dirac equation solved in the Weyl basis in it? I'd like to check my method to make sure I'm on the correct lines. Thanks
  36. B

    I Dirac Matrices and the Pythagorean Theorem

    I understand that momentum, rest mass and energy can be put on the sides of a right triangle such that the Pythagorean Theorem suggests E^2=p^2+m^2. I understand that the Dirac equation says E=aypy+axpx+azpz+Bm and that when we square both sides the momentum and mass terms square while the cross...
  37. TAKEDA Hiroki

    I Double sided arrow notation in Dirac Field Lagrangian

    In a thesis, I found double sided arrow notation in the lagrangian of a Dirac field (lepton, quark etc) as follows. \begin{equation} L=\frac{1}{2}i\overline{\psi}\gamma^{\mu}\overset{\leftrightarrow}{D_{\mu}}\psi \end{equation} In the thesis, Double sided arrow is defined as follows...
  38. T

    I Trying to understand Dirac Hamiltonian

    The Dirac Hamiltonian is essentially ##H = m + \vec{p}##. I found a issue with this relation, because we know from relativity that ##E^2 = m^2 + p^2## and there seems to be no way of ##E = \pm \sqrt{m^2 + p^2} = m + p##. To get out of this issue, I tried the following. I considered ##E## as a...
  39. RJLiberator

    Valid Representation of Dirac Delta function

    Homework Statement Show that this is a valid representation of the Dirac Delta function, where ε is positive and real: \delta(x) = \frac{1}{\pi}\lim_{ε \rightarrow 0}\frac{ε}{x^2+ε^2} Homework Equations https://en.wikipedia.org/wiki/Dirac_delta_function The Attempt at a Solution I just...
  40. K

    I What happens when we replace the Dirac Delta function with a sine function?

    If we were to replace δ(x), the orginal Dirac Delta, with δ(sin(ωx)), what would be the result? Would we have an infinite spike everywhere on the graph of sinx where x is a multiple integer of π/ω? and 0 everywhere else? I apologize in advance if I had posted in the wrong category.
  41. E

    I Confusion about Dirac Notation (interferometer)

    Hello everybody, Dirac notation uses "bras"( <a| ) and "kets"( |b> ), which are row vectors and column vectors respectively, but what would something like |a, b> mean? It makes no notational sense to me Context: A couple of photons going through beam splitters in an interferometer. One is...
  42. S

    I Did Paul Dirac say anything about Bohmian mechanics?

    Could you, please, give me reference to any paper or talk by Paul Dirac where he expresses his views about or give comments to the de Broglie-Bohm theory (Bohmian mechanics)?
  43. U

    Functional Derivative with respect to Dirac Spinors

    Homework Statement I am currently working on an exercise list where I need to calculate the second functional derivative with respect to Grassmann valued fields. $$ \dfrac{\overrightarrow{\delta}}{\delta \psi_{\alpha} (-p)} \left( \int_{x} \widetilde{\bar{\psi}}_{\mu} (x) i \partial_{s}^{\mu...
  44. J

    A Probability density of dirac spinors

    The probability density of the dirac spinor is known to be ∑(Ψ)2 and I know how it is derived. However, I'm just wondering why it should be positive definite. Since the lower two components represent antiparticles, so shouldn't the probability density contribution of those two components be...
  45. D

    I Why and how Dirac cones are "tilted"?

    Given a Weyl Hamiltonian, at rest, \begin{align} H = \vec \sigma \cdot \vec{p} \end{align} A Lorentz boost in the x-direction returns \begin{align} H = \vec\sigma\cdot\vec{p} - \gamma\sigma_0 p_x \end{align} The second term gives rise to a tilt in the "light" cone of graphene. My doubts...
  46. D

    Charge density using the Dirac delta funciton

    Currently, I am reading this article which introduces electromagnetism. It gives a function for the charge density as: $$\rho = q\delta(x-r(t))$$ The paper states that "the delta-function ensures that all the charge sits at a point," but how does it do that? Also, if ##r(t)## is the trajectory...
  47. I

    I Questions about the Dirac delta

    Hi, Consider this definition of the Dirac delta: $$\delta (x-q)=\lim_{a \rightarrow 0}\frac{1}{a\sqrt \pi}e^{-(x-q)^2/a^2}$$ First, this would make a normalized position eigenfunction $$\psi (x)=\lim_{a \rightarrow 0}\frac{1}{\sqrt{a\sqrt \pi}}e^{-x^2/2a^2}$$ right? If that is so, why do...
  48. S

    I Dirac vs KG propagation amplitude

    Hello! Can someone explain to me the physical meaning of ##\bar{\psi}=\psi^\dagger\gamma^0## in the Dirac equation? For example when calculating propagation amplitude I see that what we calculate is ##<0|\psi(x)\bar{\psi(y)}|0>## and not ##<0|\psi(x)\psi(y)|0>## (as we do for KG equation) and I...
  49. S

    I Understanding the Mistake in Dirac's Hamiltonian for Field Quantization

    Hello! I read that if we apply the exactly same procedure for Dirac theory as we did for Klein Gordon, in quantizing the field, we obtain this hamiltonian: ##H=\int{\frac{d^3p}{(2\pi)^3}\sum(E_pa_p^{s\dagger}a_p^s-E_pb_p^{s\dagger}b_p^s)}## and this is wrong as by applying the creation operator...
  50. S

    I Understanding the Dirac Commutation Relations in QFT

    Hello! I am reading Peskin's book on QFT and at a point he wants to show that the Dirac field can't be quantified using this commutation relations: ##[\psi_a(x),\psi_b^\dagger(x)]=\delta^3(x-y)\delta_{ab}## (where ##\psi## is the solution to Dirac equation). I am not sure I understand the math...
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