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Exact wave functions in a noncommutative field theory.

D Bak1, S K Kim, K S Soh

  • 1Physics Department, University of Seoul, Seoul 130-743 Korea.

Physical Review Letters
|October 6, 2000
PubMed
Summary

We studied scattering amplitudes in noncommutative field theory. The resulting wave functions show string-like behavior, with two centers in relative coordinates.

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Area of Science:

  • Quantum Field Theory
  • String Theory
  • Mathematical Physics

Background:

  • Noncommutative field theory extends quantum mechanics to noncommuting coordinates.
  • Quartic interactions are fundamental in quantum field theory.
  • Perturbative analysis is a standard method for calculating scattering amplitudes.

Purpose of the Study:

  • To compute the 2-->2 scattering amplitude in a nonrelativistic field theory with quartic interaction on a noncommutative plane.
  • To analyze the wave functions of the two-particle Schrödinger equation in this theory.
  • To investigate the emergence of stringy behavior in noncommutative field theories.

Main Methods:

  • Perturbative analysis to all orders for scattering amplitude calculation.
  • Solving the two-particle Schrödinger equation to find scattering and bound state wave functions.
  • Analyzing the properties of the resulting wave functions in relative coordinates.

Main Results:

  • The 2-->2 scattering amplitude was computed to all orders.
  • Scattering and bound state wave functions were derived.
  • Wave functions exhibit unusual two-center behavior in relative coordinates.
  • The separation of these centers scales linearly with total momentum and is transverse to it.

Conclusions:

  • The study confirms the stringy nature of noncommutative field theories.
  • The two-center wave function property is a key indicator of this stringy behavior.
  • This work provides insights into the fundamental properties of quantum field theories on noncommutative spaces.

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