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Cell[CellGroupData[{
Cell["Gauge transformations of the Maxwell equations", "Subtitle"],

Cell[TextData[StyleBox["doug <sweetser@world.com>"]], "Subsubtitle"],

Cell["\<\
Introduction
A quaternion gauge transformation
Implications\
\>", "Text"],

Cell[CellGroupData[{

Cell[TextData[StyleBox["Introduction"]], "Subsection",
  CellMargins->{{0, Inherited}, {Inherited, Inherited}}],

Cell["\<\
A gauge defines how one measures the electromagnetic 4-potential, \
phi and A.  Within limitations, one is free to choose a standard for the \
4-potential.  For example, if one decides that the divergence of A should \
always be zero, this is called choosing the Coulomb gauge.  Gauge \
transformations are a very powerful technique for solving practical problems. \
 Gauge symmetry also has profound implications theoretically, particularly \
for quantum field theory.  Spacetime-dependent gauge symmetry leads to the \
gauge fields that form the symmetry of the forces in the standard model, \
U(1)xSU(2)xSU(3).  \
\>", "Text"],

Cell[TextData[StyleBox[
"In this notebook, I will explore gauge transformations with quaternions.  \
This work suggests two types of constraints on those transformations.  The \
first is the continuity equation for the scalar field.  The second is a \
\"continuity-like\" equation for the vector field.  This second constraint is \
relevant only under relativistic conditions."]], "Text"]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[StyleBox[" A quaternion gauge transformation"]], "Subsection",
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Cell["\<\
The E and B fields can be generated from the 4-potential phi and A \
with the following quaternion equation:\
\>", "Text"],

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Cell["\<\
The vector term is B - E.  The scalar term has the form of a gauge \
relation.  The typical scalar field used in a gauge transformation involves \
the gradient and the time derivative of the scalar field.  For a quaternion \
field, there is also a 3-vector component.  Consider the analogous quaternion \
field L (small \"g\" is a scalar field, and big \"G\" is a 3-vector field).\
\
\>", "Text"],

Cell[BoxData[
    \(L = {
        \(g'\)[t] + \ 
          \[EmptyDownTriangle]\&\[RightVector]\[CenterDot]G\&\[RightVector][
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              \[EmptyDownTriangle]\&\[RightVector]\[InvisibleComma] g[t])
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Cell["\<\
The terms with the small g are the typical scalar field gauge transformation. \
 The terms with the big G are my guess at a reasonable extension from a \
scalar to a quaternion field.  Big G is handled in a manner that parallels \
small g, namely there is a time derivative and del operation that transforms \
vector big G into the scalar div G, just like scalar small g was transformed \
to vector Grad g.  Transform the quaternion potential with L.\
\>", "Text"],

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            \[EmptyDownTriangle]\&\[RightVector]\[CenterDot]A
                \&\[RightVector]\  + \[PartialD]\^2 g\/\[PartialD]t\^2 + \ 
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Cell["\<\
An equation should not be altered by a gauge transformation, but \
that does not appear to be the case with the quaternion field L at first \
glance!  There are 5 extra terms here (one of the extra terms, curl grad g, \
is always zero).\
\>", "Text"],

Cell["\<\
The two extra scalar terms must always add up to zero.  These terms \
involve the time derivative of a scalar and the divergence of a vector.  That \
sounds like the continuity equation, so test out the following mapping: grad \
g -> J, dg/dt -> rho.\
\>", "Text"],

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Cell["\<\
This is the continuity equation.  It is noteworthy that the \
continuity equation arises naturally from an analysis of a quaternion gauge \
transformation.  The J must be irrotational (Curl J = Curl Grad g = 0).  This \
may be due to my choice for big G which lacked a curl, but I am uncertain on \
this point.\
\>", "Text"],

Cell["\<\
What about the three vector terms?  They reform the vector \
potential with the following mapping.\
\>", "Text"],

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Cell["\<\
This mapping proposes that the a gauge transformation will be valid \
only if B - E = 0.  In some sense, this is like a continuity equation for the \
vector field big G.  The time rate of change of A must balance the gradient \
phi and the curl of A, which all can be expressed in terms of the same vector \
field big G.  This is a new constraint, but it neatly parallels the scalar \
continuity equation, which applied only to the scalar field g with the \
mapping discussed here.\
\>", "Text"]
}, Open  ]],

