Does a Functional Integral Really Need a Lagrangian?

• Main Author: D. Kochan
• Format: Article
• Language: English
• Published: CTU Central Library 2010-01-01
• Series: Acta Polytechnica
• Subjects: quantization of (non-)Lagrangian systems; path vs. surface functional integral
• Online Access: https://ojs.cvut.cz/ojs/index.php/ap/article/view/1269

<p>Path integral formulation of quantum mechanics (and also other equivalent formulations) depends on a Lagrangian and/or Hamiltonian function that is chosen to describe the underlying classical system. The arbitrariness presented in this choice leads to a phenomenon called Quantization ambiguity. For example both L₁ = ˙q² and L₂ = e^q˙ are suitable Lagrangians on a classical level (δL₁ = δL₂), but quantum mechanically they are diverse.</p> This paper presents a simple rearrangement of the path integral to a surface functional integral. It is shown that the surface functional integral formulation gives transition probability amplitude which is free of any Lagrangian/Hamiltonian and requires just the underlying classical equations of motion. A simple example examining the functionality of the proposed method is considered.