# Questions tagged [analyticity]

The tag has no usage guidance.

179 questions
Filter by
Sorted by
Tagged with
1 vote
98 views

### 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 ...
1 vote
15 views

### Discontinuities in the $u$ channel

if we consider a 2-to-2 scattering, we have normally an $s$ channel a $t$ channel and $u$ channel. In CMS frame $s$ is positive and $t$ and $u$ negative, by crossing symmetry there are kinematics ...
1 vote
60 views

### Is it possible to determine a final orientation from an initial angular velocity and constant angular acceleration analytically?

I am looking to model the rotation of a ball over time. I have the following information: an initial orientation, as a quaternion an initial angular velocity, as X/Y/Z components, fixed to the global ...
1 vote
143 views

### Analyticity in the upper half plane and causality

Can you, please, help me to understand the following How is the analyticity of a complex-valued function in the upper half plane related to causality and Kramers-Kronig relations? Namely, why is it ...
97 views

### Proof of commutation relation in Lattice Vertex Operator Algebra

In DGM  on page 548 below Equation 5.4, it is claimed that the operators $\frac{dX^j(z)}{dz}$ and $\frac{dX^k(\zeta)}{d\zeta}$ commute, where \begin{equation} X^j(z)=q^j-i p^j \log z+i \sum_{n \neq ...
124 views

### Is the $S$-Matrix analytic in Planck constant?

Taking the scattering amplitude as a function of $\hbar$, is such function necessarily analytic in this variable. Suppose I'm concerned with Relativistic Quantum Field Theory. In QED, the tree level ...
145 views

61 views

1 vote
23 views

182 views

### Does Feynman's path integral include complex trajectories?

The WKB approximation provides the correct exponential decay of eigenstates inside classically forbidden regions if one allows classical momenta to be imaginary. The typical example is a double well ...
122 views

### Do finite sized 1D Hamiltonians have free energies which are analytic everywhere in the complex plane?

It's well known that 1D classical and quantum short-ranged Hamiltonians have free energies which are analytic/holomorphic everywhere as a function of inverse temperature $\beta=1/k_BT$ (see Araki, &...
1 vote
104 views

### How to analytically continue Schwinger functions?

To get Wightman functions $W(t_1, \dots, t_{k-1})$ from Schwinger functions $S(\tau_1 = i t_1, \dots)$, we use analytical continuation. But I don't think this is simply an issue of plugging $it_a$ for ...
352 views

### Residue of the Fermi Distribution Function

In the "Lecture notes on many-body theory" by Michele Fabrizio, it is stated: How we do show that the Fermi distribution function $f(z)$ has residue $-T$? In the examples on Wikipedia, the ...
77 views

### Complex time theories with spacetime $\mathbb{R}^3\times\mathbb{C}$

Are there any well-developed (string?..) theories assuming that, what we perceive as a (3+1) Minkowskian manifold, is a projection/compactification of a 5-dim spacetime, locally obtained via ...