- added Dirac gammaL and gammaR objects (chiral projectors)
authorChristian Bauer <Christian.Bauer@uni-mainz.de>
Wed, 20 Nov 2002 20:35:06 +0000 (20:35 +0000)
committerChristian Bauer <Christian.Bauer@uni-mainz.de>
Wed, 20 Nov 2002 20:35:06 +0000 (20:35 +0000)
- fixed a typo in add.cpp

ginac/add.cpp
ginac/clifford.cpp
ginac/clifford.h
ginac/tinfos.h

index 1c995aa..b3fd1f6 100644 (file)
@@ -315,7 +315,7 @@ ex add::coeff(const ex & s, int n) const
  *  x stands for a symbolic variables of type ex and c stands for such
  *  an expression that contain a plain number.
  *  - +(;c) -> c
- *  - +(x;1) -> x
+ *  - +(x;0) -> x
  *
  *  @param level cut-off in recursive evaluation */
 ex add::eval(int level) const
index 1b3d034..c7499db 100644 (file)
@@ -44,6 +44,8 @@ GINAC_IMPLEMENT_REGISTERED_CLASS(diracone, tensor)
 GINAC_IMPLEMENT_REGISTERED_CLASS(diracgamma, tensor)
 GINAC_IMPLEMENT_REGISTERED_CLASS(diracgamma5, tensor)
 
+GINAC_IMPLEMENT_REGISTERED_CLASS(diracgammaL, tensor)
+GINAC_IMPLEMENT_REGISTERED_CLASS(diracgammaR, tensor)
 //////////
 // default ctor, dtor, copy ctor, assignment operator and helpers
 //////////
@@ -64,6 +66,8 @@ DEFAULT_CTORS(diracone)
 DEFAULT_CTORS(diracgamma)
 DEFAULT_CTORS(diracgamma5)
 
+DEFAULT_CTORS(diracgammaL)
+DEFAULT_CTORS(diracgammaR)
 //////////
 // other constructors
 //////////
@@ -117,6 +121,8 @@ DEFAULT_ARCHIVING(diracone)
 DEFAULT_ARCHIVING(diracgamma)
 DEFAULT_ARCHIVING(diracgamma5)
 
+DEFAULT_ARCHIVING(diracgammaL)
+DEFAULT_ARCHIVING(diracgammaR)
 //////////
 // functions overriding virtual functions from base classes
 //////////
@@ -144,7 +150,9 @@ bool clifford::match_same_type(const basic & other) const
 
 void clifford::print(const print_context & c, unsigned level) const
 {
-       if (!is_a<diracgamma5>(seq[0]) && !is_a<diracgamma>(seq[0]) && !is_a<diracone>(seq[0])) {
+       if (!is_a<diracgamma5>(seq[0]) && !is_a<diracgammaL>(seq[0]) &&
+           !is_a<diracgammaR>(seq[0]) && !is_a<diracgamma>(seq[0]) &&
+           !is_a<diracone>(seq[0])) {
 
                // dirac_slash() object is printed differently
                if (is_a<print_tree>(c))
@@ -165,10 +173,14 @@ void clifford::print(const print_context & c, unsigned level) const
 DEFAULT_COMPARE(diracone)
 DEFAULT_COMPARE(diracgamma)
 DEFAULT_COMPARE(diracgamma5)
+DEFAULT_COMPARE(diracgammaL)
+DEFAULT_COMPARE(diracgammaR)
 
 DEFAULT_PRINT_LATEX(diracone, "ONE", "\\mathbb{1}")
 DEFAULT_PRINT_LATEX(diracgamma, "gamma", "\\gamma")
 DEFAULT_PRINT_LATEX(diracgamma5, "gamma5", "{\\gamma^5}")
+DEFAULT_PRINT_LATEX(diracgammaL, "gammaL", "{\\gamma_L}")
+DEFAULT_PRINT_LATEX(diracgammaR, "gammaR", "{\\gamma_R}")
 
