Dirac Definition and 859 Threads

If we consider nonrelativistic QM, we will find Galilean group under the hood. Thanks to this, group theory enables us to find equations of motion directly from the symmetry principles. For example, if we take only geometric symmetries, we will get that the state space is broken into irreducible...

Let's have a theory involving Dirac field \psi. This theory is decribed by some Lagrangian density \mathcal{L}(\psi,\partial_\mu\psi). Taking \psi as the canonical dynamical variable, its conjugate momentum is defined as \pi=\frac{\partial\mathcal{L}}{\partial(\partial_0\psi)} Than the...

Trying to solve the ODE mx''(t) + bx'(t) + kx(t) = F(t) with m measured in Kg, b in Kg/s and Kg/s^2, F(t) in Kgm/s^2 and x(t) in m with initial conditions x(0) = 0 and x'(0) = 0, i got the following Green's function G(t,t') = \frac{1}{m\omega} e^{-\omega_1(t-t')}\sinh\left[\omega(t-t')\right]...

OK, so my basic understanding of Dirac Delta Function is that it shows the probability of finding a point at (p,q) at time t. Dirac Delta is 0 everywhere except for (p_{0},q_{0}). So my question comes Is it possible that a point enters the (p_{0},q_{0}) and stays there (for some period of...

I have a question about the Dirac Equation. I know that if I have a given initial state in non-relativistic quantum mechanics, I can find the Fourier coefficients using that state, and then write down the wavefunction for any time. But if I have an initial state wavefunction (that is, the...

Does anyone know what the Dirac delta function would look like in a space with curvature and torsion? The Dirac delta function is a type of distribution. But that distribution might look differently in curved spacetime than in flat spacetime. I wonder what it would look like in curved spacetime...

Alright...so I've got a question about the convolution of a dirac delta function (or unit step). So, I know what my final answer is supposed to be but I cannot understand how to solve the last portion of it which involves the convolution of a dirac/unit step function. It looks like this: 10 *...

Alright, I'm in my first QM course right now, and one of the topics we've looked at is solving the one-dimensional time-independent Schrodinger equation for various potentials, such as the harmonic oscillators, infinite and finite square wells, free particles, and last, but not least, the dirac...

Homework Statement The function \delta(cosx) can be written as a sum of Dirac delta functions: \delta(cosx)=\sum_{n} a_{n}\delta(x-x_{n}) Find the range for n and the values for a_{n} and x_{n} The Attempt at a Solution Well, taking the integral of \delta(cosx), we only get spikes when...

The Dirac delta function, \delta (x) has the property that: (1) \int_{-\infty}^{+\infty} f(x) \delta (x) dx = f(0) Will this same effect happen for the following bounds on the integral: (2) \int_{0}^{+\infty} f(x) \delta (x) dx = f(0)...

Dirac equation and friends :) I was playing with Dirac equations and deriving some usefull details, Note sure for a calculation, is all the math right? Beginning: we require for a pure Lorentz trasf that the spinor field trasform linearly as: \psi'(x')=S(\Lambda)\psi(x)...

I have a line charge of length L and charge density /lambda on the Z-axis. I need to express the charge density in terms of the Dirac Delta function of theta and phi. How would I go about doing this?

I'm wondering how in Peskin & Schroeder they go from i\mathcal{M} = {\overline{v}^s^'} (p^{'}) (-ie\gamma^\mu)u^s(p) \left( \frac{-ig_{\mu\nu}}{q^2} \right) \overline{u}^r (k) (-ie\gamma^\nu) v^{r^{'}} (k) at the bottom of page 131 to (5.1) at the top of 132 which reads i\mathcal{M}...

I am trying to evaluate the following integral. \int_{-\infty}^{\infty}{\delta(2t-3)\sin(\pi t) dt} where delta represents the Dirac delta function. I am told that the answer is -1. However, when I evaluate it in MATLAB and Maple 11, I get an answer of -1/2. What is the correct way...

Homework Statement I'm trying to prove that \delta'(y)=-\delta'(-y). Homework Equations The Attempt at a Solution I'm having trouble getting the LHS and the RHS to agree. I've used a test function f(y) and I am integrating by parts. For the LHS, I have...

