Physics Asked on January 2, 2022

The scattering $S$ operator which is defined to be the operator corresponding to $S$ matrix should be rotational invariance, does this imply $S$ operator is a scalar operator?

In a typical collider experiment, two particles, generally in approximate momentum eigenstates at $t = -infty$, are collided with each other and it is measured the probability of finding particular outgoing momentum eigenstates at $t = +infty$.

In the Heisenberg picture the probability amplitude for the initial states $vert i rangle$ to evolve to the final states $vert f rangle$ is defined as $langle f vert S vert i rangle$ where the time evolution is put in the scattering or S-matrix.

The S-matrix element $langle f vert S vert i rangle$ for $n$ asymptotic momentum eigenstates is given by the LSZ (Lehmann-Symanzik-Zimmermann) reduction formula which for scalar quantum fields $phi (x)$ states

$$langle f|S| i rangle = [i int d^4 x_1 exp (-i p_1 x_1) (Box_1 + m^2)] cdot cdot cdot [i int d^4 x_n exp (i p_n x_n) (Box_n + m^2)] langle Omega | T { phi (x_1) cdot cdot cdot phi (x_n)} | Omega rangle$$

where $−i$ in the exponent applies to initial states and $+i$ to final states.

The LSZ formula is constructed from Lorentz covariant fields, hence the S-matrix element is an invariant.

Answered by Michele Grosso on January 2, 2022

6 Asked on May 6, 2021 by john-hippisley

1 Asked on May 6, 2021

centripetal force classical mechanics newtonian mechanics reference frames rotational kinematics

3 Asked on May 6, 2021

functional determinants path integral quantum field theory regularization

2 Asked on May 6, 2021 by siqi-wu

condensed matter crystals group theory solid state physics symmetry

0 Asked on May 6, 2021

0 Asked on May 6, 2021

energy conservation lagrangian formalism moment of inertia reference frames rotational dynamics

1 Asked on May 5, 2021 by richard-hum

1 Asked on May 5, 2021 by john-hunter

big bang galaxies general relativity gravity physical constants

2 Asked on May 5, 2021

0 Asked on May 5, 2021

1 Asked on May 5, 2021

4 Asked on May 5, 2021 by humancl

2 Asked on May 5, 2021 by george-orwell

0 Asked on May 5, 2021 by marcosko

phase space potential quantum mechanics schroedinger equation wavefunction

3 Asked on May 5, 2021 by parvathy

electric circuits electric current electrical resistance homework and exercises

Get help from others!

Recent Answers

- Joshua Engel on Why fry rice before boiling?
- Lex on Does Google Analytics track 404 page responses as valid page views?
- haakon.io on Why fry rice before boiling?
- Peter Machado on Why fry rice before boiling?
- Jon Church on Why fry rice before boiling?

Recent Questions

- How Do I Get The Ifruit App Off Of Gta 5 / Grand Theft Auto 5
- Iv’e designed a space elevator using a series of lasers. do you know anybody i could submit the designs too that could manufacture the concept and put it to use
- Need help finding a book. Female OP protagonist, magic
- Why is the WWF pending games (“Your turn”) area replaced w/ a column of “Bonus & Reward”gift boxes?
- Does Google Analytics track 404 page responses as valid page views?

© 2023 AnswerBun.com. All rights reserved. Sites we Love: PCI Database, UKBizDB, Menu Kuliner, Sharing RPP