O hidrodinamiki kot efektivni teoriji polja

O hidrodinamiki se da razmišljati kot o efektivni teoriji, ki opiše obnšanje sistema okoli termičnega ravnovesja na dolgih razdaljah. Enega od načinov formulacije predstavlja razvoj po odvodih hidrodinamskih spremenljivk, katere je moč izračunati iz particijske funkcije sistema v termičnem ravnovesju. Po uvedbi terminologije sledi diskusija o redu hidrodinamike v relaciji na red najvišjih odvodov, ki so vključeni v razvoj. Podrobno je opisana hidrodinamika ničtega reda (idealna hidrodinamika) za normalne relativistične tekočine, kar poda opis idealnih tekočin. Po tem vzorcu je opredeljena moderna formulacija hidrodinamike. Sledijo komentarji o visokoenergijskih (kratke razdalje) in nizkoenergijskih (velike razdalje) prostostnih stopnjah v kontekstu efektivnih teorij polja. S tem je motiviran opis hidrodinamike kot efektivne teorije polja ob upoštevanju njene intrinzične narave. Sledi formulacije hidrodinamike iz principa minimizacije akcije. Ob upoštevanju relevantnih simetrij in identifikaciji termodinamskih količin je pokazano, kako enačba stanja definira obliko najbolj splošne akcije. Iz očitnih razlogov se temu formalizmu reče bolj moderna formulacija hidrodinamike.

On hydrodynamics as an effective field theory

Hydrodynamics can be thought of as an effective theory which describes the long-distance behaviour of a system around thermal equilibrium. At an ever-increasing difficulty, it can be formulated as a derivative expansion in terms of hydrodynamic variables which are to be read off the partition function of the system in thermal equilibrium. The explanation of all this terminology is followed by a discussion on the truncation of hydrodynamics in the order of derivatives. Truncation at 0th order for normal relativistic fluids is discussed in more detail, which gives rise to 0th order hydrodynamics (ideal hydrodynamics) for a perfect fluid. It is noted that in the nonrelativistic limit, those equations become the usual equations of fluid dynamics. This is what is referred to as the modern formulation of hydrodynamics. Then, changing perspective, comments follow on high-energy (short-distance) and low-energy (long-distance) degrees of freedom, in the context of effective field theories. This is to inspire considering hydrodynamics itself as an effective field theory, when having its intrinsic nature in mind. Having motivated the discussion, the focus falls on formulating ideal hydrodynamics from an action principle. To that end, symmetries are pointed out, the thermodynamic quantities are identified, and finally it is shown how a specified equation of state restricts the form of the generic action. For obvious reasons, this is what is referred to as the more modern formulation of hydrodynamics.