atlas[`&L`] - Hodge-de Rham Laplacian operator 

Calling Sequence: 

    &L(expr) 

Parameters: 

    expr - any expression. 

Description: 

• The &L - procedure allows one to calculate the Hodge-de Rham Laplacian on an expression that is p-form.

 

• The Hodge-de Rham Laplacian is the operator  : ->  where and are p-forms which are defined as follows:

 

• If is  a p-form then, where δ is the codifferential (see atlas[`&d`]).

 

Examples: 

>	restart: with(atlas):

 

>	Constants(n);

 

(2.1)

 

Declare p-forms:  

>	Forms(omega=n);

 

(2.2)

 

Using d- procedure: 

- declared as a p-form so we have:
'Delta(omega)'=&L(omega);
 

(2.3)

 

>

 

See Also:  

atlas, atlas[Constants], atlas[Functions], atlas[Forms], atlas[`&^`],  atlas[`&**`], atlas[d], atlas[`&d`].