Recent content by kassem84

Hello, I have an analytical expression E_{i} that I want to fit it to some data E(Ref)_{i} . I fitted this expression for N-points: I have calculated the value of chi-squared using the following formula: \chi^{2}=\frac{1}{N-1}\sum_{i=1}^{N}\frac{(E_i-E(Ref)_i)^{2}}{σ_{i}^{2}} where...

Hello, I am calculating some integrals in 3 dimensions. However, the difficulties of such integrals lie in the determination of the boundaries of the variables integrated over. \int_{C} d^{3}\vec{t} e^{-\vec{s}.\vec{t}} For example, if we consider (C) as the region of the intersection of 2...

Thanks. For the vector version, it difficult for me to determine the boundaries on the angles θ and \phi.

How can we use mathematica to determine the boundaries- the intersection of the three spheres?

Yes, it is the correct notation of the integral I. All the vectors are 3-dimensional in the definition of the function and in the boundary D. Thanks.

Hello, F=e^{-(q^{2}+q.k+q.p)} The most important thing is how to obtain the boundaries of the integrals. i.e. q,p,k go from where to where? Thanks.

Hello, I have some difficulties of calculating the following integral: I=\int _{D}\:\:\:d^{3}q\: d^{3}k\: d^{3}p\:\:F(q^{2}, q.k, q.p, k^{2}, p^{2}) where: D=|k|>1, |k+q|<1 and |p-q|<1 Thanks in advance.

Thanks Simon for your answers.

Hello, As you may know in the context of dimensional regularization, integration is performed in d-dimension where d can take non-integer values. For example: \int d^{d}q f(q^2)=S_{D}\int_{0}^{∞}q^{q-1}f(q^2)dq My questions are: 1) Is the integration in d-dimension performed is well defined...

Thanks very much, it is a useful note.

The integral: \intd^{3}k\frac{1}{k^{2}+m^{2}} is linearly divergent i.e. ultraviolet divergent. However, If one performs dimensional regularization to the above integral: \frac{1}{(2\pi)^d}\intd^{d}k\frac{1}{k^{2}+m^{2}}=\frac{(m^{2})^{d/2-1}}{(4\pi)^{d/2}}\Gamma(1-d/2) As you can notice...

Dear all, Dimensional regularization is a very important technique to remove the divergence from momentum integrals. Suppose that you have to calculate a quantity composed of three integrals over k_1, k_2 and k_3 (each one is three dimensional). the integral over k_3 gives ultra violet...