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Area of Science:

  • Theoretical Physics
  • Quantum Mechanics
  • General Relativity

Background:

  • The Dirac equation describes relativistic quantum mechanics.
  • Simulating quantum systems in curved spacetimes is challenging.
  • Existing quantum simulators are primarily designed for flat spacetimes.

Purpose of the Study:

  • To develop a method for transforming Dirac equations from curved to flat spacetimes.
  • To enable the use of existing quantum simulators for curved spacetime problems.
  • To find new solutions for the Dirac equation in curved static backgrounds.

Main Methods:

  • Local phase transformation of the Dirac equation.
  • Mapping solutions from flat to curved static spacetimes.
  • Encoding spacetime metric into a phase transformation.

Main Results:

  • Demonstrated a transformation for the free massless Dirac equation in 1+1 dimensions.
  • Showed that curved static spacetimes can be incorporated into flat spacetime simulations.
  • Obtained solutions for the Dirac equation in specific curved spacetimes.

Conclusions:

  • The proposed transformation technique is effective for incorporating curved static spacetimes into quantum simulations.
  • This method provides a pathway to study relativistic quantum phenomena in curved backgrounds using current technology.
  • The technique opens avenues for exploring novel solutions and phenomena in quantum field theory in curved spacetimes.