545 research outputs found
A general formulation of discrete-time quantum mechanics, restrictions on the action and the relation of unitarity to the existence theorem for initial-value problems
A general formlulation for discrete-time quantum mechanics, based on
Feynman's method in ordinary quantum mechanics, is presented. It is shown that
the ambiguities present in ordinary quantum mechanics (due to noncommutativity
of the operators), are no longer present here. Then the criteria for the
unitarity of the evolution operator is examined. It is shown that the unitarity
of the evolution operator puts restrictions on the form of the action, and also
implies the existence of a solution for the classical initial-value problem.Comment: 13 pages, Te
Nonuniform autonomous one-dimensional exclusion nearest-neighbor reaction-diffusion models
The most general nonuniform reaction-diffusion models on a one-dimensional
lattice with boundaries, for which the time evolution equations of corre-
lation functions are closed, are considered. A transfer matrix method is used
to find the static solution. It is seen that this transfer matrix can be
obtained in a closed form, if the reaction rates satisfy certain conditions. We
call such models superautonomous. Possible static phase transitions of such
models are investigated. At the end, as an example of superau- tonomous models,
a nonuniform voter model is introduced, and solved explicitly.Comment: 14 page
-point functions of Yang-Mills theories on Riemann surfaces
Using the simple path integral method we calculate the -point functions of
field strength of Yang-Mills theories on arbitrary two-dimensional Riemann
surfaces. In case we show that the correlators consist of two parts , a
free and an -independent part. In the case of non-abelian semisimple compact
gauge groups we find the non-gauge invariant correlators in Schwinger-Fock
gauge and show that it is also divided to a free and an almost -independent
part. We also find the gauge-invariant Green functions and show that they
correspond to a free field theory.Comment: 8 pages,late
Derivation of theories: structures of the derived system in terms of those of the original system in classical mechanics
We present the technique of derivation of a theory to obtain an
-degrees-of-freedom theory from an -degrees-of-freedom theory and
show that one can calculate all of the quantities of the derived theory from
those of the original one. Specifically, we show that one can use this
technique to construct, from an integrable system, other integrable systems
with more degrees of freedom.Comment: LaTex, 10 page
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