- color/clifford objects have representation label to distinguish elements
[ginac.git] / ginac / clifford.cpp
index ecd95b7e95afca94265036741133875f2511b008..06d9e5415a361d95b3305133e1032f84c10bae52 100644 (file)
@@ -36,54 +36,61 @@ namespace GiNaC {
 GINAC_IMPLEMENT_REGISTERED_CLASS(clifford, indexed)
 GINAC_IMPLEMENT_REGISTERED_CLASS(diracone, tensor)
 GINAC_IMPLEMENT_REGISTERED_CLASS(diracgamma, tensor)
+GINAC_IMPLEMENT_REGISTERED_CLASS(diracgamma5, tensor)
 
 //////////
 // default constructor, destructor, copy constructor assignment operator and helpers
 //////////
 
-clifford::clifford()
+clifford::clifford() : representation_label(0)
 {
        debugmsg("clifford default constructor", LOGLEVEL_CONSTRUCT);
        tinfo_key = TINFO_clifford;
 }
 
-DEFAULT_COPY(clifford)
+void clifford::copy(const clifford & other)
+{
+       inherited::copy(other);
+       representation_label = other.representation_label;
+}
+
 DEFAULT_DESTROY(clifford)
 DEFAULT_CTORS(diracone)
 DEFAULT_CTORS(diracgamma)
+DEFAULT_CTORS(diracgamma5)
 
 //////////
 // other constructors
 //////////
 
+/** Construct object without any indices. This constructor is for internal
+ *  use only. Use the dirac_ONE() function instead.
+ *  @see dirac_ONE */
+clifford::clifford(const ex & b, unsigned char rl) : inherited(b), representation_label(rl)
+{
+       debugmsg("clifford constructor from ex", LOGLEVEL_CONSTRUCT);
+       tinfo_key = TINFO_clifford;
+}
+
 /** Construct object with one Lorentz index. This constructor is for internal
  *  use only. Use the dirac_gamma() function instead.
  *  @see dirac_gamma */
-clifford::clifford(const ex & b, const ex & mu) : inherited(b, mu)
+clifford::clifford(const ex & b, const ex & mu, unsigned char rl) : inherited(b, mu), representation_label(rl)
 {
        debugmsg("clifford constructor from ex,ex", LOGLEVEL_CONSTRUCT);
        GINAC_ASSERT(is_ex_of_type(mu, varidx));
        tinfo_key = TINFO_clifford;
 }
 
-/** Construct object without any indices. This constructor is for internal
- *  use only. Use the dirac_one() function instead.
- *  @see dirac_one */
-clifford::clifford(const ex & b) : inherited(b)
+clifford::clifford(unsigned char rl, const exvector & v, bool discardable) : inherited(indexed::unknown, v, discardable), representation_label(rl)
 {
-       debugmsg("clifford constructor from ex", LOGLEVEL_CONSTRUCT);
+       debugmsg("clifford constructor from unsigned char,exvector", LOGLEVEL_CONSTRUCT);
        tinfo_key = TINFO_clifford;
 }
 
-clifford::clifford(const exvector & v, bool discardable) : inherited(indexed::unknown, v, discardable)
+clifford::clifford(unsigned char rl, exvector * vp) : inherited(indexed::unknown, vp), representation_label(rl)
 {
-       debugmsg("clifford constructor from exvector", LOGLEVEL_CONSTRUCT);
-       tinfo_key = TINFO_clifford;
-}
-
-clifford::clifford(exvector * vp) : inherited(indexed::unknown, vp)
-{
-       debugmsg("clifford constructor from exvector *", LOGLEVEL_CONSTRUCT);
+       debugmsg("clifford constructor from unsigned char,exvector *", LOGLEVEL_CONSTRUCT);
        tinfo_key = TINFO_clifford;
 }
 
@@ -91,9 +98,24 @@ clifford::clifford(exvector * vp) : inherited(indexed::unknown, vp)
 // archiving
 //////////
 
-DEFAULT_ARCHIVING(clifford)
+clifford::clifford(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
+{
+       debugmsg("clifford constructor from archive_node", LOGLEVEL_CONSTRUCT);
+       unsigned rl;
+       n.find_unsigned("label", rl);
+       representation_label = rl;
+}
+
+void clifford::archive(archive_node &n) const
+{
+       inherited::archive(n);
+       n.add_unsigned("label", representation_label);
+}
+
+DEFAULT_UNARCHIVE(clifford)
 DEFAULT_ARCHIVING(diracone)
 DEFAULT_ARCHIVING(diracgamma)
+DEFAULT_ARCHIVING(diracgamma5)
 
 //////////
 // functions overriding virtual functions from bases classes
@@ -101,13 +123,24 @@ DEFAULT_ARCHIVING(diracgamma)
 
 int clifford::compare_same_type(const basic & other) const
 {
+       GINAC_ASSERT(other.tinfo() == TINFO_clifford);
+       const clifford &o = static_cast<const clifford &>(other);
+
+       if (representation_label != o.representation_label) {
+               // different representation label
+               return representation_label < o.representation_label ? -1 : 1;
+       }
+
        return inherited::compare_same_type(other);
 }
 
