Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Framework for Systematic Study of QCD Vacuum Structure I: Kolmogorov
  Entropy and the Principle of Chiral Ordering   In this series of articles we describe a systematic approach to studying QCD
vacuum structure using the methods of lattice gauge theory. Our framework
incorporates four major components. (i) The recently established existence of
space-time order at all scales (fundamental structure) observed directly in
typical configurations of regularized path-integral ensembles. (ii) The notion
of scale-dependent vacuum structure (effective structure) providing the means
for representing and quantifying the influence of fluctuations at various
scales on physical observables (phenomena). (iii) The unified description of
gauge and fermionic aspects of the theory which facilitates a high level of
space-time order in the path-integral ensembles. (iv) The strict ``Bottom-Up''
approach wherein the process of identifying the vacuum structure proceeds
inductively, using the information from valid lattice QCD ensembles as the only
input. In this work we first elaborate on the meaning of the notion of
space-time order in a given configuration which is conceptually at the heart of
the path-integral approach to vacuum structure. It is argued that the
algorithmic complexity of binary strings associated with coarse-grained
descriptions of the configuration provides a relevant quantitative measure. The
corresponding ensemble averages define the ranking of different lattice
theories at given cutoff by the degree of space-time order generated via their
dynamics. We then introduce the set of local transformations of a
configuration, chiral orderings, in which the transformed gauge connection
represents an effective matrix phase acquired by chiral fermion when hopping
over a given link. It is proposed that chiral orderings facilitate the
evolution in the set of actions which increases the degree of space-time order
while preserving the physical content of the theory, and should thus be used in
the search for the fundamental QCD vacuum structure. The relation to
renormalization group ideas is discussed, and the first step in general
formulation of effective lattice QCD realizing the notion of scale-dependent
vacuum structure is given.

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The categories of this paper are: solv-int
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex
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The categories of this paper are: q-bio
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The categories of this paper are: eess
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The categories of this paper are: math
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The categories of this paper are: ao-sci
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The categories of this paper are: astro-ph
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The categories of this paper are: physics
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The categories of this paper are: econ
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The categories of this paper are: q-fin
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The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: quant-ph