cc.redberry.physics.oneloopdiv

Class OneLoopInput

java.lang.Object

cc.redberry.physics.oneloopdiv.OneLoopInput

public final class OneLoopInput
extends java.lang.Object

This class is a container of input parameters for one-loop counterterms calculation. It is always used in conjunction with 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.h.s of input expressions should have only Latin lowercase indices
• Each l.h.s tensor should have string name defind by the following rules: tensor iK - "iK", tensor K - "K", tensor S - "S", tensor W - "W", tensor N - "N", tensor F - "F".
• The first (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.
• Each of the input tensors, except F and iK must be symmetric on their 'covariant' indices.
• The Riemann and Ricci tensors identified as R_{\mu\nu\alpha\beta} and R_{\mu\nu} respectively.

If the symmetries of the Riemann or Ricci tensors are not set up, it will be done automatically.

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.

Since:

1.0

See Also:

OneLoopCounterterms

Constructor Summary

Constructors

Constructor and Description
OneLoopInput(int operatorOrder, Expression iK, Expression K, Expression S, Expression W, Expression N, Expression M, Expression F) Constructs the OneLoopInput instance with specified operatorOrder (i.e.
OneLoopInput(int operatorOrder, Expression iK, Expression K, Expression S, Expression W, Expression N, Expression M, Expression F, Transformation[] riemannBackground) Constructs the OneLoopInput instance with specified operatorOrder (i.e.

Method Summary

Modifier and Type	Method and Description
Expression	getF()
Expression	getHatF() Returns \hat F^{...}_{..} expression
Expression[]	getHatQuantities(int k) Return the array of hat-quantities according to their position in the [HATK[],HATS[],HATW[], HATN[], HATM[]] array.
Expression	getInputParameter(int i) Return i-th input expression from the [iK, K, S, W, N, M] array.
Expression[]	getKnQuantities() Returns the array of Kn expressions.
Expression	getL() Returns an operator order as expression
int	getMatrixIndicesCount() Returns the number of 'matrix' indices in the expressions
Expression[]	getNablaS()
int	getOperatorOrder() Returns an operator order
Transformation[]	getRiemannBackground()

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

OneLoopInput

public OneLoopInput(int operatorOrder,
                    Expression iK,
                    Expression K,
                    Expression S,
                    Expression W,
                    Expression N,
                    Expression M,
                    Expression F)

Constructs the OneLoopInput instance with specified operatorOrder (i.e. L value) and input expressions. Input expressions must be in the notation, discussed in the class summary.

Parameters:

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^{...}_{...} = .....

Throws:

java.lang.IllegalArgumentException - if operatorOrder is not eqaul to 2 or 4

java.lang.IllegalArgumentException - if S or N are not zeroed

java.lang.IllegalArgumentException - if some of the input tensors have name different from the specified

java.lang.IllegalArgumentException - if indices number of some of the input tensors does not corresponds to the actual operatorOrder

java.lang.IllegalArgumentException - if indices of l.h.s. of input expressions contains non Latin lowercase indices.

OneLoopInput

public OneLoopInput(int operatorOrder,
                    Expression iK,
                    Expression K,
                    Expression S,
                    Expression W,
                    Expression N,
                    Expression M,
                    Expression F,
                    Transformation[] riemannBackground)

Constructs the 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.

Parameters:

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.

Throws:

java.lang.IllegalArgumentException - if operatorOrder is not eqaul to 2 or 4

java.lang.IllegalArgumentException - if S or N are not zeroed

java.lang.IllegalArgumentException - if some of the input tensors have name different from the specified

java.lang.IllegalArgumentException - if indices number of some of the input tensors does not corresponds to the actual operatorOrder

java.lang.IllegalArgumentException - if indices of l.h.s. of input expressions contains non Latin lowercase indices.

See Also:

OneLoopUtils.antiDeSitterBackground()

Method Detail

getInputParameter

public Expression getInputParameter(int i)

Return i-th input expression from the [iK, K, S, W, N, M] array.

Parameters:

i - position of the input expression in the array [iK, K, S, W, N, M]

Returns:

i-th expression from the [iK, K, S, W, N, M] array

getHatQuantities

public Expression[] getHatQuantities(int k)

Return the array of hat-quantities according to their position in the [HATK[],HATS[],HATW[], HATN[], HATM[]] array.

Parameters:

k - position of the [HATK[],HATS[],HATW[], HATN[], HATM[]] array

Returns:

k-th array from [HATK[],HATS[],HATW[], HATN[], HATM[]]

getKnQuantities

public Expression[] getKnQuantities()

Returns the array of Kn expressions.

Returns:

array of Kn expressions

getHatF

public Expression getHatF()

Returns \hat F^{...}_{..} expression

Returns:

\hat F^{...}_{..} expression

getF

public Expression getF()

getNablaS

public Expression[] getNablaS()

getL

public Expression getL()

Returns an operator order as expression

Returns:

operator order as expression

getMatrixIndicesCount

public int getMatrixIndicesCount()

Returns the number of 'matrix' indices in the expressions

Returns:

number of 'matrix' indices in the expressions

getOperatorOrder

public int getOperatorOrder()

Returns an operator order

Returns:

operator order

getRiemannBackground

public Transformation[] getRiemannBackground()