Functional Definition and 380 Threads

Hi, if I want to calculate the generating functional for the free Dirac Field, I have to evaluate a general Gaussian Grassmann integral. The Matrix in the argument of the exponential function is (according to a book) given by: I don't understand the comment with the minus-sign and the...

Hello, I want to derive the connected two point function for the interacting boson-fermion theory. I know that the generating functional is Z(J, \overline{\eta}, \eta) = N \; exp \left( \int d^4 z \; L_{int} \left(-i \frac{\delta}{\delta J(z)} \right) \left(-i \frac{\delta}{\delta...

I'm thinking about getting this book. I'm a physics major, and I think the only analysis course I'm required to take later as a prerequisite for graduate courses is Introduction to Complex Analysis. So far, I've taken Cal I-III and Linear Algebra. Differential Equations will probably be in the...

My second PHP question this week...:smile: I'm writing a PHP app which includes things such as form validation and database interaction. So far, almost everything has been written procedurally. However, I started playing around with PHP's OO stuff, and it's cool. Problem is, this app is being...

In free-field theory, the functional integral \int \mathcal{D}\varphi \exp\left(i \frac{1}{2} \int d^4 x (\partial_\mu \varphi \partial^\mu \varphi - m^2 \varphi^2)\right) can be done exactly (see e.g., Peskin and Schroeder p. 285). I'm tyring to understand the step in their derivation...

Can you recommend me some low-cost universities in Canada(or US) that specialise in functional programming? I am looking for Bachelor Degrees. I have noticed that many interesting stuff, that I would call functional proramming, are in degrees such as electrical engineering and computer science...

Homework Statement I have two scalar functions u(x,y,z) and v(x,y,z) which are differentiable..Now it is required to prove that a necessary and sufficient condition for these two to be functionally related by equation F(u,v)=0 is [\nablau] \times [\nablav]=0 The Attempt at a Solution...

Hello, I am currently looking for a book on functional analysis. However most books I have seen assume knowledge real and complex analysis. But I am looking for a more superficial introduction covering the important results, some examples of applications (mainly to computational problems)...

Could someone please give me an example of an ether and an ester. In words, not drawing them. Thank you!

I'm looking for a entry-level book discussing the application of functional analysis to differential equations- mostly the Navier-Stokes equation, but PDEs in general. The books I have or have seen are either math books, full of proofs and definitions without application, or physics papers...

Homework Statement http://img357.imageshack.us/img357/8695/38808719uw6.png Homework Equations \lim_n a_n := \lim_{n \rightarrow \infty} a_n The Attempt at a Solution I'm stuck at exercise (c). Since if n heads to infinity the m doesn't play the role the limit must be one. So...

Does anyone know of where I should look to find lots of good functional analysis problems? I am currently reading Kreyszig which has great commentary, but the majority of the exercises are simple.

Something seems a little weird to me: What are the dimensions of a generating functional, Z[j] -- say for real scalar field theory? Z[j]=\int\mathcal{D}\phi\,\exp\, i\!\int d^4x\left(\frac{1}{2}\partial_\mu\phi\partial^\mu\phi-\frac{1}{2}m^2\phi^2+j\phi\right) Also, what about mass dimensions...

I've had a Meade DS 114 for a while. My kids dismantled it and apparently a piece is missing. The focuser tube is 2"; my eye pieces are 1.25" Meade says there was a piece which adapted the 1.25" eye pieces for use in the 2" hole (which also allowed for use of 2" eye pieces I guess). My...

Given that F = \int{f[h(s),s]ds} does \frac{\partial}{\partial h}ln(F)=\frac{1}{F}\frac{\delta F}{\delta h}=\frac{1}{F}\frac{\partial f}{\partial h} ?

While working out a problem I got a result which gave rise to this doubt regarding value of action functional. Suppose I start from an action, obtain the equation of motion and when I try to check if that solution gives a finite value of action, I get, surprisingly, vanishing value. The actual...

I try to learn DFT by myself(Kohn-Sham Equations), but the concept is still not so clear for me. So far, if I start with assuming any density, and then I would be able to find V(KS) Then I use this hamiltonian and solve for a wave function. And I use this wave function to find another...

