- added Clifford contractions:

[ginac.git] / ginac / clifford.cpp

diff --git a/ginac/clifford.cpp b/ginac/clifford.cpp
index 5875bbb836e80a7c4ed80789b5c934c0d618f469..c1c069dcb0ff8d0723048f91d0bcfec601804a4c 100644 (file)
--- a/ginac/clifford.cpp
+++ b/ginac/clifford.cpp
@@ -33,6 +33,7 @@
 namespace GiNaC {
 
 GINAC_IMPLEMENT_REGISTERED_CLASS(clifford, indexed)
+GINAC_IMPLEMENT_REGISTERED_CLASS(diracone, tensor)
 GINAC_IMPLEMENT_REGISTERED_CLASS(diracgamma, tensor)
 
 //////////
@@ -47,6 +48,7 @@ clifford::clifford()
 
 DEFAULT_COPY(clifford)
 DEFAULT_DESTROY(clifford)
+DEFAULT_CTORS(diracone)
 DEFAULT_CTORS(diracgamma)
 
 //////////
@@ -63,6 +65,15 @@ clifford::clifford(const ex & b, const ex & mu) : inherited(b, mu)
        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)
+{
+       debugmsg("clifford constructor from ex", LOGLEVEL_CONSTRUCT);
+       tinfo_key = TINFO_clifford;
+}
+
 clifford::clifford(const exvector & v, bool discardable) : inherited(indexed::unknown, v, discardable)
 {
        debugmsg("clifford constructor from exvector", LOGLEVEL_CONSTRUCT);
@@ -80,6 +91,7 @@ clifford::clifford(exvector * vp) : inherited(indexed::unknown, vp)
 //////////
 
 DEFAULT_ARCHIVING(clifford)
+DEFAULT_ARCHIVING(diracone)
 DEFAULT_ARCHIVING(diracgamma)
 
 //////////
@@ -91,15 +103,82 @@ int clifford::compare_same_type(const basic & other) const
        return inherited::compare_same_type(other);
 }
 
+DEFAULT_COMPARE(diracone)
 DEFAULT_COMPARE(diracgamma)
+DEFAULT_PRINT(diracone, "ONE")
 DEFAULT_PRINT(diracgamma, "gamma")
 
+/** Contraction of a gamma matrix with something else. */
+bool diracgamma::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
+{
+       GINAC_ASSERT(is_ex_of_type(*self, indexed));
+       GINAC_ASSERT(is_ex_of_type(*other, indexed));
+       GINAC_ASSERT(is_ex_of_type(self->op(0), diracgamma));
+
+       if (is_ex_of_type(other->op(0), diracgamma)) {
+
+               ex dim = ex_to_idx(self->op(1)).get_dim();
+
+               // gamma~mu*gamma.mu = dim*ONE
+               if (other - self == 1) {
+                       *self = dim;
+                       *other = dirac_one();
+                       return true;
+
+               // gamma~mu*gamma~alpha*gamma.mu = (2-dim)*gamma~alpha
+               } else if (other - self == 2
+                       && is_ex_of_type(self[1], clifford)) {
+                       *self = 2 - dim;
+                       *other = _ex1();
+                       return true;
+
+               // gamma~mu*gamma~alpha*gamma~beta*gamma.mu = 4*g~alpha~beta+(dim-4)*gamam~alpha*gamma~beta
+               } 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[1] = _ex1();
+                       self[2] = _ex1();
+                       *other = _ex1();
+                       return true;
+
+               // gamma~mu*gamma~alpha*gamma~beta*gamma~delta*gamma.mu = -2*gamma~delta*gamma~beta*gamma~alpha+(4-dim)*gamma~alpha*gamma~beta*gamma~delta
+               } else if (other - self == 4
+                       && is_ex_of_type(self[1], clifford)
+                       && is_ex_of_type(self[2], clifford)
+                       && is_ex_of_type(self[3], clifford)) {
+                       *self = -2 * self[3] * self[2] * self[1] + (4 - dim) * self[1] * self[2] * self[3];
+                       self[1] = _ex1();
+                       self[2] = _ex1();
+                       self[3] = _ex1();
+                       *other = _ex1();
+                       return true;
+               }
+       }
+
+       return false;
+}
+
 /** Perform automatic simplification on noncommutative product of clifford
- *  objects. */
+ *  objects. This removes superfluous ONEs. */
 ex clifford::simplify_ncmul(const exvector & v) const
 {
-       //!! to be implemented
-       return nonsimplified_ncmul(v);
+       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++;
+       }
+
+       if (s.size() == 0)
+               return clifford(diracone());
+       else if (s.size() == v.size())
+               return simplified_ncmul(v);
+       else
+               return simplified_ncmul(s);
 }
 
 ex clifford::thisexprseq(const exvector & v) const
@@ -116,10 +195,16 @@ ex clifford::thisexprseq(exvector * vp) const
 // global functions
 //////////
 
+ex dirac_one(void)
+{
+       return clifford(diracone());
+}
+
 ex dirac_gamma(const ex & mu)
 {
        if (!is_ex_of_type(mu, varidx))
                throw(std::invalid_argument("index of Dirac gamma must be of type varidx"));
+
        return clifford(diracgamma(), mu);
 }