Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Collective fields in the functional renormalization group for fermions,
  Ward identities, and the exact solution of the Tomonaga-Luttinger model   We develop a new formulation of the functional renormalization group (RG) for
interacting fermions. Our approach unifies the purely fermionic formulation
based on the Grassmannian functional integral, which has been used in recent
years by many authors, with the traditional Wilsonian RG approach to quantum
systems pioneered by Hertz [Phys. Rev. B 14, 1165 (1976)], which attempts to
describe the infrared behavior of the system in terms of an effective bosonic
theory associated with the soft modes of the underlying fermionic problem. In
our approach, we decouple the interaction by means of a suitable
Hubbard-Stratonovich transformation (following the Hertz-approach), but do not
eliminate the fermions; instead, we derive an exact hierarchy of RG flow
equations for the irreducible vertices of the resulting coupled field theory
involving both fermionic and bosonic fields. The freedom of choosing a momentum
transfer cutoff for the bosonic soft modes in addition to the usual band cutoff
for the fermions opens the possibility of new RG schemes. In particular, we
show how the exact solution of the Tomonaga-Luttinger model emerges from the
functional RG if one works with a momentum transfer cutoff. Then the Ward
identities associated with the local particle conservation at each Fermi point
are valid at every stage of the RG flow and provide a solution of an infinite
hierarchy of flow equations for the irreducible vertices. The RG flow equation
for the irreducible single-particle self-energy can then be closed and can be
reduced to a linear integro-differential equation, the solution of which yields
the result familiar from bosonization. We suggest new truncation schemes of the
exact hierarchy of flow equations, which might be useful even outside the weak
coupling regime.

23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
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The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
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The categories of this paper are: adap-org