Questions tagged [functional-determinants]

Question 1

In Altland & Simons (2nd ed., pp. 117-124), there is a discussion on path integrals and instantons where I cannot understand where the factor $e^{-\omega\tau}$ comes from. The calculation goes the ...

Question 2

I have a question regarding regularization in quantum field theory. Hagen Kleinert talks about analytic regularization in his book "Path Integrals". In chapter 2.15 he calculates the ...

Question 3

I am trying to understand the connection between loop diagrams and the $1/N$ expansion, the general picture. Generally, when we have a quadratic action in the field, we obtain a trace log of the Green ...

Question 4

I want to calculate a functional determinant coming from a Gaussian path integral with operator Matrix $M$. The determinant is given by the product over the eigenvalues according to $$\text{det}(M) = \...

Question 5

I wish to get a better feel for the Heat kernel ansatz below $$\hat{K}(s \mid x, y)=\frac{\Delta^{1 / 2}(x, y)}{(4 \pi s)^{d / 2}} g^{1 / 2}(y) e^{-\sigma(x, y) / 2 s-s m^2} \sum_{n=0}^{\infty} s^n \...

Question 6

Whilst doing the first exercise in chapter 6.7 of A. Atland's & B. Simons' Condensed Matter Field Theory, I came across the following expression $$\text{tr}\ln[\mathcal{G}_0^{-1}+g(\partial_xu)]\...

Question 7

In physics the path integral is given, after a Wick rotation, by $$Z^{-1} \int e^{-S[\phi]/\hbar}d\phi. \tag{1}$$ where $d\phi$ is formally Lebesgue measure over fields. To make this rigorous one ...

Question 8

I’m preparing a workshop on the evolution of physics, focusing on nano topics, particularly van der Waals forces. My idea is to simulate the interaction between two hydrogen atoms using C programming ...

Question 9

In Peskin QFT book page 295 it is said that: $$\det(\delta G(A^\alpha)/ \delta \alpha) = \det(\partial^2/e)\tag{p.295}$$ where $$G(A^\alpha) = \partial^\mu A_\mu^\alpha = \partial^\mu A_\mu + (1/e)\...

Question 10

I'm reading this review about the Cosmological Schwinger effect by Jérôme Martin and I have a doubt computing the following functional trace \begin{align} |\langle 0^-|0^+\rangle|^2=&\det\left(\...

Question 11

In my current homework, we have to get familiar with quadratic theory in order to reach $\phi^4$-theory. So the starting point is $$Z = \int Dx e^{-S[\phi]}$$ with the action for the real scalar ...

Question 12

I'm following an introductory lecture on instantons by Hilmar Forkel. In a non-relativistic quantum mechanical setting we have the potential $$ V(x) = \dfrac{\alpha^2 m}{2 x_0^2} (x^2 - x_0^2)^2 \tag{...

Question 13

I am following the book String Theory in a nutshell (From Elias Kiritsis). In chapter 4.18, it takes a theory following the action: $$S=\frac{1}{4\pi l_s^2}\int X\square X\ d\sigma,\tag{4.18.1}$$ $$ \...

Question 14

I have been studying the book on Quantum Field Theory by Lewis H. Ryder and I am finding a Gaussian integration a little bit confusing. In the book, the transition amplitude (Eq. $(5.15)$) is given as ...

Question 15

I'm trying to solve an exercise on path integrals, in which I have to move from a path integral in phase space $$ \int \mathcal{D}q \dfrac{\mathcal{D}p}{\hbar} \exp \left(\dfrac{i}{\hbar} \int dt\ (p\...

Stack Exchange Network

Questions tagged [functional-determinants]

How to find the correct propagator prefactor in the dilute instanton gas in 1D quantum mechanics?

Regularization of determinants in QFT

One-loop diagram and $1/N$ expansion

Zeta-function regularization of an uncountably infinite product of constant factors

What is the point of the Pauli-Van Vleck-Morette determinant?

Struggling with Fourier transform in functional integration [closed]

What justifies the choice of covariance $C$ in rigorous path integrals?

Can you suggest a real-world analogy for nanophysics, specifically focusing on van der Waals forces, that is practical and suitable for a workshop?

Functional derivative of gauge fixing condition - Peskin QFT page 295

Functional trace in Schwinger effect

Fourier transform of the Gaussian action for the real scalar bosonic field

Instantons and Spontaneous Symmetry Breaking

How do Dedekind's eta function arise while computing the partition function of a compact scalar field over circle?

Calculation of the Effective action - Lewis H. Ryder

How to do the Gaussian $p$ integration in path integrals?

Hot Network Questions