Topology of D-Operator Space. Algorithm for Checking the Physical Admissibility of Linear Differential Operators (Admissibility Criteria for Free Kinetic Operators)

Key Points

• The aim is to develop a step-by-step algorithm for checking if linear differential operators can be deemed physically acceptable in field theories.
• Formulate the D-operator space and establish criteria for evaluating certain properties of operators.
• Illustrate the algorithm with examples and counterexamples, demonstrating different operator types and their admissibility.
• Conduct rigorous mathematical evaluations of locality, hyperbolicity, gauge invariance, and energy positivity.
• The algorithm provides clear criteria for the admissibility of various linear differential operators in field theory.
• Illustrated examples clarify how to apply the algorithm to well-known operators and edge cases like tachyons.
• Each criterion aids in ensuring the theoretical consistency and physical relevance of the operators discussed.

Abstract