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Unique Translation between Hamiltonian Operators and Functional Integrals.

Gollisch1, Wetterich

  • 1Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany.

Physical Review Letters
|January 3, 2001
PubMed
Summary
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Discretization errors in quantum mechanics path integrals yield a unique Hamiltonian-to-action translation. This correction impacts the chemical potential in many-body bosonic systems, as confirmed by perturbation theory.

Area of Science:

  • Quantum mechanics
  • Many-body systems
  • Statistical physics

Background:

  • Path integral formulation is crucial for quantum mechanics.
  • Discretization errors can affect the accuracy of path integral calculations.
  • Understanding many-body bosonic systems often involves functional integrals.

Purpose of the Study:

  • To develop a unique prescription for translating the Hamiltonian to the action in functional integrals.
  • To investigate the impact of discretization errors on the path integral formulation.
  • To analyze corrections to the chemical potential in many-body bosonic systems.

Main Methods:

  • Careful treatment of discretization errors in the path integral formulation.
  • Application to an interaction quadratic in the occupation number.

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  • Perturbative calculation for validation.

    • Main Results:

    • A unique prescription for Hamiltonian-to-action translation was derived.
    • A correction to the chemical potential term was identified for many-body bosonic systems.
    • The relevance of this correction was supported by perturbative calculations.

    Conclusions:

    • The derived prescription offers a more accurate path integral formulation.
    • Discretization errors introduce significant corrections, particularly to the chemical potential.
    • The findings are relevant for the study of many-body bosonic systems.