Is it possible to find the extrema of an integral equation if the integral depends on a variable and an integral of that variable, i.e. the integrand is f(x) * g(integral(x)). I'm not sure if this is a "nonlocal" functional, or not a functional at all, but I can't find any references that...

what is the result of Fourier transformation of functional theta [Heaviside] function?

In the space of Riemannian metrics Riem(M), over a compact 3-manifold without boundary M, we have a pointwise (which means here "for each metric g") inner product, defined, for metric velocities k^1_{ab},k^2_{cd} (which are just symmetric two-covariant tensors over M)...

This is supposedly the chain rule with functional derivative: \frac{\delta F}{\delta\psi(x)} = \int dy\; \frac{\delta F}{\delta\phi(y)}\frac{\delta\phi(y)}{\delta\psi(x)} I have difficulty understanding what everything in this identity means. The functional derivative is usually a derivative...

Show that the extermals of any functional of the form integ (a->b) F(x,y') dx have no conjugate points. Not sure how to start this question, any help would be appreciated

Hello I need help with an analysis proof and I was hoping someone might help me with it. The question is: Let (X,d) be a metric space and say A is a subset of X. If x is an accumulation point of A, prove that every r-neighbourhood of x actually contains an infinite number of distinct...

Hello Would anyone out there be able to help me with a problem I'm having? I have to prove that a function is open and that another is closed. The question is: Consider C [0,1] with the sup metric. Let f:[0,1]→R be the function given by f(x)=x²+2 Let A={g Є C[0,1]: d(g,f) > 3}. Prove...

Hello Would anyone out there be able to help me with a problem I'm having? I have to prove that a function is open and that another is closed. The question is: Consider C [0,1] with the sup metric. Let f:[0,1]→R be the function given by f(x)=x²+2 Let A={g Є C[0,1]: d(g,f) > 3}. Prove...

Homework Statement I have to show that the functional C_n on the space of polynomials on the interval [0,1], that takes the n'th coefficient ie C_n\left( \sum_{j=0}^m a_j t^j \right) = a_n is discontinuous with respect to the supremum norm \|p\|_{\infty} = \sup_{t\in[0,1]}|p(t)| ...

Hi! I was thinking about taking an introductory course in Functional analysis the commming spring, and was wondering if you more experienced guys can tell me if this is a good complement to understand theoretical quantum physics better? Cheers

first of all how do you write in latex

given the functional integral with 'g' small coupling constant \int \mathcal D [\phi]exp(iS_{0}[\phi]+\int d^{4}x \phi ^{k}) so k >2 then could we use a similar 'Functional determinant approach' to this Feynman integral ?? in the sense that the integral above will be equal to...

Is it correct to think, that with a scalar complex Klein-Gordon field the wave function \Psi:\mathbb{R}^3\to\mathbb{C} of one particle QM is replaced with an analogous wave functional \Psi:\mathbb{C}^{\mathbb{R}^3}\to\mathbb{C}? Most of the introduction to the QFT don't explain anything like...

HOw can you compute a Gaussian functional integral? i mean integral of the type e^{-iS_{0}[\phi]+i(J,\phi)} if J=0 then i believe that we can describe the Functional integral as \frac{c}{(Det(a\partial +b)} a,b,c constant so Det(a\partial +b)}= exp^{-\zeta '(0)} \zeta (s) =...

I say what is a functional determinant ?? for example Det( \partial ^{2} + m) is this some kind of Functional determinant? then i also believe (althouhg it diverges ) that Det( \partial ^{2} + m)= \lambda_{1}\lambda_{2}\lambda_{3}\lambda_{4}... (the determinant of a Matrix is the...

I was studying my brother's old notes to prepare me for my upcoming AP Biology class. I read over six main functional groups (hydroxyl, carbonyl, carboxyl, amino, sulfhydrl, phosphate) and subsequently, there were follow-up questions. One of them asked to draw a molecule with all of the six...