Cell[CellGroupData[{

Cell["Implications", "Subsection",
  CellMargins->{{0, Inherited}, {Inherited, Inherited}}],

Cell["\<\
Every constraint has regions where is is applicable.  Newtonian \
physics works until the speed of light is approached.  Classical atomic \
physics works until the number of particles gets small.  The vector gauge \
continuity constraint is not relevant for classical electrodynamics.  The \
classical region of spacetime happens for intervals where\
\>", "Text"],

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Cell["An analogous region for a gauge transformation is", "Text"],

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Cell["In this region, the gauge transformation then simplifies to", "Text"],

Cell[BoxData[{
    \(\[Phi]\  -> \ \[Phi]'\  = \ 
      \[Phi]\  - \ \[PartialD]g[t]\/\[PartialD]t\), 
    \(A\  -> \ A'\  = \ A\  + \ \[EmptyDownTriangle]\&\[RightVector]\ g\)}], 
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Cell["\<\
This is precisely the type of transformation that has been used so \
often before, and it is still part of the quaternion formulation of the \
Maxwell equations in the classical domain.\
\>", "Text"],

Cell["\<\
The question now concerns the validity of gauge freedom of the \
Maxwell equations under relativistic conditions, a cornerstone of quantum \
field theory.  I prefer to constrain the vector portion of gauge \
transformations under relativistic conditions with a continuity equation for \
the vector field that has symmetry with the scalar continuity equation.  This \
may help avoid the difficulties of regularization and renomalization, but \
that issue needs more investigation.\
\>", "Text"]
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    CounterAssignments->{{"Subsection", 0}, {"Subsubsection", 0}},
    AspectRatioFixed->True,
    FontFamily->"Times New Roman",
    FontSize->18,
    FontWeight->"Bold",
    FontVariations->{"Underline"->True}],
  
  Cell[StyleData["Section", "Presentation"],
    CellMargins->{{40, 10}, {11, 32}},
    LineSpacing->{1, 0},
    FontFamily->"Times New Roman",
    FontSize->24],
  
  Cell[StyleData["Section", "Condensed"],
    CellMargins->{{18, Inherited}, {6, 12}},
    FontFamily->"Times New Roman",
    FontSize->12],
  
  Cell[StyleData["Section", "Printout"],
    CellMargins->{{13, 0}, {7, 22}},
    FontFamily->"Times New Roman",
    FontSize->14]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Subsection"],
    CellDingbat->"\[FilledSquare]",
    CellMargins->{{19, Inherited}, {8, 15}},
    Evaluatable->False,
    CellGroupingRules->{"SectionGrouping", 40},
    CellHorizontalScrolling->False,
    PageBreakBelow->False,
    CounterIncrements->"Subsection",
    CounterAssignments->{{"Subsubsection", 0}},
    AspectRatioFixed->True,
    FontFamily->"Times New Roman",
    FontSize->14,
    FontWeight->"Bold"],
  
  Cell[StyleData["Subsection", "Presentation"],
    CellMargins->{{36, 10}, {11, 32}},
    LineSpacing->{1, 0},
    FontFamily->"Times New Roman",
    FontSize->22],
  
  Cell[StyleData["Subsection", "Condensed"],
    CellMargins->{{16, Inherited}, {6, 12}},
    FontFamily->"Times New Roman",
    FontSize->12],
  
  Cell[StyleData["Subsection", "Printout"],
    CellMargins->{{9, 0}, {7, 22}},
    FontFamily->"Times New Roman",
    FontSize->12]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Subsubsection"],
    CellDingbat->"\[EmptySquare]",
    CellMargins->{{18, Inherited}, {8, 12}},
    Evaluatable->False,
    CellGroupingRules->{"SectionGrouping", 50},
    CellHorizontalScrolling->False,
    PageBreakBelow->False,
    CounterIncrements->"Subsubsection",
    AspectRatioFixed->True,
    FontFamily->"Times New Roman",
    FontSize->12,
    FontWeight->"Bold"],
  
  Cell[StyleData["Subsubsection", "Presentation"],
    CellMargins->{{34, 10}, {11, 26}},
    LineSpacing->{1, 0},
    FontFamily->"Times New Roman",
    FontSize->18],
  
  Cell[StyleData["Subsubsection", "Condensed"],
    CellMargins->{{17, Inherited}, {6, 12}},
    FontFamily->"Times New Roman",
    FontSize->10],
  
