Wave Liquidity Redistribution Theory: Toward a Field-Theoretic Definition of Market Liquidity

This paper proposes a field-theoretic definition of market liquidity within the framework of Wave Liquidity Redistribution Theory (WLRT). Unlike conventional market microstructure approaches that describe liquidity through execution-based proxies such as spreads, depth, turnover, and price impact, this work introduces liquidity as a primary state variable represented by a non-negative density field over price space. The paper develops: an axiomatic definition of liquidity, a constructive mapping from observable execution characteristics to a liquidity density field, continuity and wave-based dynamics of liquidity redistribution, a functional definition of price as an observable derived from the liquidity field, a set of empirically testable hypotheses, and a formal interpretation of automated market makers (AMMs) and constant-function market makers (CFMMs) as structurally defined liquidity mechanisms. The work is intended as a conceptual and theoretical contribution toward a unified definition of liquidity in market microstructure and liquidity-centered market theory.