I've been looking for some decent info on functional space but could not find anything. Googling gives lots of defenitions, but no explanations as such. Basically I'd like to understand why a function can be decomposed into other function, e.g. understand a meaning of inner product with...

Let be a set of LInear functionals U_{n}[f] n=1,2,3,4,... so for every n U_{n}[\lambda f+ \mu g]=\lambda U_{n}[f]+\mu U[g] (linearity) the question is if we can define the product of 2 linear functionals so U_{i}U_{j}[f] makes sense.

I'm intrigued by the fact that apparently no general theory of functional integration has been developed - something along the lines of Riemann, Cauchy, and Lebesgue. Feynman developed an approach to evaluating functional integrals for paths in spacetime - but I'm wondering whether it is...

I have a problem with this simple (?) derivation u(f(t),t) = \frac{\partial }{\partial f(t)} \int_0^T \ g(f(t),f(t'),t,t') \ dt'

Hmm, I've been working with functional derivatives lately, and some things aren't particularly clear. I took the definition Wikipedia gives, but since I know little of distribution theory I don't fully get it all (I just read the bracket thing as a function inner product :)). Anyway, I tried...

Homework Statement Consider an iteration function of the form F(x) = x + f(x)g(x), where f(r) = 0 and f'(r) != 0. Find the precise conditions on the function g so that the method of functional iteration will converge cubically to r if started near r. Homework Equations I really don't know...

I need to study all of these names for my orgo II exam next week. Can someone help me to find the general trend or functional group name for the following attached compounds? I have tried some of them let me know if I made any mistake on these two sheets. ie. #1 gem-diol (hydrate)...

If to calculate the propagator K(x,x') (vaccuum)for a theory so: (i\hbar \frac{\partial}{\partial t}\Psi - H\Psi )K(x,x')=\delta (x-x') (1) we use the functional integral approach: K(x,x')=<0|e^{iS[x]/\hbar }|0> my question is, let's suppose we use the semiclassical WKB approach...

I am writing a solution for the following problem, I hope someone can correct it, because I am not sure what I am missing. Q. V is a finite dim. vsp over K, and W is a subspace of V. Let f be a linear functional on W. Show that there exists a linear functional g on V s. t. g(w)=f(w). Ans...

Does there exist a chain rule for functional derivatives? For example, in ordinary univariate calculus, if we have some function y=y(x) then the chain rule tells us (loosely) that \frac{d}{dy} = \frac{dx}{dy}\frac{d}{dx}. Now suppose that we have a functional F[f;x) of some function...

So far all I know is that a functional is a function that has a set of functions as its domain. So what does that mean? I have a functional that looks like dy/dx = a bunch of constants. What I'd like to know is how to take that and plot it. Can this be done?

im given: u=arcsin(x)+arccos(y) v=xsqrt(1-y^2)+ysqrt(1-x^2) and i need to find the functional connection between u and v. i know that: v'_x/u'_x=dv/du and i have got: dv/du=sqrt(1-x^2)sqrt(1-y^2)-xy now i need to show the rhs as a function of v or u, obviously of v should be much...

Homework Statement For f\in C([0,1]), let N(f)=\int_0^1(f(t))^2dt. Show that N\in C^{\infty} and calculate the first derivative.Homework Equations Can I use Leibniz's integral rule for this?The Attempt at a Solution If I just blindly plug in the formula, I get dN/df=\int_0^12f(t)dt

I am thinking about taking a class on functional analysis. I am eventually planning on doing derivatives trading as a career. Is this class worth taking or should I try to find something more applied. I guess I am saying that I don't see how applied functional analysis is.

I'd like to be as familiar with functional methods as with calculus. Otherwise I always fell not to grasp QFT comprehensively. Any help is much appreciated!

Hi, i am looking for papers, books, etc, related with the Density functional theory, and Kohn Sham equations, i appreciate any help. Thanks. :rolleyes:

Strangely a good introductory internet resource on this subject doesn't seem to be readily available. Where can I look for information on this subject? --I am mainly interested in the concepts behind functional multi-threading rather than the syntax for any specific language.