TL;DR
This paper discusses a subtlety in the Batalin-Vilkovisky (BV) formalism where the standard BV complex is not acyclic under common conditions unless second-order antifields are introduced, with examples from harmonic oscillator and electromagnetic field.
Contribution
It explicitly demonstrates the non-acyclicity of the standard BV complex in typical cases and highlights the necessity of second-order antifields for acyclicity.
Findings
Standard BV complex is not acyclic with general function classes.
Introducing second-order antifields restores acyclicity.
Explicit examples include harmonic oscillator and electromagnetic field.
Abstract
The standard BV complex is never acyclic provided that the equations of motion have solutions and the admissible class of functions is general enough, unless one introduces second-order antifields. This phenomenon is explicitly illustrated for the harmonic oscillator and the free electromagnetic field.
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Taxonomy
TopicsPower Line Communications and Noise · ECG Monitoring and Analysis · Electrostatic Discharge in Electronics