  Cell[StyleData["Subsubsection", "Printout"],
    CellMargins->{{9, 0}, {7, 14}},
    FontFamily->"Times New Roman",
    FontSize->11]
  }, Closed]]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[TextData[StyleBox["Styles for Body Text"]], "Section",
    FontFamily->"Times New Roman"],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Text"],
    CellMargins->{{7, 10}, {7, 7}},
    Evaluatable->False,
    CellHorizontalScrolling->False,
    PageBreakWithin->Automatic,
    LineSpacing->{1, 3},
    CounterIncrements->"Text",
    AspectRatioFixed->True,
    FontFamily->"Times New Roman",
    FontSize->12],
  
  Cell[StyleData["Text", "Presentation"],
    CellMargins->{{24, 10}, {10, 10}},
    LineSpacing->{1, 5},
    FontFamily->"Times New Roman"],
  
  Cell[StyleData["Text", "Condensed"],
    CellMargins->{{8, 10}, {6, 6}},
    LineSpacing->{1, 1},
    FontFamily->"Times New Roman"],
  
  Cell[StyleData["Text", "Printout"],
    CellMargins->{{2, 2}, {6, 6}},
    FontFamily->"Times New Roman"]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["SmallText"],
    CellMargins->{{7, 10}, {6, 6}},
    Evaluatable->False,
    CellHorizontalScrolling->False,
    PageBreakWithin->Automatic,
    LineSpacing->{1, 3},
    CounterIncrements->"SmallText",
    AspectRatioFixed->True,
    FontFamily->"Times New Roman",
    FontSize->10],
  
  Cell[StyleData["SmallText", "Presentation"],
    CellMargins->{{24, 10}, {8, 8}},
    LineSpacing->{1, 5},
    FontFamily->"Times New Roman",
    FontSize->12],
  
  Cell[StyleData["SmallText", "Condensed"],
    CellMargins->{{8, 10}, {5, 5}},
    LineSpacing->{1, 2},
    FontFamily->"Times New Roman",
    FontSize->9],
  
  Cell[StyleData["SmallText", "Printout"],
    CellMargins->{{2, 2}, {5, 5}},
    FontFamily->"Times New Roman",
    FontSize->7]
  }, Closed]]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[TextData[StyleBox["Styles for Input/Output"]], "Section",
    FontFamily->"Courier",
    FontSize->14,
    FontWeight->"Plain"],
  
  Cell[TextData[StyleBox[
  "The cells in this section define styles used for input and output to the \
kernel.  Be careful when modifying, renaming, or removing these styles, \
because the front end associates special meanings with these style names."]], 
    "Text",
    FontFamily->"Courier",
    FontSize->14],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Input"],
    PageWidth->Infinity,
    CellMargins->{{42, 10}, {5, 7}},
    Evaluatable->True,
    CellGroupingRules->"InputGrouping",
    CellHorizontalScrolling->True,
    PageBreakWithin->False,
    GroupPageBreakWithin->False,
    CellLabelMargins->{{23, Inherited}, {Inherited, Inherited}},
    DefaultFormatType->DefaultInputFormatType,
    LineSpacing->{1, 0},
    AutoItalicWords->{},
    FormatType->InputForm,
    ShowStringCharacters->True,
    NumberMarks->True,
    CounterIncrements->"Input",
    AspectRatioFixed->True,
    FontFamily->"Courier",
    FontSize->14,
    FontWeight->"Plain",
    FontSlant->"Plain",
    FontTracking->"Plain",
    FontVariations->{"Underline"->False,
    "Outline"->False,
    "Shadow"->False}],
  
  Cell[StyleData["Input", "Presentation"],
    CellMargins->{{72, Inherited}, {8, 10}},
    LineSpacing->{1, 0},
    FontFamily->"Courier",
    FontSize->14,
    FontWeight->"Plain"],
  
  Cell[StyleData["Input", "Condensed"],
    CellMargins->{{40, 10}, {2, 3}},
    FontFamily->"Courier",
    FontSize->14,
    FontWeight->"Plain"],
  
  Cell[StyleData["Input", "Printout"],
    CellMargins->{{39, 0}, {4, 6}},
    FontFamily->"Courier",
    FontSize->14,
    FontWeight->"Plain"]
  }, Closed]],
  
