Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Problems With Complex Actions   We consider Euclidean functional integrals involving actions which are not
exclusively real. This situation arises, for example, when there are $t$-odd
terms in the the Minkowski action. Writing the action in terms of only real
fields (which is always possible), such terms appear as explicitly imaginary
terms in the Euclidean action. The usual quanization procedure which involves
finding the critical points of the action and then quantizing the spectrum of
fluctuations about these critical points fails. In the case of complex actions,
there do not exist, in general, any critical points of the action on the space
of real fields, the critical points are in general complex. The proper
definition of the function integral then requires the analytic continuation of
the functional integration into the space of complex fields so as to pass
through the complex critical points according to the method of steepest
descent. We show a simple example where this procedure can be carried out
explicitly. The procedure of finding the critical points of the real part of
the action and quantizing the corresponding fluctuations, treating the
(exponential of the) complex part of the action as a bounded integrable
function is shown to fail in our explicit example, at least perturbatively.

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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ph
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The categories of this paper are: atom-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: q-bio
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
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The categories of this paper are: cs
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The categories of this paper are: adap-org
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The categories of this paper are: eess
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ex