# Questions tagged [functional-determinants]

The tag has no usage guidance.

72 questions
Filter by
Sorted by
Tagged with
145 views

• 691
477 views

### Computing a Gaussian path integral with a zero-mode constraint

I have the following partition function: Z=\int_{a(0)=a(1)} \mathcal{D}a\,\delta\left(\int_0^1 d\tau \,a -\bar{\mu}\right)\exp\left(-\frac{1}{g^2}\int_0^1d\tau\, a^2\right) \end{...
1 vote
117 views

### Four-point correlation function path integral for free scalars

In An Introduction to Quantum Field Theory by Peskin and Schroeder, section 9.2, they calculate the four-point correlation function for a free real scalar field $\phi(x)$ using the path integral ...
• 180
1 vote
44 views

### Disappearing symmetry in gaussian functional determinant

I have the following integral $$I=\int D\varphi \; e^{-\int d^4p d^4p' \left[ -\frac{1}{2}\varphi(p) g(p) \delta(p+p') \varphi(p') \right]}.\tag{1}$$ This is the continuum limit of a gaussian matrix ...
• 691
1 vote
87 views

• 767
1 vote
39 views

### Is there still a Gribov ambiguity when the Faddeev-Popov determinant is treated without ghosts?

In this document (Gribov Ambiguity by Thitipat Sainapha) the setup leading to the equation $3.77$ seems to strongly depend on the treatment of the Faddeev-Popov determinants with ghosts. Indeed the ...
• 1,772
81 views

• 780
1 vote
95 views

### 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 ...
• 1,772
1 vote
51 views

### 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 ...
• 1,814
288 views

• 10.6k
1 vote
54 views

### 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 ...
• 41
305 views

955 views

### How does the functional measure transform under a field redefinition?

My question is: how does the path integral functional measure transform under the following field redefinitions (where $c$ is an arbitrary constant and $\phi$ is a scalar field): \begin{align} \phi(x)&...
• 1,992
1 vote
385 views

### Vacuum Energy Calculation using Path Integral

I am currently reading Zee's book on quantum field theory, and I am in the chapter where he is introducing Grassmann integrals. He re-introduces the path integral evaluated for the vacuum, i.e. no ...
• 162
580 views

• 3,431