  Cell[StyleData["InputOnly"],
    Evaluatable->True,
    CellGroupingRules->"InputGrouping",
    CellHorizontalScrolling->True,
    DefaultFormatType->DefaultInputFormatType,
    AutoItalicWords->{},
    FormatType->InputForm,
    ShowStringCharacters->True,
    NumberMarks->True,
    CounterIncrements->"Input",
    StyleMenuListing->None,
    FontFamily->"Courier",
    FontSize->14,
    FontWeight->"Plain",
    FontSlant->"Plain",
    FontTracking->"Plain",
    FontVariations->{"Underline"->False,
    "Outline"->False,
    "Shadow"->False}],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Output"],
    PageWidth->Infinity,
    CellMargins->{{42, 10}, {7, 5}},
    CellEditDuplicate->True,
    Evaluatable->False,
    CellGroupingRules->"OutputGrouping",
    CellHorizontalScrolling->True,
    PageBreakWithin->False,
    GroupPageBreakWithin->False,
    GeneratedCell->True,
    CellAutoOverwrite->True,
    CellLabelMargins->{{23, Inherited}, {Inherited, Inherited}},
    DefaultFormatType->DefaultOutputFormatType,
    LineSpacing->{1, 0},
    AutoItalicWords->{},
    FormatType->InputForm,
    CounterIncrements->"Output",
    AspectRatioFixed->True,
    FontFamily->"Courier",
    FontSize->14,
    FontWeight->"Plain",
    FontSlant->"Plain",
    FontTracking->"Plain",
    FontVariations->{"Underline"->False,
    "Outline"->False,
    "Shadow"->False}],
  
  Cell[StyleData["Output", "Presentation"],
    CellMargins->{{72, Inherited}, {10, 8}},
    LineSpacing->{1, 0},
    FontFamily->"Courier",
    FontSize->14],
  
  Cell[StyleData["Output", "Condensed"],
    CellMargins->{{41, Inherited}, {3, 2}},
    FontFamily->"Courier",
    FontSize->14],
  
  Cell[StyleData["Output", "Printout"],
    CellMargins->{{39, 0}, {6, 4}},
    FontFamily->"Courier",
    FontSize->14]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Message"],
    PageWidth->Infinity,
    CellMargins->{{42, Inherited}, {Inherited, Inherited}},
    Evaluatable->False,
    CellGroupingRules->"OutputGrouping",
    PageBreakWithin->False,
    GroupPageBreakWithin->False,
    GeneratedCell->True,
    CellAutoOverwrite->True,
    ShowCellLabel->False,
    CellLabelMargins->{{23, Inherited}, {Inherited, Inherited}},
    DefaultFormatType->DefaultOutputFormatType,
    LineSpacing->{1, 0},
    AutoItalicWords->{},
    FormatType->InputForm,
    CounterIncrements->"Message",
    AspectRatioFixed->True,
    StyleMenuListing->None,
    FontFamily->"Courier",
    FontSize->14,
    FontWeight->"Plain",
    FontSlant->"Plain",
    FontTracking->"Plain",
    FontColor->RGBColor[0.500008, 0, 0],
    FontVariations->{"Underline"->False,
    "Outline"->False,
    "Shadow"->False}],
  
  Cell[StyleData["Message", "Presentation"],
    CellMargins->{{72, Inherited}, {Inherited, Inherited}},
    LineSpacing->{1, 0},
    FontFamily->"Courier",
    FontSize->14],
  
  Cell[StyleData["Message", "Condensed"],
    CellMargins->{{41, Inherited}, {Inherited, Inherited}},
    FontFamily->"Courier",
    FontSize->14],
  
  Cell[StyleData["Message", "Printout"],
    CellMargins->{{39, Inherited}, {Inherited, Inherited}},
    FontFamily->"Courier",
    FontSize->14,
    FontColor->GrayLevel[0]]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Print"],
    PageWidth->Infinity,
    CellMargins->{{42, Inherited}, {Inherited, Inherited}},
    Evaluatable->False,
    CellGroupingRules->"OutputGrouping",
    CellHorizontalScrolling->True,
    PageBreakWithin->False,
    GroupPageBreakWithin->False,
    GeneratedCell->True,
    CellAutoOverwrite->True,
    ShowCellLabel->False,
    CellLabelMargins->{{23, Inherited}, {Inherited, Inherited}},
    DefaultFormatType->DefaultOutputFormatType,
    LineSpacing->{1, 0},
    AutoItalicWords->{},
    FormatType->InputForm,
    CounterIncrements->"Print",
    AspectRatioFixed->True,
    StyleMenuListing->None,
    FontFamily->"Courier",
    FontSize->14,
    FontWeight->"Plain",
    FontSlant->"Plain",
    FontTracking->"Plain",
    FontVariations->{"Underline"->False,
    "Outline"->False,
    "Shadow"->False}],
  
