- #1

- 287

- 0

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter touqra
- Start date

In summary: Here, M is the maximum length of the interval [a,b] in which |h(z)|<M.Is ML estimate maximum likelihood estimate? How can ML estimate be used here since it is about probability?When I said ML-estimate I mean the following:Suppose C is a piecewise smooth curve. If h(z) is continuous function on C then\displaystyle{\left|\int_{C} h(z)\, dz\right| \leq \int_{C}|h(z)|\, |dz|}.and if C has length L and |h(z)|\leq M on C

- #1

- 287

- 0

Physics news on Phys.org

- #2

Homework Helper

- 726

- 3

describing the loop: first bit is the original bit the flat/horizontal (-R,+R) bit with R eventually taken to infinity, then to complete the loop you need to add a 1/4 of an arc going from +R to +iR, then comes down to avoid the branch cut, go around the pole and goes up again before arch back from +iR to -R.

- #3

- 287

- 0

mjsd said:

describing the loop: first bit is the original bit the flat/horizontal (-R,+R) bit with R eventually taken to infinity, then to complete the loop you need to add a 1/4 of an arc going from +R to +iR, then comes down to avoid the branch cut, go around the pole and goes up again before arch back from +iR to -R.

Why would the arc or circular bit dies away as the variable goes infinity?

- #4

Homework Helper

- 726

- 3

- #5

- 287

- 0

mjsd said:

I looked up on Jordan's lemma, and yeah the integrand of the semicircular path (excluding the real axis) tends to zero as R goes infinity.

OOOooo contour integrals are so interesting !

Thank you!

Is ML estimate maximum likelihood estimate? How can ML estimate be used here since it is about probability?

- #6

Homework Helper

- 726

- 3

Suppose C is a piecewise smooth curve. If [tex]h(z)[/tex] is continuous function on C then

[tex]\displaystyle{\left|\int_{C} h(z)\, dz\right| \leq

\int_{C}|h(z)|\, |dz|}.[/tex]

and if C has length L and [tex]|h(z)|\leq M[/tex] on C then

[tex]\displaystyle{\left|\int_{C} h(z)\, dz\right| \leq ML}[/tex]

Quantum Field Theory (QFT) is a theoretical framework that combines the principles of quantum mechanics and special relativity to describe the behavior of subatomic particles and their interactions.

In QFT, integrals are used to calculate the probability amplitudes of different particle interactions. By evaluating these integrals, we can determine the likelihood of certain particle interactions occurring.

In classical mechanics, integrals are computed over a continuous range of values. In QFT, the integrals are computed over a discrete set of values, which corresponds to the discrete energy levels of particles in a quantum system.

One of the main challenges in evaluating integrals in QFT is dealing with infinities that arise in the calculations. These infinities can be dealt with using various techniques such as renormalization.

Feynman diagrams are graphical representations of mathematical expressions that describe the behavior of particles in QFT. They are used to simplify the evaluation of integrals and make predictions about particle interactions.

Share:

- Replies
- 1

- Views
- 481

- Replies
- 2

- Views
- 687

- Replies
- 4

- Views
- 629

- Replies
- 1

- Views
- 705

- Replies
- 2

- Views
- 258

- Replies
- 1

- Views
- 83

- Replies
- 2

- Views
- 855

- Replies
- 5

- Views
- 2K

- Replies
- 10

- Views
- 120

- Replies
- 3

- Views
- 1K