Homework Statement Hi there, I'm stuck at a problem where I have (sorry i don't know how to use mathtype so I'll try my best at making this clear) the integral of a dirac delta function squared: int[delta(x*-x)^2] between minus infinity and infinity (x*=constant) I know that the function...

Yep, another quick question on the Dirac Equation! I've become slightly more clued about the use of the DE now in illustrating the negative energy problem in relativistic QM as well as the existence of spin, however one thing is still puzzling me. I've read this excerpt in a text: I'm...

[SOLVED] The Dirac Equation I'm trying to understand the following property of the Dirac equation: (i \gamma^{\mu}\partial_{\mu} - m)\Psi(x) = 0 Acting twice with (i \gamma^{\mu}\partial_{\mu} - m): (i \gamma^{\mu}\partial_{\mu} - m)^{2} \Psi(x) = 0 = [ -...

So what we have so far is that any and all subsets are implied by a set. If there exist a set, then all the subsets within it are implied to exist also. This includes the elements of a set. The elements of a set are implied by the existence of a set. One of the most natural things to do with...

A question concerning Feynman rules for Dirac vs Majorana neutrinos. Take e.g. the scattering process: electron + positron -> electron neutrino + electron antineutrino. Following the electroweak Feynman rules we can calculate an expression for the unpolarized differential cross section...

\PsiHow to intepret the four components of the dirac spinor? the volume integral of the \Psi^T*\Psi give the probability of finding the releativistic electron in a given volume of space but what exactly do the four components really mean. I have read in many Pop physics books that the 4...

Dirac Delta Function: If, at time t =a, the upper end of an undamped spring-mass system is jerked upward suddenly and returned to its original position, the equation that models the situation is mx'' + kx = kH delta(t-a); x(0) = x(sub zero), x'(0) = x(sub 1), where m is the mass, k is the...

1. The ProblemHomework Statement 4 Parts to the Assignment. Finding the Displacement of a beam assuming w to be constant. 1. Cantilever beam, free at one end. Length =l, Force P applied concentrated at a point distance rl from the clamped end. Boundary Conditions y(0)=0, y'(0)=0, y"(l)=0, and...

Homework Statement Show that if {x_k} is any sequence of points in space R^n with |{x_k}| \rightarrow \infty , then \delta(x-x_k) \rightarrow 0 weakly Homework Equations The Attempt at a Solution I'm still trying to grasp the concept of weak convergence for distributions. It...

[b]1. Homework Statement \int x[delta(x)-delta(x/3+4)] dx Homework Equations so I'm supposed to use this principle: \int f(x)delta(x-xo)dx=f(xo) The Attempt at a Solution So it seems simple but I just want to make sure that I'm applying the above principle correctly. I...

but I am confused how do you proof that the dirac field describes spin half quanta when quantized? please refer me to a link on the net where this derivation is shown if possible i can't find it in any of the books on quantized field theory

Homework Statement SO I'm given a dirac delta function, also known as a unit impulse function. d(t-t'_=(1/P) sum of e^[in(t-t')], for n from negative to positive infinity. I need to graph this. Homework Equations I understand that at t', there is a force made upon the system which...

Hey guys, I am having difficulty interpreting M(x,x') into dirac notation. How do i write M(x,x') in dirac notation? The actual problem is to write the following in dirac notation: int { int { m(x)* M(x,x') g(x') } dx} dx' I would appreciate your help.

Does the Dirac equation predicts the fact that there are no right handed neutrinos?

Q: Integral of Delta(x-b)dx and the lower limit is (-) infinity and upper is a Please help me in steps tried my best to solve.Note this is not homework I was doing the book problems or my practice Thanks

I figured out this one, just thought it was quite nice... We start with the only requirement that the Green's function of the propagator is causal in the sense that it propagates stricktly forward in time, so that the Green's function is zero at t<0. Using the Heaviside step function we can...

Homework Statement How would one show that dirac delta is the limit of the normal distribution? http://en.wikipedia.org/wiki/Dirac_delta using the definition \delta(k) = 1/(2\pi)\int_{-\infty}^{\infty}e^{ikx}dx Homework Equations The Attempt at a Solution

Homework Statement I need to solve the Klein-Gordon-Schrodinger and the Dirac equation for the Coulombian potential.Homework Equations KGS: [(\partial^{\mu}\partial_{\mu} + m^2c^2/h^2)\Psi=0 I don't know how I can add the potential term... Dirac: [\gamma^{\mu}(ih\partial_{\mu} - (e/c)...

