Questions tagged [analyticity]
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224 questions
3 votes
1 answer
113 views
Confusion about Cutkosky rules
The standard Cutkosky rules go as follows: Cut the appropriate propagators (replace them with $(-2\pi i) \delta(p^2-m^2)$). Sum over all cuts. This gives $\operatorname{Im}$ (I am dropping factors ...
- 483
5 votes
1 answer
323 views
What kind of procedure is the Wick rotation to Euclidean formulation?
I'm learning QFT via the path integral formalism. I've been struggling understanding the Wick rotation to Euclidean formulation, towards which I feel very uncomfortable. In particular I cannot find a ...
- 864
2 votes
1 answer
161 views
Have exceptional points (for $PT$-symmetric Hamiltonians) been measured?
I am aware that exceptional points have been observed in optics by noting the similarity between Schrödinger's equation and Helmholtz's equation. Thus, exceptional points can be measured in optical ...
- 310
3 votes
1 answer
136 views
2D CFT decoupling of holomorphic and anti-holomorphic parts
I saw this post but it didn't really help me Decoupling of Holomorphic and Anti-holomorphic parts in 2D CFT I am trying to fully understand as to why the holomorpic and anti-holomorphic part decouple. ...
- 357
3 votes
0 answers
128 views
Cutkosky cutting rules in many-body theory
I have read about the Cutkosky cutting rules and optical theorem when I was studying for theoretical particle physics. I.e. Imaginary part of Greens function is directly correlated to the sum of decay ...
3 votes
0 answers
113 views
Is it possible to analytically continue magnetization in one-dimensional Ising models?
I am asking about the infinitely long layered Ising model with a finite number of layers. The model is assumed to be invariant under translations along the direction in which it is infinite. All ...
- 7,827
3 votes
1 answer
210 views
6-point NMHV gluon amplitude using BCFW recursion diagrams
Doing some self-learning on the BCFW shift using spinor-helicity formalism, so essentially just wanted to know where I am going wrong when it comes to deciding which diagrams are valid or not. I am ...
- 72
0 votes
0 answers
51 views
Understanding the Wick Rotation [duplicate]
I understand the logic behind the Wick rotation by considering an imaginary time and in this way achieving an Euclidean-type metric. However, I am trying to understand this in a deeper way. Why ...
- 150
2 votes
1 answer
141 views
Are the Kramers-Kronig relations valid for time-translation variant systems?
For definiteness, consider a linear response theory context. Generically, we have a linear response function $$\chi(t,t') = \Theta(t-t')f(t,t').$$ Suppose the system is not time-translation invariant, ...
- 4,113
3 votes
1 answer
320 views
Are the eigenstates of a holomorphic Hamiltonian holomorphic?
In Kato's book Perturbation Theory for Linear Operators, Chapter 2, Section 6.2, it is claimed that, for a Hamiltonian which is a holomorphic function of a real parameter $x$ (i.e. a time-dependent ...
- 375
1 vote
0 answers
155 views
Is numerical analytic continuation necessary if one can directly set $\mathrm{i}\omega_n\rightarrow\omega+\mathrm{i}0^+$ in numerics?
Analytic continuation refers to the formal procedure $\mathrm{i}\omega_n\rightarrow\omega+\mathrm{i}0^+$ applied to many kinds of Green or correlation function, via which we go from Matsubara Green's ...
- 3,981
1 vote
1 answer
159 views
Analytical Method used in harmonics oscillator v.s the Hydrogen Atom in quantum mechanics
I was studying quantum mechanics by Griffthis, he used Analytical Method in two times, first with harmonic oscillator in chapter(2), and second in chapter(4) for Hydogen Atom, in each case we got a ...
- 77
4 votes
1 answer
176 views
Regulating certain integral
I am interested in regulating an integral of the type, \begin{equation} I = \frac{1}{2\pi^2}\int_0^\infty p^2\ dp\ \frac{g(p)}{p^2 - k^2 - i\epsilon} = \frac{1}{4\pi^2}\int_{-\infty}^\infty p^2\ dp\ ...
- 664
2 votes
0 answers
92 views
From real variables function to complex variables function?
I'm confused with notations physicists using. They change real variables $$(x_1,x_2,...,x_n)\in (\mathbb{R^2})^n$$ of a function to complex variables $$(z_1,z_1^*,z_2,z_2^*,...,z_n,z_n^*)\in(\mathbb{C^...
1 vote
1 answer
110 views
Do we find systems whose Lagrangian is unconstrained, smooth but not analytic?
All of the toy problems in Lagrangian mechanics I have come across are analytic. Most of the non-analytic functions I know don't seem to appear in Lagrangian mechanics. I can, of course, see how a ...
- 54.6k