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In typing of an article, I need to type many formulas like

$ left( a, b,c,d | e,f,g,h right) $.

Since they are too tight, I should add space using , command to obtain

$ left( a, , b, , c, , d | e, , f, , g, , h right) $.

But my problem is there are too many of such formulas. Is there any command which changes the default spacing between characters in the math mode?

Assuming you don't need the thing in subscripts or superscripts, the easiest way is to exit from math mode, doubling the thinmuskip, reentering math mode, typesetting the lists and go back.

documentclassarticle
usepackageamsmath

newcommandcls[2]%
 mathordmbox%
 thinmuskip=2thinmuskip
 $(#1mid#2)$%
 %


begindocument

$( a, b,c,d mid e,f,g,h)$

$(a,, b,, c,, d mid e,, f,, g,, h)$

$clsa,b,c,de,f,g,h$

enddocument

A different solution that allows for resizing the parentheses as usual for commands defined with DeclarePairedDelimiter, see the examples. It also has a friendlier syntax.

documentclassarticle
usepackageamsmath
usepackagexparse

AtBeginDocumentmathchardefclscomma=mathcode`, 

ExplSyntaxOn
NewDocumentCommandclssom
 
 group_begin:
 IfBooleanTF#1
 
 hs_cls_auto:n #3 
 
 
 hs_cls_manual:nn #2 #3 
 
 group_end:
 

cs_new_protected:Nn hs_cls_auto:n
 
 __hs_cls_activate_comma:
 __hs_cls_activate_bar:n ;middlevert; 
 left( #1 right)
 

cs_new_protected:Nn hs_cls_manual:nn
 
 __hs_cls_activate_comma:
 __hs_cls_activate_bar:n __hs_cls_mid:n #1 
 __hs_cls_open:n #1 #2 __hs_cls_close:n #1
 

cs_new_protected:Nn __hs_cls_activate_comma:
 
 char_set_active_eq:nN `, __hs_cls_comma:
 mathcode`,="8000 scan_stop:
 

cs_new_protected:Nn __hs_cls_comma: clscomma, 

cs_new_protected:Nn __hs_cls_activate_bar:n
 
 cs_set_protected:Nn __hs_cls_bar: #1 
 char_set_active_eq:nN ` __hs_cls_bar:
 mathcode`

cs_new_protected:Nn __hs_cls_open:n
 
 tl_if_novalue:nTF #1 ( mathopen#1( 
 
cs_new_protected:Nn __hs_cls_mid:n
 
 tl_if_novalue:nTF #1 mid mathrel#1vert 
 
cs_new_protected:Nn __hs_cls_close:n
 
 tl_if_novalue:nTF #1 ) mathclose#1) 
 
ExplSyntaxOff

begindocument

$( a, b,c,d mid e,f,g,h)$

$(a,, b,, c,, d mid e,, f,, g,, h)$

$clsa,b,c,d$

$cls[Big]a,b,c,d$

$cls*dfraca2,b,c,d$

enddocument

You can process each of the two lists (left and right) using etoolbox and a cunning delimiter trick:

documentclassarticle

usepackageetoolbox

% https://tex.stackexchange.com/a/89187/5764
newcommandprintlist[2][,]%
 defitemdelimdefitemdelim#1% Item delimiter delayed by one cycle
 renewcommand*do[1]itemdelim##1% How each item is processed
 docsvlist#2% Process CSV list

makeatletter
def@LandR#1|#2relaxdefleftlist#1defrightlist#2%
defLandR#1%
 @LandR#1relax
 left( % Left bracket
 edefxnoexpandprintlist[,,]leftlistx
 ,middle
makeatother

begindocument

$left( a, b, c, d | e, f, g, h right)$

$LandRa, b, c, d $

enddocument

Each list is printed using printlist[,,], which adds a small space , after each delimiter ,. You can adjust the layout of the left/right bracket and middle divider.

If you wish to include larger constructions, you may need to use noexpand, as in

LandRnoexpandfracab, c, d, e