Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized S-matrix in Mixed Representations   A generalized scattering amplitude where momenta of incoming-particles and
outgoing-particles as well as positions of incoming-particles and
outgoing-particles are specified is formulated. Idealistic beams and idealistic
measuring instruments where momenta and positions satisfy minimum uncertainty
are studied with a use of minimum wave packets, coherent states. In the present
work, we show general features of the generalized scattering amplitudes based
on ${\phi}^4$ theory. We give a proof of completeness of many body states,
asymptotic behaviors in the large distance region, and factorization of the
amplitudes. Despite of the non-orthogonal properties of wave packets, we found
that the probability interpretation is verified. A differential probability
depends upon the wave packet size but a total probability that is integrated in
the final states is independent from the size of final state wave packet and
becomes universal. Few body amplitudes are studied as examples.

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The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
2
The categories of this paper are: math
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex