IndexType

Description

IndexType represents a type of a single index. It encodes mathematical nature of indices with different types (e.g. Lorentz, SU(N) etc.). One can print all available index types as follows: 

println IndexType.values()

   > [LatinLower, LatinUpper, GreekLower, GreekUpper, Matrix1, Matrix2, 
      Matrix3, Matrix4]

If two indices have different types, then they have different mathematical nature. Thus, for example, two tensors f_ab and f_AB have different mathematical nature and one can not rename indices of tensor f_ab to _AB. This, in turn, enables us to associate different space dimensions with different index types: 

//dimension for Latin lower case indices
def dimLower = 'd^a_a = X'.t
//dimension for Latin upper case indices
def dimUpper = 'd^A_A = Y'.t
//expression contains both lower and upper case indices
def t = 'g_ab*g^ab + g_AB*g^AB'.t
t = (EliminateMetrics & dimLower & dimUpper) >> t
println t

   > X + Y
By default, all types except Matrix are metric, and a corresponding metric tensor is set up (g_ab for LatinLower, g_\\alpha\\beta for Greek lower etc.).

In order to obtain IndexType of a particular index one can use .type property; in order to check whether IndexType is metric, one can use isMetric() method: 

def indices = '''_{a}^{A \\alpha}_{a'} '''.si
println indices.collect { [[type: it.type, metric: it.type.isMetric()]] }

   > [[[type:LatinLower, metric:true]], [[type:LatinUpper, metric:true]], 
        [[type:GreekLower, metric:true]], [[type:Matrix1, metric:false]]]

Available types

The possible values of IndexType are:

IndexType Description
LatinLower Latin lower case indices from a to z and subscripted like a_{12} etc.
LatinUpper Latin upper case indices from A to Z and subscripted like X_{12} etc.
GreekLower Greek lower case indices like \\alpha, \\theta and subscripted like \\rho_{123} etc.
GreekUpper Greek upper case indices like \\Lambda, \\Theta and subscripted like \\Psi_{123} etc. Note, that some letters are excluded since they have same UTF8 representation as Latin letters (e.g. capital alpha to beta).
Matrix1 Latin lower case indices with strokes from a' to z' and subscripted like a'_{12} etc.
Matrix2 Latin upper case indices with strokes like A' or E'_{12}.
Matrix3 Greek lower case indices with strokes like \\alpha' or \\theta'_{12}.
Matrix4 Greek upper case indices with strokes like \\Lambda' or \\Psi'_{12}.

By default all Matrix index types are used for matrix indices and there is no metric specified for indices of Matrix types.

See also