 /** This function decomposes gamma~mu -> (1, mu) and a\ -> (a.ix, ix) */
 static void base_and_index(const ex & c, ex & b, ex & i)
@@ -179,7 +191,7 @@ static void base_and_index(const ex & c, ex & b, ex & i)
        if (is_a<diracgamma>(c.op(0))) { // proper dirac gamma object
                i = c.op(1);
                b = _ex1;
-       } else if (is_a<diracgamma5>(c.op(0))) { // gamma5
+       } else if (is_a<diracgamma5>(c.op(0)) || is_a<diracgammaL>(c.op(0)) || is_a<diracgammaR>(c.op(0))) { // gamma5/L/R
                i = _ex0;
                b = _ex1;
        } else { // slash object, generate new dummy index
@@ -272,7 +284,7 @@ bool diracgamma::contract_with(exvector::iterator self, exvector::iterator other
 }
 
 /** Perform automatic simplification on noncommutative product of clifford
- *  objects. This removes superfluous ONEs, permutes gamma5's to the front
+ *  objects. This removes superfluous ONEs, permutes gamma5/L/R's to the front
  *  and removes squares of gamma objects. */
 ex clifford::simplify_ncmul(const exvector & v) const
 {
@@ -290,17 +302,67 @@ ex clifford::simplify_ncmul(const exvector & v) const
        bool something_changed = false;
        int sign = 1;
 