What results in Chirality? And what is the physical implication of chirality in Dirac equation?

are spinors just wavefunctions in the dirac field?

OK, I'm currently reading Hughes' Finite Element Method book, and I'm stuck on a chapter the goal of which is to prove that the Galerkin solution to a boundary value problem is exact at the nodes. So, the author first speaks about the Dirac delta function: "Let \delta_{y}(x) = \delta(x-y)...

I have seen two formulations of the dirac delta function with the Fourier transform. The one on wikipedia is \int_{-\infty}^\infty 1 \cdot e^{-i 2\pi f t}\,dt = \delta(f) and the one in my textbook (Robinett) is 1/2\pi \int_{-\infty}^\infty 1 \cdot e^{-i f t}\,dt = \delta(f) I...

hi! I have a system from which i want to compute a expression for a time domain impulse response. The expressions for modulus and phase of the system is quite complicated and I'm using maple in order to do the inverse transforming. now, maple tells me the inverse transform is an expression...

I do not know if it is true but is this identity true \frac{\delta _{n}^{x} }{h} \rightarrow \delta (x-n) as h tends to 0 ?, the first is Kronecker delta the second Dirac delta. i suspect that the above it is true but can not give a proof

If the universe is a Dirac Sea, then wouldn't the light generated from virtual particle annihilation be detectable? Not only this, but wouldn't it drown out all other light sources? I can't find any good explanations so far for why virtual particle annihilation does/doesn't produce photons or...

Dirac developed his delta function in the context of QM. But there are various functions under the integral that give the delta function. My question is does one Dirac delta function equal any other? Are all ways of getting the Dirac delta function equivalent? Thanks.

Fourier transforms were invented before dirac delta functions but hidden in every Fourier transform is a dirac delta function. But it went unnoticed until dirac came along? Then they argued for the legitamacy of the delta function but it is present in every Fourier transform which is legitamate.

Dear All, Could you pls remind me how do I decompose arbitrary 4x4 matrix into Dirac 16 matrices... I ve forgotten. Thank you

Defining the state | \alpha > such that: | \alpha > = Ce^{\alpha {\hat{a}}^{\dagger}} | 0 >\ ,\ C \in \mathbf{R};\ \alpha \in \mathbf{C}; Now, | \alpha > is an eigenstate of the lowering operator \hat{a}, isn't it? In other words, the statement that \hat{a} | \alpha >\ =\ \alpha | \alpha >...

Homework Statement int[d(x-a)f(x)dx]=f(a) is the dirac delta fn but is int[d(a-x)f(x)]=f(a) as well? If so why?The Attempt at a Solution Is it because at x=a, d(0)=infinite and integrate dirac delta over a region including x=0 when d(0) is in the value in the integral will produce 1 hence f(a).

I've had some trouble with the argument "spin angular mometum has no classical analogue", that everyone seems to be repeating. I used Noether's theorem to calculate angular momentum of a classical Dirac's field, and found that it has internal angular mometum density, that cannot be written as a...

Dear all, I need a simple proof of the following: Let [tex]u \in C(\mathbb{R}^3)[\tex] and [tex]\|u\|_{L^1(\mathbb{R}^3)} = 1[\tex]. For [tex]\lambda \geq 1[\tex], let us define the transformation [tex]u\mapsto u_{\lambda}[\tex], where [tex] u_{\lambda}(x)={\lambda}^3 u(\lambda...

A professor of mine recently remarked that dirac notation is easily the best in physics & we'd quickly realize this once we take a course in relativity. I've already taken the course & I find myself disagreeing with him, but maybe that's only because I enjoy relativity more. Curious what you...

A vector function V(\vec{r}) = \frac{ \hat r}{r^2} If we calculate it's divergence directly: \nabla \cdot \vec{V} = \frac{1}{r^2} \frac{\partial}{\partial r} \left( r^2 \frac{1}{r^2} \right) = 0 However, by divergence theorem, the surface integral is 4\pi . This paradox can be solved by...

Did Feynman write about the Dirac Equation? I would like to see how to derive it, and how it reduces to the Schrodenger equation.