Abstract
We investigate a Wilson real space renormalization gorup approach for theories in which composite fields are needed at low energies. It furnishes a sequence of effective actions S{sub {Lambda}} which depend on an UV cut-off {Lambda}. We adopt Wilsons fundamental postulate that these effective actions should be local. This is our basic guiding principle on how to construct ``blockspins``, i.e. the fields which appear in the effective actions. Given a fundamental high energy theory which does not contain composite fields we gradually integrate out high frequency modes in order to lower the cut-off {Lambda}. Eventually appearing nonlocalities at some cut-off value {Lambda}{sub c} indicate the necessity to introduce new composite degrees of freedom into the theory. An analysis based on Symanzik`s infinite set of Bethe-Salpeter equations for all n-point functions shows that a local low energy effective action containing composite fields can be constructed at the compositeness scale {Lambda}{sub c}. Further integration of high frequency modes generates new nonlocalities which can be absorbed into the composite degrees of freedom. There are indications from an 1/N expansion that this suffices already to eliminate high energy degrees of freedom from the composite field so that no separate integration is needed to achieve
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Grabowski, M
[1]
- Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik
Citation Formats
Grabowski, M.
Low energy effective actions with composite fields.
Germany: N. p.,
1994.
Web.
Grabowski, M.
Low energy effective actions with composite fields.
Germany.
Grabowski, M.
1994.
"Low energy effective actions with composite fields."
Germany.
@misc{etde_10121449,
title = {Low energy effective actions with composite fields}
author = {Grabowski, M}
abstractNote = {We investigate a Wilson real space renormalization gorup approach for theories in which composite fields are needed at low energies. It furnishes a sequence of effective actions S{sub {Lambda}} which depend on an UV cut-off {Lambda}. We adopt Wilsons fundamental postulate that these effective actions should be local. This is our basic guiding principle on how to construct ``blockspins``, i.e. the fields which appear in the effective actions. Given a fundamental high energy theory which does not contain composite fields we gradually integrate out high frequency modes in order to lower the cut-off {Lambda}. Eventually appearing nonlocalities at some cut-off value {Lambda}{sub c} indicate the necessity to introduce new composite degrees of freedom into the theory. An analysis based on Symanzik`s infinite set of Bethe-Salpeter equations for all n-point functions shows that a local low energy effective action containing composite fields can be constructed at the compositeness scale {Lambda}{sub c}. Further integration of high frequency modes generates new nonlocalities which can be absorbed into the composite degrees of freedom. There are indications from an 1/N expansion that this suffices already to eliminate high energy degrees of freedom from the composite field so that no separate integration is needed to achieve this. In general the composite field will have self interactions. (orig.)}
place = {Germany}
year = {1994}
month = {Aug}
}
title = {Low energy effective actions with composite fields}
author = {Grabowski, M}
abstractNote = {We investigate a Wilson real space renormalization gorup approach for theories in which composite fields are needed at low energies. It furnishes a sequence of effective actions S{sub {Lambda}} which depend on an UV cut-off {Lambda}. We adopt Wilsons fundamental postulate that these effective actions should be local. This is our basic guiding principle on how to construct ``blockspins``, i.e. the fields which appear in the effective actions. Given a fundamental high energy theory which does not contain composite fields we gradually integrate out high frequency modes in order to lower the cut-off {Lambda}. Eventually appearing nonlocalities at some cut-off value {Lambda}{sub c} indicate the necessity to introduce new composite degrees of freedom into the theory. An analysis based on Symanzik`s infinite set of Bethe-Salpeter equations for all n-point functions shows that a local low energy effective action containing composite fields can be constructed at the compositeness scale {Lambda}{sub c}. Further integration of high frequency modes generates new nonlocalities which can be absorbed into the composite degrees of freedom. There are indications from an 1/N expansion that this suffices already to eliminate high energy degrees of freedom from the composite field so that no separate integration is needed to achieve this. In general the composite field will have self interactions. (orig.)}
place = {Germany}
year = {1994}
month = {Aug}
}