public final class OneLoopInput extends Object
OneLoopCounterterms,
which performs the main calculation. The notation used for input matrices is
same as used in original works (see references in package info).
summary.
The main goal of this class is to prepare the hat-quantities
(\hat K, \hat W etc.) for further processing in OneLoopCounterterms.
All input expressions must be in the same notation as in the original works
(see references in package info) and
satisfy the following conditions:
(L - k) indices of each l.h.s. of expression are specified
to be 'covariant' indices, i.e. indices which are contracted with derivatives in
operator expansion. The rest 2n indices are the 'matrix' indices, i.e.
indices which are contracted with fields in the Lagrangian.F and iK must be
symmetric on their 'covariant' indices.R_{\mu\nu\alpha\beta} and
R_{\mu\nu} respectively.Look the OneLoopCounterterms description for the example of usage.
Note: Currently supported are not all arbitrary Lagrangians. There
is a full support of L = 2 and L = 4 theories with no odd on
the number of derivatives terms in the operator, so input tensors S^{...}_{...}
and N^{...}_{...} should be always zero. Also, input tensors should
have only Latin lowercase indices.
OneLoopCounterterms| Constructor and Description |
|---|
OneLoopInput(int operatorOrder,
cc.redberry.core.tensor.Expression iK,
cc.redberry.core.tensor.Expression K,
cc.redberry.core.tensor.Expression S,
cc.redberry.core.tensor.Expression W,
cc.redberry.core.tensor.Expression N,
cc.redberry.core.tensor.Expression M,
cc.redberry.core.tensor.Expression F)
Constructs the
OneLoopInput instance with specified operatorOrder
(i.e. |
OneLoopInput(int operatorOrder,
cc.redberry.core.tensor.Expression iK,
cc.redberry.core.tensor.Expression K,
cc.redberry.core.tensor.Expression S,
cc.redberry.core.tensor.Expression W,
cc.redberry.core.tensor.Expression N,
cc.redberry.core.tensor.Expression M,
cc.redberry.core.tensor.Expression F,
cc.redberry.core.transformations.Transformation[] riemannBackground)
Constructs the
OneLoopInput instance with specified operatorOrder
(i.e. |
| Modifier and Type | Method and Description |
|---|---|
cc.redberry.core.tensor.Expression |
getF() |
cc.redberry.core.tensor.Expression |
getHatF()
Returns \hat F^{...}_{..} expression
|
cc.redberry.core.tensor.Expression[] |
getHatQuantities(int k)
Return the array of hat-quantities according to their
position in the [HATK[],HATS[],HATW[], HATN[], HATM[]] array.
|
cc.redberry.core.tensor.Expression |
getInputParameter(int i)
Return i-th input expression from the [iK, K, S, W, N, M] array.
|
cc.redberry.core.tensor.Expression[] |
getKnQuantities()
Returns the array of Kn expressions.
|
cc.redberry.core.tensor.Expression |
getL()
Returns an operator order as expression
|
int |
getMatrixIndicesCount()
Returns the number of 'matrix' indices in the expressions
|
cc.redberry.core.tensor.Expression[] |
getNablaS() |
int |
getOperatorOrder()
Returns an operator order
|
cc.redberry.core.transformations.Transformation[] |
getRiemannBackground() |
public OneLoopInput(int operatorOrder,
cc.redberry.core.tensor.Expression iK,
cc.redberry.core.tensor.Expression K,
cc.redberry.core.tensor.Expression S,
cc.redberry.core.tensor.Expression W,
cc.redberry.core.tensor.Expression N,
cc.redberry.core.tensor.Expression M,
cc.redberry.core.tensor.Expression F)
OneLoopInput instance with specified operatorOrder
(i.e. L value) and input expressions. Input expressions must be in the
notation, discussed in the class summary.operatorOrder - the order of the differential operator in the
Lagrangian, i.e. the integer value of L.
