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2
votes
0answers
110 views

Number theoretical function applied in physics? [closed]

I have a series of number theoretic phenomena (mathematics) that I can describe exactly by the superpositions or linear combination of the below function (I know it is an inverse Fourier type). Does ...
4
votes
3answers
251 views

Completing the square for Grassmann variables

When working with path integrals of both bosonic and fermionic field variables, I'm a bit unsure of how to do the usual complete the square trick when an interaction between the two is concerned. Say ...
3
votes
2answers
475 views

Canonical partition of a boson gas

I have a 1D gas made of $N$ particles placed in a harmonic potential well, so the Hamiltonian is: $$ \mathcal H = \sum_{j=1}^N \left ( \frac{p_j^2}{2m} + \frac{1}{2}m\omega^2 x_j^2 \right )$$ The ...
4
votes
1answer
77 views

Same partition functions, different theories

I am reading the book "Basic Concepts of String Theory" by Blumenhagen, Lust and Theisen and in page 290 they say: "It follows that the $E8\times E8$ and the $SO(32)$ heterotic string theories have ...
1
vote
1answer
127 views

How to prove useful property of logarithm of generating functional in QFT?

How to prove that $\ln(Z(J))$ generates only connected Feynman diagrams? I can't find the proof of this statement, and have only met its demonstrations for case of 2- and 4-point.