Questions tagged [analyticity]
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16
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Loop Effect of $\phi$ Propagator in $t$-channel of scalar $\phi^3$ theory [closed]
In Schwartz's QFT chapter 16, he calculates the loop effect (vaccum polarization) of $\phi$ propagator in $\phi^3$ theory, with the choice of Pauli-Villars regulator, the scattering amplitude would be
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210
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Splitting Scalar into Holomorphic and Anti-Holomorphic Parts
I am reading Tong’s string theory lecture notes. On page 78, he splits the 2d free scalar into left- and right-moving parts, seemingly using the classical equation of motion as justification.
Why is ...
- 123
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1
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Complex BCFW-shift of Parke-Taylor amplitude
(This question stems from problem 3.3 of Elvang's and Huang's "Scattering Amplitudes in Gauge Theory and Gravity" book).
Consider the Parke-Taylor amplitude given as
\begin{equation}
A_n[1^- ...
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52
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Analytic continuation Matsubara/imaginary-time to retarded function in complex time domain
In linear response theory, one may either use the real-time retarded correlation function, or analytically continue to imaginary time/frequency to use the Matsubara Green's function instead. While ...
1
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1
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51
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On complex impedance representation and Riemann surfaces
We know that a complex number, $z=re^{i\phi}$, can be represented with infinitely many phases, $\phi+2\pi n$, for integer $n$, as can be easily seen from the equivalent picture of a vector on the ...
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1
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Analytical continuation as regularization in Quantum Field Theory, the remaining questions
There is an old question posted (Regularization) which did not get an answer, about the validation of analytic continuation as regularization. It did get some discussion in the comments, referring to ...
- 4,993
1
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1
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89
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Kramers-Kronig relations for a Gaussian function
Consider a function of a complex variable $\omega$ which is given by $f(\omega) = e^{-\omega^2/2}$.
This function is symmetric, holomorphic everywhere, and vanishes as $|\omega| \rightarrow \infty$. ...
- 221
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How is Wick rotation an analytic continuation?
Wick rotation is formally described by the transformation
$$t \mapsto it.$$
In many place it is stated more rigorously as an analytic continuation into imaginary time. I understand why we do it but ...
- 3,370
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102
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Discontinuity of the scattering amplitude and optical theorem
The generalized optical theorem is given by:
\begin{equation}\label{eq:optical_theorem}
M(i\to f) - M^*(f\to i) = i \sum_X \int d\Pi_X (2\pi)^4 \delta^4(p_i-p_X)M(i\to X)M^*(f\to X).\tag{Box 24.1}
...
- 53
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270
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Branch cut of a one-loop bubble diagram after cutting a single propagator
I am trying to understand Cutkosky cutting rules and generalized unitarity. Consider the article https://arxiv.org/abs/0808.1446 by Arkani-Hamed, Cachazo & Kaplan. In chapter 5.1 equation 133, the ...
- 53
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Does an initially analytic wavefunction remain analytic under time evolution?
My question has to do with when "mathematically nice" properties of a wavefunction (e.g. analyticity) are preserved under time evolution.
Consider the Schrodinger equation $i\frac{d}{dt}|\...
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0
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87
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What is the position-space form of the photon propagator in axial gauge?
I'm interested in the form of the photon propagator in position space, when expressed in an axial gauge $ n \cdot A =0$, where in the case I am interested in, $n^\mu = \{1,0,0 \dots, 0\}$ (for a $D$-...
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About Second-Order Poles of Matsubara Sum
I would like to ask about the calculation regarding Matsubara sum of the form
\begin{equation}
\frac{1}{\beta}\sum_{i\omega_n} \frac{1}{(i\omega_n-\xi)^2}
\end{equation}
which is a second order pole ...
- 1
3
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1
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327
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General interpretation of the poles of the propagator
I am somewhat familiar with the fact that the poles of the Feynman propagator in QFT give the momentum of particle states. I'm also familiar with the KL spectral representation in that context (See ...
- 4,827
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Polchinski's doubling trick for extending open string theory to the whole complex plane
Open string theory can be described on the upper-half complex plane. To simplify the description of open string theory, Polchinski asserts (eq. 2.6.28 in his Vol. I String Theory book) that it is ...
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