  Cell[StyleData["Print", "Presentation"],
    CellMargins->{{72, Inherited}, {Inherited, Inherited}},
    LineSpacing->{1, 0},
    FontFamily->"Courier",
    FontSize->14],
  
  Cell[StyleData["Print", "Condensed"],
    CellMargins->{{41, Inherited}, {Inherited, Inherited}},
    FontFamily->"Courier",
    FontSize->14],
  
  Cell[StyleData["Print", "Printout"],
    CellMargins->{{39, Inherited}, {Inherited, Inherited}},
    FontFamily->"Courier",
    FontSize->14]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Graphics"],
    PageWidth->Infinity,
    CellMargins->{{7, Inherited}, {Inherited, Inherited}},
    Evaluatable->False,
    CellGroupingRules->"GraphicsGrouping",
    CellHorizontalScrolling->True,
    PageBreakWithin->False,
    GroupPageBreakWithin->False,
    GeneratedCell->True,
    CellAutoOverwrite->True,
    ShowCellLabel->False,
    DefaultFormatType->DefaultOutputFormatType,
    FormatType->InputForm,
    CounterIncrements->"Graphics",
    AspectRatioFixed->True,
    ImageSize->{387, 393},
    ImageMargins->{{34, Inherited}, {Inherited, 0}},
    StyleMenuListing->None,
    FontFamily->"Courier",
    FontSize->14,
    FontWeight->"Plain",
    FontSlant->"Plain",
    FontTracking->"Plain",
    FontVariations->{"Underline"->False,
    "Outline"->False,
    "Shadow"->False}],
  
  Cell[StyleData["Graphics", "Presentation"],
    ImageMargins->{{62, Inherited}, {Inherited, 0}},
    FontFamily->"Courier",
    FontSize->14],
  
  Cell[StyleData["Graphics", "Condensed"],
    ImageSize->{175, 175},
    ImageMargins->{{38, Inherited}, {Inherited, 0}},
    FontFamily->"Courier",
    FontSize->14],
  
  Cell[StyleData["Graphics", "Printout"],
    ImageSize->{250, 250},
    ImageMargins->{{30, Inherited}, {Inherited, 0}},
    FontFamily->"Courier",
    FontSize->14]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["CellLabel"],
    StyleMenuListing->None,
    FontFamily->"Courier",
    FontSize->14,
    FontWeight->"Plain",
    FontSlant->"Plain",
    FontTracking->"Plain",
    FontColor->RGBColor[0, 0, 1],
    FontVariations->{"Underline"->False,
    "Outline"->False,
    "Shadow"->False}],
  
  Cell[StyleData["CellLabel", "Presentation"],
    FontFamily->"Courier",
    FontSize->14],
  
  Cell[StyleData["CellLabel", "Condensed"],
    FontFamily->"Courier",
    FontSize->14],
  
  Cell[StyleData["CellLabel", "Printout"],
    FontFamily->"Courier",
    FontSize->14,
    FontColor->GrayLevel[0]]
  }, Closed]]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[TextData[StyleBox["Formulas and Programming"]], "Section"],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["InlineFormula"],
    CellMargins->{{10, 4}, {0, 8}},
    CellHorizontalScrolling->True,
    ScriptLevel->1,
    SingleLetterItalics->True],
  
  Cell[StyleData["InlineFormula", "Presentation"],
    CellMargins->{{24, 10}, {10, 10}},
    LineSpacing->{1, 5}],
  
  Cell[StyleData["InlineFormula", "Condensed"],
    CellMargins->{{8, 10}, {6, 6}},
    LineSpacing->{1, 1}],
  
  Cell[StyleData["InlineFormula", "Printout"],
    CellMargins->{{2, 0}, {6, 6}}]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["DisplayFormula"],
    CellMargins->{{42, Inherited}, {Inherited, Inherited}},
    CellHorizontalScrolling->True,
    DefaultFormatType->DefaultInputFormatType,
    ScriptLevel->0,
    SingleLetterItalics->True,
    UnderoverscriptBoxOptions->{LimitsPositioning->True}],
  
