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Field Operators in Real Space.

Lorenz S Cederbaum1

  • 1Theoretische Chemie, Physikalisch-Chemisches Institut, Universität Heidelberg , Im Neuenheimer Feld 229, 69120 Heidelberg, Germany.

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Summary
This summary is machine-generated.

Field operators in many-body theory can be represented in position space, simplifying calculations. This work provides explicit expressions and connects first quantization to second quantization for arbitrary particle numbers.

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Area of Science:

  • Quantum mechanics
  • Many-body theory
  • Quantum field theory

Background:

  • Field operators are fundamental in many-body theory for indistinguishable particles.
  • Representing these operators in various spaces is crucial for theoretical advancements.

Purpose of the Study:

  • To demonstrate that field operators can be exclusively represented in position space.
  • To derive explicit expressions for position-space field operators.
  • To establish a connection between first and second quantization operators for arbitrary particle numbers.

Main Methods:

  • Developing explicit mathematical expressions for field operators in position space.
  • Generalizing operators from first quantization to accommodate arbitrary particle numbers.
  • Applying derived expressions to establish connections with second quantization operators.

Main Results:

  • Successful representation of field operators solely in position space.
  • Derivation of explicit position-space field operator expressions.
  • Demonstrated a direct link between first and second quantization operators through generalization.

Conclusions:

  • Position space representation offers a simplified approach to field operators in many-body theory.
  • The derived methods provide a unified framework connecting different quantization formalisms.
  • Illustrative examples confirm the validity and utility of the presented approach.