Establishing Conservation Laws in Pair Correlated Many Body theories: T matrix Approaches

Abstract

We address conservation laws associated with current, momentum and energy and show how they can be satisfied within many body theories which focus on pair correlations. Of interest are two well known t-matrix theories which represent many body theories which incorporate pairing in the normal state. The first of these is associated with Nozieres Schmitt-Rink theory, while the second involves the t-matrix of a BCS-Leggett like state as identified by Kadanoff and Martin. T-matrix theories begin with an ansatz for the single particle self energy and are to be distinguished from $\Phi$-derivable theories which introduce an ansatz for a particular contribution to the thermodynamical potential. Conservation laws are equivalent to Ward identities which we address in some detail here. Although $\Phi$-derivable theories are often referred to as "conserving theories", a consequence of this work is the demonstration that these two t-matrix approaches similarly can be made to obey all conservation laws. Moreover, simplifying approximations in $\Phi$-derivable theories, frequently lead to results which are incompatible with conservation.

12 pages, 1 figure

References in corpus (10)

• Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
• Nonrelativistic conformal field theories
• Thermodynamics of the BCS-BEC crossover
• Universal Quantum Viscosity in a Unitary Fermi Gas
• Kubo formulas for viscosity: Hall viscosity, Ward identities, and the relation with conductivity
• Viscosity and scale invariance in the unitary Fermi gas
• Shear viscosity of a superfluid Fermi gas in the unitarity limit
• Shear viscosity and damping for a Fermi gas in the unitarity limit
• Is a gas of strongly interacting atomic fermions a nearly perfect fluid?
• Microscopic Approach to Shear Viscosities in Superfluid Gases: From BCS to BEC

Cited by in corpus (9)

• Cuprate diamagnetism in the presence of a pseudogap: Beyond the standard fluctuation formalism
• Medium effects and the shear viscosity of the dilute Fermi gas away from the conformal limit
• Second order fluid dynamics for the unitary Fermi gas from kinetic theory
• Shear viscosity and Strong-Coupling Corrections in the BCS-BEC crossover Regime of an Ultracold Fermi Gas
• Establishing the Gauge Invariant Linear Response of Fermionic Superfluids with Pair Fluctuations: A Diagrammatic approach
• Shear Viscosity of Uniform Fermi Gases with Population Imbalance
• Conserving Approximation of Pairing theories in Fermionic superfluid phase
• Kovtun-Son-Starinets Conjecture and Effects of Mass Imbalance in the Normal State of an Ultracold Fermi Gas in the BCS-BEC Crossover Region
• Ward identities for charge and heat currents of particle-particle and particle-hole pairs