Unanswered Questions
5,206 questions with no upvoted or accepted answers
63
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answers
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How to apply the Faddeev-Popov method to a simple integral
Some time ago I was reviewing my knowledge on QFT and I came across the question of Faddeev-Popov ghosts. At the time I was studying thеse matters, I used the book of Faddeev and Slavnov, but the ...
57
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0
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Systematic approach to deriving equations of collective field theory to any order
The collective field theory (see nLab for a list of main historical references) which came up as a generalization of the Bohm-Pines method in treating plasma oscillations often used in the study of ...
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28
votes
1
answer
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Electric charges on compact four-manifolds
Textbook wisdom in electromagnetism tells you that there is no total electric charge on a compact manifold. For example, consider space-time of the form $\mathbb{R} \times M_3$ where the first factor ...
CommunityBot
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24
votes
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answers
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Why does analytic continuation as a regularization work at all?
The question is about why analytical continuation as a regularization scheme works at all, and whether there are some physical justifications. However, as this is a relatively general question, I ...
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TQFTs and Feynman motives
Questions
Is a topological quantum field theory metrizable? Or else a TQFT coming from a subfactor?
For a given metric, are there always renormalization and Feynman diagrams?
Is there always a Feynman ...
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17
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Time Reversal, CPT, spin-statistics, mass gap and chirality of Euclidean fermion field theory
In Minkowski space even-dim (say $d+1$ D) spacetime dimension, we can write fermion-field theory as the Lagrangian:
$$
\mathcal{L}=\bar{\psi} (i\not \partial-m)\psi+ \bar{\psi} \phi_1 \psi+\bar{\psi} ...
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15
votes
0
answers
872
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Wick theorem and OPE
I'm trying to work out in detail how the Wick theorem is used for constructing OPEs in CFT. One of the first things which bothers me is the difference in definitions of normal ordered product and ...
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14
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437
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How to perform a derivative of a functional determinant?
Let us consider a functional determinant
$$\det G^{-1}(x,y;g_{\mu\nu})$$
where the operator $G^{-1}(x,y;g_{\mu\nu})$ reads
$$G^{-1}(x,y;g_{\mu\nu})=\delta^{(4)}(x-y)\sqrt{-g(y)}\left(g^{\mu\nu}(y)\...
- 3,691
13
votes
0
answers
185
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Is it known whether Wightman's axiomatic QFT is logically equivalent to Osterwalder–Schrader's axiomatic QFT?
Constructive QFT has provided some interesting models for dimension $d < 4$ of space-time, satisfying specific axiomatic versions of QFT. On the other hand, it is a well known fact that an ...
- 64.2k
13
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0
answers
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Penrose's Zig-Zag Model and Conservation of Momentum
I was reading through Penrose's Road to Reality when I saw his interesting description of the Dirac electron (Chapter 25, Section 2). He points out that in the two-spinor formalism, Dirac's one ...
- 1,064
13
votes
1
answer
807
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Interpreting the Klein-Gordon Annihilation Operator Expression
I can derive $$a(k) = \int d^3 x e^{ik_{\mu} x^{\mu}} (\omega_{\vec{k}} \psi + i \pi)$$ for a free real scalar Klein-Gordon field in three ways mathematically: the usual Fourier transform way in ...
CommunityBot
- 1
13
votes
1
answer
527
views
Why is it hard to give a lattice definition of string theory?
In Polyakov's book, he explains that one possible way to compute the propagator for a point particle is to compute the lattice sum $\sum_{P_{x,x'}}\exp(-m_0L[P_{x,x'}])$, where the sum goes over all ...
12
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383
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Deriving non-relativistic potentials from QFT
Some systems, like atoms, are described well by quantum mechanics, where one just gives the Hamiltonian in the form $H=T+V$ and computes the eigenvalues and eigenvectors of this operator to figure out ...
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12
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What motivates clockwork theory?
Clockwork is a new model-building gadget that produces very small couplings starting from a theory with no small numbers at all, in an attempt to solve the hierarchy problem.
To describe it as ...
- 4,693
12
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answers
512
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Capturing (perturbatively) non-equilibrium field theory effects using "elementary" methods
I am considering a system of two interacting scalar fields: $\psi$, and $\phi$. The Lagrangian is given by:
\begin{equation}
\mathcal{L}[\psi]=\frac{1}{2}\partial_\mu\psi\partial^\mu\psi+\frac{1}{2}\...
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