Recent content by jtceleron

but I think the Cauchy principal value is available only when the pole is of first order.

A necessary condition that a function f(x) can be Fourier transformed is that f(x) is absolutely integrable. However, some function, such as |t|, still can be Fourier transformed and the result is 1/w^2, apart from some coefficients. This can be worked out, as we can add a exponential...

Homework Statement the function is Exp[-w^2]/w^2, how to solve the Fourier transform analytically with Residue theorem? It is better if there is more general results. Mathematica can solve it analytically, but I need a human-soluable way. Homework Equations The Attempt at a...

it seems to have many different ways to express a determinant, when we are using indices to write vectors and tensors, e.g. in General Relativity. is there any summary about how to express a determinant, for example, in Levi-Civita Tensor and so on?

This question is from K. Huang, Quantum Field Theory: from operators to path integrals. He says that, under a continuous infinitesimal transformation, \phi(x)->\phi(x)+\delta\phi the change of the Lagrangian density must be in the from \deltaL=∂^{\mu}W_{\mu}(x) It is easily understood...

As we know, spin is an internal symmetry. but it seems a bit different from other internal symmetry, e.g. electrical charge, color, flavor... because it can be coupled with orbital angular momentum and in some aspects be linked to space-time. further more, we can classify all the particles into...

thank you!

How to calculate something relating to the determinant of metric tensor? for example, its derivative ∂_{λ}g. and how to calculate1/g* ∂_{λ}g, which is from (3.33) in the book Spacetime and Geometry, in which the author says that it can be related to the Christoffel connection.

what is the difference of the two in mechanism? Does the period of luminosity relate to the period of orbit of the companion star? but if so, why does the stellar wind one not have a period of luminosity.

In an X-ray binary system, in which one of the two objects is black hole candidate, there are several ways to exchange mass. A paper states that" their host systems are mass-exchange binaries containing a nondegenerate star that supplies gas to the black hole via a stellar wind or via...

You mean that, for example, in the last equation of transformation for A(x), the partial derivative should act on U-1, rather than taking U-1 as a constant?

Homework Statement Homework Equations I am learning QFT, and I am confused of such transformations. For example, first, in these equations, especially the one that defines the transformation of A(x), whether should the partial derivative acts on U(or U-1), or just take U as a constant...

in #1. the topology on X has already defined, which mean if choosing rationals as the subset A, then U are all the subsets including A, it is like a discrete topology, so imposing a metric topology on it seems not right.

I mean, in #2, that if every point in the open set (a,b) has a compact subset, then the open set is locally compact.

Q1. if A is a subset of X, choose the topology on X as {∅,U|for every U in X that A is a subset of U}. Then is this topology a locally compact space? Q2. X=[-1,1], the topology on X is {∅, X, [-1, b), (a,b), (a,1] | for all a<0<b}. How to prove every open set (a,b) in X is NOT locally compact...