Currently supported second and fourth order
operators.iK - inverse of Kn tensor. The input
expression should be in the form
iK^{...}_{...} = ....K - tensor K in the form K^{...}_{...} = .....S - tensor S. Since odd terms in operator expansion
is not supported yet, this tensor should be zeroed, so
the r.h.s. of the expression should be always zero:
S^{...}_{...} = 0.W - tensor W in the form W^{...}_{...} = .....N - tensor N. Since odd terms in operator expansion
is not supported yet, this tensor should be zeroed, so
the r.h.s. of the expression should be always zero:
N^{...}_{...} = 0. Note: if
operatorOrder = 2 this param should be null.M - tensor M in the form M^{...}_{...} = .....
Note: if operatorOrder = 2 this param
should be null .F - tensor F in the form F^{...}_{...} = .....IllegalArgumentException - if operatorOrder is not eqaul to 2 or 4IllegalArgumentException - if S or N are not zeroedIllegalArgumentException - if some of the input tensors have name different
from the specifiedIllegalArgumentException - if indices number of some of the input tensors
does not corresponds to the actual operatorOrderIllegalArgumentException - if indices of l.h.s. of input expressions contains non Latin lowercase indices.public OneLoopInput(int operatorOrder,
cc.redberry.core.tensor.Expression iK,
cc.redberry.core.tensor.Expression K,
cc.redberry.core.tensor.Expression S,
cc.redberry.core.tensor.Expression W,
cc.redberry.core.tensor.Expression N,
cc.redberry.core.tensor.Expression M,
cc.redberry.core.tensor.Expression F,
cc.redberry.core.transformations.Transformation[] riemannBackground)
OneLoopInput instance with specified operatorOrder
(i.e. L value), input expressions and riemann background rules. Input
expressions must be in the notation, discussed in the class summary. The Riemann
background is a number of transformations (usually substitutions) which defines the
additional rules for Riemann tensor processing. For example, it can be the anti de
Sitter background (OneLoopUtils.antiDeSitterBackground) or flat background
(with R_abcd = 0) and so on.operatorOrder - the order of the differential operator in the
Lagrangian, i.e. the integer value of L.
Currently supported second and fourth order
operators.iK - inverse tensors to tensor Kn. The input
expression should be in the form
iK^{...}_{...} = ....K - tensor K in the form K^{...}_{...} = .....S - tensor S. Since odd terms in operator expansion
is not supported yet, this tensor should be zeroed, so
the r.h.s. of the expression should be always zero:
S^{...}_{...} = 0.W - tensor W in the form W^{...}_{...} = .....N - tensor N. Since odd terms in operator expansion
is not supported yet, this tensor should be zeroed, so
the r.h.s. of the expression should be always zero:
N^{...}_{...} = 0. Note: if
operatorOrder = 2 this param should be null.M - tensor M in the form M^{...}_{...} = .....
Note: if operatorOrder = 2 this param
should be null .F - tensor F in the form F^{...}_{...} = .....riemannBackground - additional background conditions, such as anti de Sitter etc.
Empty array should be placed if no conditions specified.IllegalArgumentException - if operatorOrder is not eqaul to 2 or 4IllegalArgumentException - if S or N are not zeroedIllegalArgumentException - if some of the input tensors have name different
from the specifiedIllegalArgumentException - if indices number of some of the input tensors
does not corresponds to the actual operatorOrderIllegalArgumentException - if indices of l.h.s. of input expressions contains non Latin lowercase indices.OneLoopUtils.antiDeSitterBackground()public cc.redberry.core.tensor.Expression getInputParameter(int i)
i - position of the input expression in the array [iK, K, S, W, N, M]public cc.redberry.core.tensor.Expression[] getHatQuantities(int k)
k - position of the [HATK[],HATS[],HATW[], HATN[], HATM[]] arraypublic cc.redberry.core.tensor.Expression[] getKnQuantities()
public cc.redberry.core.tensor.Expression getHatF()
public cc.redberry.core.tensor.Expression getF()
public cc.redberry.core.tensor.Expression[] getNablaS()
public cc.redberry.core.tensor.Expression getL()
public int getMatrixIndicesCount()
public int getOperatorOrder()
public cc.redberry.core.transformations.Transformation[] getRiemannBackground()
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