  Cell[StyleData["DisplayFormula", "Presentation"],
    LineSpacing->{1, 5}],
  
  Cell[StyleData["DisplayFormula", "Condensed"],
    LineSpacing->{1, 1}],
  
  Cell[StyleData["DisplayFormula", "Printout"]]
  }, Closed]]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[TextData[StyleBox["Styles for Headers and Footers"]], "Section"],
  
  Cell[StyleData["Header"],
    CellMargins->{{7, 0}, {4, 1}},
    Evaluatable->False,
    PageBreakWithin->Automatic,
    AspectRatioFixed->True,
    StyleMenuListing->None,
    FontFamily->"Times",
    FontSize->12,
    FontSlant->"Italic"],
  
  Cell[StyleData["Footer"],
    CellMargins->{{7, 0}, {0, 4}},
    Evaluatable->False,
    PageBreakWithin->Automatic,
    TextAlignment->Center,
    AspectRatioFixed->True,
    StyleMenuListing->None,
    FontFamily->"Times",
    FontSize->12,
    FontSlant->"Italic"],
  
  Cell[StyleData["PageNumber"],
    CellMargins->{{0, 0}, {4, 1}},
    StyleMenuListing->None,
    FontFamily->"Times",
    FontSize->10]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[TextData[StyleBox["Palette Styles"]], "Section"],
  
  Cell[TextData[StyleBox[
  "The cells below define styles that define standard ButtonFunctions, for \
use in palette buttons."]], "Text"],
  
  Cell[StyleData["Paste"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`NotebookApply[ 
          FrontEnd`InputNotebook[ ], #, After]}]&)}],
  
  Cell[StyleData["Evaluate"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`NotebookApply[ 
          FrontEnd`InputNotebook[ ], #, All], 
        SelectionEvaluate[ 
          FrontEnd`InputNotebook[ ], All]}]&)}],
  
  Cell[StyleData["EvaluateCell"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`NotebookApply[ 
          FrontEnd`InputNotebook[ ], #, All], 
        FrontEnd`SelectionMove[ 
          FrontEnd`InputNotebook[ ], All, Cell, 1], 
        FrontEnd`SelectionEvaluateCreateCell[ 
          FrontEnd`InputNotebook[ ], All]}]&)}],
  
  Cell[StyleData["CopyEvaluate"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`SelectionCreateCell[ 
          FrontEnd`InputNotebook[ ], All], 
        FrontEnd`NotebookApply[ 
          FrontEnd`InputNotebook[ ], #, All], 
        FrontEnd`SelectionEvaluate[ 
          FrontEnd`InputNotebook[ ], All]}]&)}],
  
  Cell[StyleData["CopyEvaluateCell"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`SelectionCreateCell[ 
          FrontEnd`InputNotebook[ ], All], 
        FrontEnd`NotebookApply[ 
          FrontEnd`InputNotebook[ ], #, All], 
        FrontEnd`SelectionEvaluateCreateCell[ 
          FrontEnd`InputNotebook[ ], All]}]&)}]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[TextData[StyleBox["Hyperlink Styles"]], "Section"],
  
  Cell[TextData[StyleBox[
  "The cells below define styles useful for making hypertext ButtonBoxes.  \
The \"Hyperlink\" style is for links within the same Notebook, or between \
Notebooks."]], "Text"],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Hyperlink"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    FontColor->RGBColor[0, 0, 1],
    FontVariations->{"Underline"->True},
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`NotebookLocate[ #2]}]&),
    Active->True,
    ButtonNote->ButtonData}],
  
  Cell[StyleData["Hyperlink", "Presentation"]],
  
  Cell[StyleData["Hyperlink", "Condensed"]],
  
  Cell[StyleData["Hyperlink", "Printout"],
    FontColor->GrayLevel[0],
    FontVariations->{"Underline"->False}]
  }, Closed]],
  
  Cell[TextData[StyleBox[
  "The following styles are for linking automatically to the on-line help \
system."]], "Text"],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["MainBookLink"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    FontColor->RGBColor[0, 0, 1],
    FontVariations->{"Underline"->True},
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`HelpBrowserLookup[ "MainBook", #]}]&),
    Active->True,
    ButtonFrame->"None"}],
  
