142 research outputs found
Classification of constraints using chain by chain method
We introduce "chain by chain" method for constructing the constraint
structure of a system possessing both first and second class constraints. We
show that the whole constraints can be classified into completely irreducible
first or second class chains. We found appropriate redefinition of second class
constraints to obtain a symplectic algebra among them.Comment: 23 pages, to appear in Int. J. Mod. Phys.
phi-fourth model on a circle
The four dimensional critical scalar theory at equilibrium with a thermal
bath at temperature is considered. The thermal equilibrium state is labeled
by the winding number of the vacua around the compact imaginary-time
direction which compactification radius is 1/T. The effective action for zero
modes is a three dimensional scalar theory in which the mass of the
the scalar field is proportional to resembling the Kaluza-Klein
dimensional reduction. Similar results are obtained for the theory at zero
temperature but in a one-dimensional potential well. Since parity is violated
by the vacua with odd vacuum number , in such cases there is also a cubic
term in the effective potential. The -term contribution to the vacuum
shift at one-loop is of the same order of the contribution from the
-term in terms of the coupling constant of the four dimensional theory
but becomes negligible as tends to infinity. Finally, the relation between
the scalar classical vacua and the corresponding SU(2) instantons on
in the 't Hooft ansatz is studied.Comment: 9 pages, revtex4, to appear in Phys.Lett.
Abelian Subset of Second Class Constraints
We show that after mapping each element of a set of second class constraints
to the surface of the other ones, half of them form a subset of abelian first
class constraints. The explicit form of the map is obtained considering the
most general Poisson structure. We also introduce a proper redefinition of
second class constraints that makes their algebra symplectic.Comment: to appear in Phys. Lett.
Abelianization of First Class Constraints
We show that a given set of first class constraints becomes abelian if one
maps each constraint to the surface of other constraints. There is no
assumption that first class constraints satisfy a closed algebra. The explicit
form of the projection map is obtained at least for irreducible first class
constraints. Using this map we give a method to obtain gauge fixing conditions
such that the set of abelian first class constraints and gauge fixing
conditions satisfy the symplectic algebra.Comment: To appear in PL
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