-       // Anticommute gamma5's to the front
+       // Anticommute gamma5/L/R's to the front
        if (s.size() >= 2) {
                exvector::iterator first = s.begin(), next_to_last = s.end() - 2;
                while (true) {
                        exvector::iterator it = next_to_last;
                        while (true) {
                                exvector::iterator it2 = it + 1;
-                               if (is_a<clifford>(*it) && is_a<clifford>(*it2) && !is_a<diracgamma5>(it->op(0)) && is_a<diracgamma5>(it2->op(0))) {
-                                       it->swap(*it2);
-                                       sign = -sign;
-                                       something_changed = true;
+                               if (is_a<clifford>(*it) && is_a<clifford>(*it2)) {
+                                       ex e1 = it->op(0), e2 = it2->op(0);
+
+                                       if (is_a<diracgamma5>(e2)) {
+
+                                               if (is_a<diracgammaL>(e1) || is_a<diracgammaR>(e1)) {
+
+                                                       // gammaL/R gamma5 -> gamma5 gammaL/R
+                                                       it->swap(*it2);
+                                                       something_changed = true;
+
+                                               } else if (!is_a<diracgamma5>(e1)) {
+
+                                                       // gamma5 gamma5 -> gamma5 gamma5 (do nothing)
+                                                       // x gamma5 -> -gamma5 x
+                                                       it->swap(*it2);
+                                                       sign = -sign;
+                                                       something_changed = true;
+                                               }
+
+                                       } else if (is_a<diracgammaL>(e2)) {
+
+                                               if (is_a<diracgammaR>(e1)) {
+
+                                                       // gammaR gammaL -> 0
+                                                       return _ex0;
+
+                                               } else if (!is_a<diracgammaL>(e1) && !is_a<diracgamma5>(e1)) {
+
+                                                       // gammaL gammaL -> gammaL gammaL (do nothing)
+                                                       // gamma5 gammaL -> gamma5 gammaL (do nothing)
+                                                       // x gammaL -> gammaR x
+                                                       it->swap(*it2);
+                                                       *it = clifford(diracgammaR(), ex_to<clifford>(*it).get_representation_label());
+                                                       something_changed = true;
+                                               }
+
+                                       } else if (is_a<diracgammaR>(e2)) {
+
+                                               if (is_a<diracgammaL>(e1)) {
+
+                                                       // gammaL gammaR -> 0
+                                                       return _ex0;
+
+                                               } else if (!is_a<diracgammaR>(e1) && !is_a<diracgamma5>(e1)) {
+
+                                                       // gammaR gammaR -> gammaR gammaR (do nothing)
+                                                       // gamma5 gammaR -> gamma5 gammaR (do nothing)
+                                                       // x gammaR -> gammaL x
+                                                       it->swap(*it2);
+                                                       *it = clifford(diracgammaL(), ex_to<clifford>(*it).get_representation_label());
+                                                       something_changed = true;
+                                               }
+                                       }
                                }
                                if (it == first)
                                        break;
@@ -320,9 +382,14 @@ ex clifford::simplify_ncmul(const exvector & v) const
                        ex & b = it[1];
                        if (!is_a<clifford>(a) || !is_a<clifford>(b))
                                continue;
-                       bool a_is_diracgamma = is_a<diracgamma>(a.op(0));
-                       bool b_is_diracgamma = is_a<diracgamma>(b.op(0));
+
+                       const ex & ag = a.op(0);
+                       const ex & bg = b.op(0);
+                       bool a_is_diracgamma = is_a<diracgamma>(ag);
+                       bool b_is_diracgamma = is_a<diracgamma>(bg);
+
                        if (a_is_diracgamma && b_is_diracgamma) {
+
                                const ex & ia = a.op(1);
                                const ex & ib = b.op(1);
                                if (ia.is_equal(ib)) { // gamma~alpha gamma~alpha -> g~alpha~alpha
@@ -330,20 +397,46 @@ ex clifford::simplify_ncmul(const exvector & v) const
                                        b = dirac_ONE(representation_label);
                                        something_changed = true;
                                }
-                       } else if (is_a<diracgamma5>(a.op(0)) && is_a<diracgamma5>(b.op(0))) {
+
+                       } else if ((is_a<diracgamma5>(ag) && is_a<diracgamma5>(bg))) {
+
                                // Remove squares of gamma5
                                a = dirac_ONE(representation_label);
                                b = dirac_ONE(representation_label);
                                something_changed = true;
-                       } else if (!a_is_diracgamma && !b_is_diracgamma) {
-                               const ex & ba = a.op(0);
-                               const ex & bb = b.op(0);
-                               if (ba.is_equal(bb)) { // a\ a\ -> a^2
-                                       varidx ix((new symbol)->setflag(status_flags::dynallocated), ex_to<idx>(a.op(1)).get_dim());
-                                       a = indexed(ba, ix) * indexed(bb, ix.toggle_variance());
-                                       b = dirac_ONE(representation_label);
-                                       something_changed = true;
-                               }
+
+                       } else if ((is_a<diracgammaL>(ag) && is_a<diracgammaL>(bg))
+                               || (is_a<diracgammaR>(ag) && is_a<diracgammaR>(bg))) {
+
+                               // Remove squares of gammaL/R
+                               b = dirac_ONE(representation_label);
+                               something_changed = true;
+
+                       } else if (is_a<diracgammaL>(ag) && is_a<diracgammaR>(bg)) {
+
+                               // gammaL and gammaR are orthogonal
+                               return _ex0;
+
+                       } else if (is_a<diracgamma5>(ag) && is_a<diracgammaL>(bg)) {
+
+                               // gamma5 gammaL -> -gammaL
+                               a = dirac_ONE(representation_label);
+                               sign = -sign;
+                               something_changed = true;
+
+                       } else if (is_a<diracgamma5>(ag) && is_a<diracgammaR>(bg)) {
+
+                               // gamma5 gammaR -> gammaR
+                               a = dirac_ONE(representation_label);
+                               something_changed = true;
+
+                       } else if (!a_is_diracgamma && !b_is_diracgamma && ag.is_equal(bg)) {
+
+                               // a\ a\ -> a^2
+                               varidx ix((new symbol)->setflag(status_flags::dynallocated), ex_to<idx>(a.op(1)).get_dim());
+                               a = indexed(ag, ix) * indexed(ag, ix.toggle_variance());
+                               b = dirac_ONE(representation_label);
+                               something_changed = true;
                        }
                }
        }
@@ -388,6 +481,16 @@ ex dirac_gamma5(unsigned char rl)
        return clifford(diracgamma5(), rl);
 }
 
+ex dirac_gammaL(unsigned char rl)
+{
+       return clifford(diracgammaL(), rl);
+}
+
+ex dirac_gammaR(unsigned char rl)
+{
+       return clifford(diracgammaR(), rl);
+}
+
 ex dirac_gamma6(unsigned char rl)
 {
        return clifford(diracone(), rl) + clifford(diracgamma5(), rl);
@@ -460,9 +563,13 @@ ex dirac_trace(const ex & e, unsigned char rl, const ex & trONE)
 {
        if (is_a<clifford>(e)) {
 
