All Questions
6
questions
4
votes
0
answers
100
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Functional determinant: linking Series, Heat-Kernel and Zeta function
I would like to express a functional determinant as a series of diagrams, using the zeta function renormalization applied to the heat-kernel method, but I don't know if it's possible. Let me explain:
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- 2,613
1
vote
0
answers
54
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Why does expressing the Faddeev-Popov determinant as this lead to such problems?
Background
In the following, I am interested in the Schwinger function associated with the gluon propagator when one considers the Gribov no-pole condition in the partition function. Defining $\nabla^{...
- 2,613
2
votes
1
answer
113
views
Conditions on the covariance operator in Gaussian Path Integrals
In field theory, one typically encounters integrals of the form:
$$ \mathcal{Z}[J] = \int \mathcal{D}[\phi] \exp \left( - \frac{1}{2} \int d^Dx d^Dx' \ \phi(x)A(x,x')\phi(x')+ \int d^Dx \phi(x) J(x)\...
- 539
4
votes
1
answer
933
views
Determinant of d'Alembert Operator $\mathop\Box-m^{2}$
In quantum field theory, the partition function of a free scalar is
$$\mathcal{Z}=\int\mathcal{D}\phi\exp i\int d^{n}x\frac{1}{2}\left[(\partial_{\mu}\phi)(\partial^{\mu}\phi)-m^{2}\phi^{2}\right]$$
$...
- 2,923
2
votes
0
answers
148
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Indexes in the Gaussian functional integral
This is a question spawning from a comment made to my previous question. There I was asking about taking some functional derivative in the effective action of the non-linear sigma model. The comment ...
- 6,067
1
vote
1
answer
1k
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One-loop effective action of QED and the partition function
Given the partition function for QED
$$ Z= \int \mathcal{D}A_{\mu}\mathcal{D}\Psi \mathcal{D}\bar{\Psi}\, \text{exp}\left(- \frac{i}{4}\int F_{\mu\nu} F^{\mu\nu} + i \int \bar{\Psi} (i {\not} D-m) \...
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