3
votes
1answer
115 views

Not satisfied with “trick” in zeta function regularization

I am not satisfied with the explanations of the $\sum_n \log \lambda_n = - \frac{d}{ds} \sum_n \lambda_n^{-s}|_{s=0}$ "trick" used in zeta function regularization, discussed here and here, or the ...
1
vote
1answer
68 views

Casimir force using Pauli-Villars regularization

In Zee's Quantum field theory in a nutshell, 2nd edition, p. 74 he claims that: $$ \sum_a c_a \Lambda_a \sum_n \frac{\omega_n}{\omega_n + \Lambda_a} = - \sum_a c_a \Lambda_a \sum_n ...
6
votes
3answers
3k views

Don't understand the integral over the square of the Dirac delta function

In Griffiths' Intro to QM [1] he gives the eigenfunctions of the Hermitian operator $\hat{x}=x$ as being $$g_{\lambda}\left(x\right)~=~B_{\lambda}\delta\left(x-\lambda\right)$$ (cf. last formula on ...
19
votes
2answers
1k views

Classical and quantum anomalies

I have read about anomalies in different contexts and ways. I would like to read an explanation that unified all these statements or point-views: Anomalies are due to the fact that quantum field ...
8
votes
2answers
540 views

Regularisation of infinite-dimensional determinants

Can a regularisation of the determinant be used to find the eigenvalues of the Hamiltonian in the normal infinite dimensional setting of QM? Edit: I failed to make myself clear. In finite ...