用车千万不能大意 方向盘套没你想象中那么简
4,306 questions with no upvoted or accepted 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 ...
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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The collective field theory (see nLab for a list of main historical references) which came up as a generalization of the Bohm-Pines method in treating plasma oscillations often used in the study of ...
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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 ...
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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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Definition of vacua in QFT in generic spacetimes
I have been learning QFT in curved spaces from various sources (Birrell/Davies, Tom/Parker, some papers), and one thing that confuses me the most is the choice of vacua in various spacetimes, and the ...
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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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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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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:
$$
\mathcal{L}=\bar{\psi} (i\not \partial-m)\psi+ \bar{\psi} \phi_1 \psi+\bar{\psi} ...
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How to perform a derivative of a functional determinant?
Let us consider a functional determinant
$$\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)\...
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Does a good path integral exist in Loop Quantum Gravity?
The Hamiltonian operator of loop quantum gravity is a totally constrained system
$$H = \int_\Sigma \mathrm{d}^3x\ (N\mathcal{H}+N^a V_a+G).$$
Here, $\Sigma$ is a 3-dimensional hypersurface; a slice of ...
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How do we know for sure a theory is non-renormalizable?
In quantum field theory, we are looking for a Lagrangian that is, amongst other, renormalizable. But how do we determine whether or not a theory is renormalizable? Is this purely done by power ...
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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 ...
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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 ...
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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 ...
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Field theory based on square-well potential?
Is it possible to find the behavior of a field theory with a square well in the Lagrangian? Usually, we have polynomial terms, and one can argue (see e.g. in [physics SE q41065]) that the simplest ...
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