# Questions tagged [functional-determinants]

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

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 ...
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### Calculation of the Effective action - Lewis H. Ryder

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 ...
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### Multiplicative property of the functional determinant

If we consider two differential operators $\mathcal{D}_1$ and $\mathcal{D}_2$, we can compose them to create the differential operator $\mathcal{D}_1 \mathcal{D}_2$. Then we could consider an action (...
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### How to integrate out the Goldstone phase in effective Ginzburg–Landau (GL) action for BCS?

In page 293 of Altland and Simons' "Condensed Matter Field Theory", just above equation (6.38), in the process of deriving the London equations from the BCS path integral, the authors say, &...
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### Spinor functional quantization unitarily equivalent and determinant

On P&S's qft page 301 and 302, the book discussed functional quantization of spinor field. The book define a Grassmann field $\psi(x)$ in terms of any set of orthonormal basis functions: \begin{...
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### How to perform a Gaussian functional integral?

I'm completely beginner to the quantum field theory and try to learn the basics of functional integrals. However, I could not understand clearly. Could someone please explain the idea with the help of ...
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### Computation of functional determinant using Feynman diagram

The above equation is from chapter 9.5 "Functional Quantization of the Spinor Field" of Peskin's and Schroeder's book $($page $305)$. I understand that the initial determinant equal to the ...
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### How to deal with path integral in curved space-time for a free scalar field?

Let's say we have a complex scalar field in a curved background whose action is: $$S=-\int d^4x \sqrt{-g}\phi^\ast(\square_g+m^2) \phi$$ For some purpose I want to ...
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### Units in the nonrelativistic free particle path integral

I am almost certain I have seen the answer to this question on this site before, but for the life of me I cannot find it after significant searching. If someone can located another question with the ...
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### How to find the determinant of a single derivative?

I am currently studying the path integral approach to stochastic processes. Recently I was reading Functional integral approach for multiplicative stochastic processes about the path integral ...
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### Regularization of functional determinant over an Instanton background

I am reading the paper "ABC of instantons" and meet some problems at section 8. I simplify this problem a little bit as follows. First, we have a Euclidean path integral like ...
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