 DEFAULT_COMPARE(diracone)
 DEFAULT_COMPARE(diracgamma)
+DEFAULT_COMPARE(diracgamma5)
+
 DEFAULT_PRINT(diracone, "ONE")
 DEFAULT_PRINT(diracgamma, "gamma")
+DEFAULT_PRINT(diracgamma5, "gamma5")
 
 /** Contraction of a gamma matrix with something else. */
 bool diracgamma::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
@@ -123,7 +156,7 @@ bool diracgamma::contract_with(exvector::iterator self, exvector::iterator other
                // gamma~mu*gamma.mu = dim*ONE
                if (other - self == 1) {
                        *self = dim;
-                       *other = dirac_one();
+                       *other = dirac_ONE();
                        return true;
 
                // gamma~mu*gamma~alpha*gamma.mu = (2-dim)*gamma~alpha
@@ -137,7 +170,7 @@ bool diracgamma::contract_with(exvector::iterator self, exvector::iterator other
                } else if (other - self == 3
                        && is_ex_of_type(self[1], clifford)
                        && is_ex_of_type(self[2], clifford)) {
-                       *self = 4 * metric_tensor(self[1].op(1), self[2].op(1)) * dirac_one() + (dim - 4) * self[1] * self[2];
+                       *self = 4 * metric_tensor(self[1].op(1), self[2].op(1)) * dirac_ONE() + (dim - 4) * self[1] * self[2];
                        self[1] = _ex1();
                        self[2] = _ex1();
                        *other = _ex1();
@@ -161,52 +194,109 @@ bool diracgamma::contract_with(exvector::iterator self, exvector::iterator other
 }
 
 /** Perform automatic simplification on noncommutative product of clifford
- *  objects. This removes superfluous ONEs. */
+ *  objects. This removes superfluous ONEs, permutes gamma5's to the front
+ *  and removes squares of gamma objects. */
 ex clifford::simplify_ncmul(const exvector & v) const
 {
        exvector s;
        s.reserve(v.size());
 
-       exvector::const_iterator it = v.begin(), itend = v.end();
-       while (it != itend) {
-               if (!is_ex_of_type(it->op(0), diracone))
-                       s.push_back(*it);
-               it++;
+       // Remove superfluous ONEs
+       exvector::const_iterator cit = v.begin(), citend = v.end();
+       while (cit != citend) {
+               if (!is_ex_of_type(cit->op(0), diracone))
+                       s.push_back(*cit);
+               cit++;
+       }
+
+       bool something_changed = false;
+       int sign = 1;
+
+       // Anticommute gamma5'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_ex_of_type(it->op(0), diracgamma5) && is_ex_of_type(it2->op(0), diracgamma5)) {
+                                       it->swap(*it2);
+                                       sign = -sign;
+                                       something_changed = true;
+                               }
+                               if (it == first)
+                                       break;
+                               it--;
+                       }
+                       if (next_to_last == first)
+                               break;
+                       next_to_last--;
+               }
+       }
+
+       // Remove squares of gamma5
+       while (s.size() >= 2 && is_ex_of_type(s[0].op(0), diracgamma5) && is_ex_of_type(s[1].op(0), diracgamma5)) {
+               s.erase(s.begin(), s.begin() + 2);
+               something_changed = true;
+       }
+
+       // Remove equal adjacent gammas
+       if (s.size() >= 2) {
+               exvector::iterator it = s.begin(), itend = s.end() - 1;
+               while (it != itend) {
+                       ex & a = it[0];
+                       ex & b = it[1];
+                       if (is_ex_of_type(a.op(0), diracgamma) && is_ex_of_type(b.op(0), diracgamma)) {
+                               const ex & ia = a.op(1);
+                               const ex & ib = b.op(1);
+                               if (ia.is_equal(ib)) {
+                                       a = lorentz_g(ia, ib);
+                                       b = dirac_ONE();
+                                       something_changed = true;
+                               }
+                       }
+                       it++;
+               }
        }
 
        if (s.size() == 0)
-               return clifford(diracone());
-       else if (s.size() == v.size())
-               return simplified_ncmul(v);
+               return clifford(diracone()) * sign;
+       if (something_changed)
+               return nonsimplified_ncmul(s) * sign;
        else
-               return simplified_ncmul(s);
+               return simplified_ncmul(s) * sign;
 }
 
 ex clifford::thisexprseq(const exvector & v) const
 {
-       return clifford(v);
+       return clifford(representation_label, v);
 }
 
 ex clifford::thisexprseq(exvector * vp) const
 {
-       return clifford(vp);
+       return clifford(representation_label, vp);
 }
 
 //////////
 // global functions
 //////////
 
-ex dirac_one(void)
+ex dirac_ONE(unsigned char rl)
 {
-       return clifford(diracone());
+       return clifford(diracone(), rl);
 }
 
-ex dirac_gamma(const ex & mu)
+ex dirac_gamma(const ex & mu, unsigned char rl)
 {
        if (!is_ex_of_type(mu, varidx))
                throw(std::invalid_argument("index of Dirac gamma must be of type varidx"));
 
-       return clifford(diracgamma(), mu);
+       return clifford(diracgamma(), mu, rl);
+}
+
+ex dirac_gamma5(unsigned char rl)
+{
+       return clifford(diracgamma5(), rl);
 }
 
 } // namespace GiNaC