Effective field theory for non-relativistic hydrodynamics
- PDF / 919,646 Bytes
- 68 Pages / 595.276 x 841.89 pts (A4) Page_size
- 114 Downloads / 248 Views
Springer
Received: September 11, 2020 Accepted: September 27, 2020 Published: October 30, 2020
Akash Jain Department of Physics & Astronomy, University of Victoria, PO Box 1700 STN CSC, Victoria, BC, V8W 2Y2, Canada
E-mail: [email protected] Abstract: We write down a Schwinger-Keldysh effective field theory for non-relativistic (Galilean) hydrodynamics. We use the null background construction to covariantly couple Galilean field theories to a set of background sources. In this language, Galilean hydrodynamics gets recast as relativistic hydrodynamics formulated on a one dimension higher spacetime admitting a null Killing vector. This allows us to import the existing field theoretic techniques for relativistic hydrodynamics into the Galilean setting, with minor modifications to include the additional background vector field. We use this formulation to work out an interacting field theory describing stochastic fluctuations of energy, momentum, and density modes around thermal equilibrium. We also present a translation of our results to the more conventional Newton-Cartan language, and discuss how the same can be derived via a non-relativistic limit of the effective field theory for relativistic hydrodynamics. Keywords: Effective Field Theories, Space-Time Symmetries, Quantum Dissipative Systems, Stochastic Processes ArXiv ePrint: 2008.03994
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP10(2020)208
JHEP10(2020)208
Effective field theory for non-relativistic hydrodynamics
Contents 1 Introduction and overview
1 7 7 7 9 11 11 13 14 16
3 Effective field theory for Galilean hydrodynamics 3.1 Fluid worldvolume formulation 3.2 Physical spacetime formulation 3.3 Schwinger-Keldysh generating functional 3.4 Explicit effective action and emergent second law 3.5 Field redefinitions and frame transformations
18 19 22 24 26 29
4 Effective action for one-derivative Galilean fluids 4.1 Non-linear effective action 4.2 Linearised stochastic fluctuations 4.2.1 Perturbative expansion in fluctuations 4.2.2 Free theory 4.2.3 Interactions 4.3 Incompressible and diffusion limits
30 30 32 32 34 35 37
5 Coupling to Newton-Cartan sources 5.1 Classical hydrodynamics with Newton-Cartan sources 5.1.1 Newton-Cartan structure 5.1.2 Coupling to Galilean field theories 5.1.3 Hydrodynamics on curved spacetime 5.2 Schwinger-Keldysh effective field theory 5.2.1 Effective field theory on fluid worldvolume 5.2.2 Effective field theory on physical spacetime 5.2.3 Schwinger-Keldysh constraints and explicit effective action
38 38 39 40 42 44 45 47 50
6 Outlook
53
A Second law constraints in Galilean hydrodynamics
55
–i–
JHEP10(2020)208
2 Review of classical Galilean hydrodynamics 2.1 Dissipative hydrodynamics on flat background 2.1.1 Conservation equations 2.1.2 Constitutive relations 2.2 Coupling to sources 2.2.1 Null backgrounds 2.2.2 Hydrodynamics on curved spacetime 2.3 Frame transformations and thermodynamic frame 2.4 Generalities and adiabaticity equation
B Effective field theory via non-relativi
Data Loading...