  Cell[StyleData["MainBookLink", "Presentation"]],
  
  Cell[StyleData["MainBookLink", "Condensed"]],
  
  Cell[StyleData["MainBookLink", "Printout"],
    FontColor->GrayLevel[0],
    FontVariations->{"Underline"->False}]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["AddOnsLink"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    FontFamily->"Courier",
    FontColor->RGBColor[0, 0, 1],
    FontVariations->{"Underline"->True},
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`HelpBrowserLookup[ "AddOns", #]}]&),
    Active->True,
    ButtonFrame->"None"}],
  
  Cell[StyleData["AddOnsLink", "Presentation"]],
  
  Cell[StyleData["AddOnsLink", "Condensed"]],
  
  Cell[StyleData["AddOnLink", "Printout"],
    FontColor->GrayLevel[0],
    FontVariations->{"Underline"->False}]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["RefGuideLink"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    FontFamily->"Courier",
    FontColor->RGBColor[0, 0, 1],
    FontVariations->{"Underline"->True},
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`HelpBrowserLookup[ "RefGuideLink", #]}]&),
    Active->True,
    ButtonFrame->"None"}],
  
  Cell[StyleData["RefGuideLink", "Presentation"]],
  
  Cell[StyleData["RefGuideLink", "Condensed"]],
  
  Cell[StyleData["RefGuideLink", "Printout"],
    FontColor->GrayLevel[0],
    FontVariations->{"Underline"->False}]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["GettingStartedLink"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    FontColor->RGBColor[0, 0, 1],
    FontVariations->{"Underline"->True},
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`HelpBrowserLookup[ "GettingStarted", #]}]&),
    Active->True,
    ButtonFrame->"None"}],
  
  Cell[StyleData["GettingStartedLink", "Presentation"]],
  
  Cell[StyleData["GettingStartedLink", "Condensed"]],
  
  Cell[StyleData["GettingStartedLink", "Printout"],
    FontColor->GrayLevel[0],
    FontVariations->{"Underline"->False}]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["OtherInformationLink"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    FontColor->RGBColor[0, 0, 1],
    FontVariations->{"Underline"->True},
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`HelpBrowserLookup[ "OtherInformation", #]}]&),
    Active->True,
    ButtonFrame->"None"}],
  
  Cell[StyleData["OtherInformationLink", "Presentation"]],
  
  Cell[StyleData["OtherInformationLink", "Condensed"]],
  
  Cell[StyleData["OtherInformationLink", "Printout"],
    FontColor->GrayLevel[0],
    FontVariations->{"Underline"->False}]
  }, Closed]]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[TextData[StyleBox["Placeholder Styles"]], "Section"],
  
  Cell[TextData[StyleBox[
  "The cells below define styles useful for making placeholder objects in \
palette templates."]], "Text"],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Placeholder"],
    Editable->False,
    Selectable->False,
    StyleBoxAutoDelete->True,
    Placeholder->True,
    StyleMenuListing->None],
  
  Cell[StyleData["Placeholder", "Presentation"]],
  
  Cell[StyleData["Placeholder", "Condensed"]],
  
  Cell[StyleData["Placeholder", "Printout"]]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["SelectionPlaceholder"],
    Editable->False,
    Selectable->False,
    StyleBoxAutoDelete->True,
    Placeholder->Primary,
    StyleMenuListing->None,
    DrawHighlighted->True],
  
  Cell[StyleData["SelectionPlaceholder", "Presentation"]],
  
  Cell[StyleData["SelectionPlaceholder", "Condensed"]],
  
  Cell[StyleData["SelectionPlaceholder", "Printout"]]
  }, Closed]]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[TextData[StyleBox["FormatType Styles"]], "Section"],
  
  Cell[TextData[StyleBox[
  "The cells below define styles that are mixed in with the styles of most \
cells.  If a cell's FormatType matches the name of one of the styles defined \
below, then that style is applied between the cell's style and its own \
options."]], "Text"],
  
  Cell[StyleData["CellExpression"],
    PageWidth->Infinity,
    CellMargins->{{6, Inherited}, {Inherited, Inherited}},
    ShowCellLabel->False,
    ShowSpecialCharacters->False,
    AllowInlineCells->False,
    AutoItalicWords->{},
    StyleMenuListing->None,
    FontFamily->"Courier",
    Background->GrayLevel[1]],
  
  Cell[StyleData["InputForm"],
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