-               if (ex_to<clifford>(e).get_representation_label() == rl
-                && is_a<diracone>(e.op(0)))
+               if (!ex_to<clifford>(e).get_representation_label() == rl)
+                       return _ex0;
+               const ex & g = e.op(0);
+               if (is_a<diracone>(g))
                        return trONE;
+               else if (is_a<diracgammaL>(g) || is_a<diracgammaR>(g))
+                       return trONE/2;
                else
                        return _ex0;
 
@@ -484,8 +591,11 @@ ex dirac_trace(const ex & e, unsigned char rl, const ex & trONE)
                if (!is_clifford_tinfo(e.return_type_tinfo(), rl))
                        return _ex0;
 
-               // Expand product, if necessary
-               ex e_expanded = e.expand();
+               // Substitute gammaL/R and expand product, if necessary
+               ex e_expanded = e.subs(lst(
+                       dirac_gammaL(rl) == (dirac_ONE(rl)-dirac_gamma5(rl))/2,
+                       dirac_gammaR(rl) == (dirac_ONE(rl)+dirac_gamma5(rl))/2
+               )).expand();
                if (!is_a<ncmul>(e_expanded))
                        return dirac_trace(e_expanded, rl, trONE);
 
index 2d1680c..2a9e73b 100644 (file)
@@ -52,8 +52,8 @@ public:
        void print(const print_context & c, unsigned level = 0) const;
 
 protected:
-       bool match_same_type(const basic & other) const;
        ex simplify_ncmul(const exvector & v) const;
+       bool match_same_type(const basic & other) const;
        ex thisexprseq(const exvector & v) const;
        ex thisexprseq(exvector * vp) const;
        unsigned return_type(void) const { return return_types::noncommutative; }
@@ -104,6 +104,30 @@ public:
 };
 
 
+/** This class represents the Dirac gammaL object which behaves like
+ *  1/2 (1-gamma5). */
+class diracgammaL : public tensor
+{
+       GINAC_DECLARE_REGISTERED_CLASS(diracgammaL, tensor)
+
+       // functions overriding virtual functions from base classes
+public:
+       void print(const print_context & c, unsigned level = 0) const;
+};
+
+
+/** This class represents the Dirac gammaL object which behaves like
+ *  1/2 (1+gamma5). */
+class diracgammaR : public tensor
+{
+       GINAC_DECLARE_REGISTERED_CLASS(diracgammaR, tensor)
+
+       // functions overriding virtual functions from base classes
+public:
+       void print(const print_context & c, unsigned level = 0) const;
+};
+
+
 // global functions
 
 /** Specialization of is_exactly_a<clifford>(obj) for clifford objects. */
@@ -131,10 +155,20 @@ ex dirac_gamma(const ex & mu, unsigned char rl = 0);
  *  @return newly constructed object */
 ex dirac_gamma5(unsigned char rl = 0);
 
-/** This returns (dirac_ONE(rl) + dirac_gamma5(rl)). */
-ex dirac_gamma6(unsigned char rl = 0);
+/** Create a Dirac gammaL object.
+ *
+ *  @param rl Representation label
+ *  @return newly constructed object */
+ex dirac_gammaL(unsigned char rl = 0);
+
+/** Create a Dirac gammaR object.
+ *
+ *  @param rl Representation label
+ *  @return newly constructed object */
+ex dirac_gammaR(unsigned char rl = 0);
 
-/** This returns (dirac_ONE(rl) - dirac_gamma5(rl)). */
+// These functions are deprecated. Use dirac_gammaL/R() instead.
+ex dirac_gamma6(unsigned char rl = 0);
 ex dirac_gamma7(unsigned char rl = 0);
 
 /** Create a term of the form e_mu * gamma~mu with a unique index mu.
index 03b7315..657a1cd 100644 (file)
@@ -82,6 +82,8 @@ const unsigned TINFO_su3d          = 0x000e100bU;
 const unsigned TINFO_diracone      = 0x000e100cU;
 const unsigned TINFO_diracgamma    = 0x000e100dU;
 const unsigned TINFO_diracgamma5   = 0x000e100eU;
+const unsigned TINFO_diracgammaL   = 0x000e100fU;
+const unsigned TINFO_diracgammaR   = 0x000e1010U;
 
 const unsigned TINFO_wildcard      = 0x000f0001U;