Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fermion picture for cellular automata   Many cellular automata admit an interpretation in terms of fermionic
particles. Reversible automata on space-lattices with a local updating rule can
be described by a partition function or Grassmann functional integral for
interacting fermions moving in this space. We discuss large classes of automata
that are equivalent to discretized fermionic quantum field theories with
various types of interactions. Two-dimensional models include relativistic
Thirring or Gross-Neveu type models with abelian or non-abelian continuous
global symmetries, a particle in a potential, local gauge symmetries, and
spinor gravity with local Lorentz symmetry as well as diffeomorphism invariance
in the (naive) continuum limit.
  Probabilistic cellular automata are characterized by a probability
distribution over initial bit-configurations. They can be described by the
quantum formalism with wave functions, density matrix and non-commuting
operators associated to observables. This formalism is useful for a discussion
of concepts as vacuum states, spontaneous symmetry breaking, coarse graining
and the continuum limit for probabilistic cellular automata. The formalism of
fermionic quantum field theories opens a new view on the statistical behavior
of automata with a very large number of cells. In the other direction, some
specific many body systems or discrete quantum field theories for fermions can
be understood by solving or simulating the associated probabilistic cellular
automaton. This opens a new access to non-equilibrium quantum field theory.

16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
2
The categories of this paper are: math
34
The categories of this paper are: chem-ph