Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Obtaining the Non-relativistic Quantum Mechanics from Quantum Field
  Theory: Issues, Folklores and Facts   Given the classical dynamics of a non-relativistic particle in terms of a
Hamiltonian or an action, it is relatively straightforward to obtain the
non-relativistic quantum mechanics (NRQM) of the system. These standard
procedures, based on either the Hamiltonian or the path integral, however, do
not work in the case of a relativistic particle. As a result we do not have a
single particle description of relativistic quantum mechanics (RQM). Instead,
the correct approach requires a transmutation of dynamical variables from the
position and momentum of a single particle to a field and its canonical
momentum. Particles, along with antiparticles, reappear in a very non-trivial
manner as the excitations of the field. The fact that one needs to adopt
completely different languages to describe relativistic and non-relativistic
free particle implies that obtaining the NRQM limit of QFT is conceptually
non-trivial. I examine this limit in several approaches (like, for e.g.,
Hamiltonian dynamics, Lagrangian and Hamiltonian path integrals, field
theoretic description etc.) and identify the precise issues which arise when
one attempts to obtain the NRQM from QFT in each of these approaches. The
dichotomy of description between NRQM and QFT does not originate just from the
square root in the Hamiltonian or from the demand of Lorentz invariance, as it
is sometimes claimed. The real difficulty has its origin in the necessary
existence of antiparticles to ensure a particular notion of relativistic
causality. Because of these conceptual issues, it turns out that one cannot, in
fact, obtain some of the popular descriptions of NRQM by any sensible limiting
procedure applied to QFT. To obtain NRQM from QFT in a seamless manner, it is
necessary to work with NRQM expressed in a language closer to that of QFT.
(Abridged)

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The categories of this paper are: dg-ga
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The categories of this paper are: mtrl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an
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The categories of this paper are: acc-phys
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The categories of this paper are: chem-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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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: nlin
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org