X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fclifford.cpp;h=8a8bfe09294e942e88023d0770784f09d5d9f289;hp=06d9e5415a361d95b3305133e1032f84c10bae52;hb=43e0a8f5ca5e1c48cef5daaf014acdbca4e44568;hpb=e58f5808a2d0fe6cb9d60370ede700d97a8bb702

diff --git a/ginac/clifford.cpp b/ginac/clifford.cpp
index 06d9e541..8a8bfe09 100644
--- a/ginac/clifford.cpp
+++ b/ginac/clifford.cpp
@@ -24,6 +24,7 @@
 #include "ex.h"
 #include "idx.h"
 #include "ncmul.h"
+#include "symbol.h"
 #include "print.h"
 #include "archive.h"
 #include "debugmsg.h"
@@ -145,9 +146,10 @@ 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
 {
-	GINAC_ASSERT(is_ex_of_type(*self, indexed));
+	GINAC_ASSERT(is_ex_of_type(*self, clifford));
 	GINAC_ASSERT(is_ex_of_type(*other, indexed));
 	GINAC_ASSERT(is_ex_of_type(self->op(0), diracgamma));
+	unsigned char rl = ex_to_clifford(*self).get_representation_label();
 
 	if (is_ex_of_type(other->op(0), diracgamma)) {
 
@@ -156,7 +158,7 @@ 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(rl);
 			return true;
 
 		// gamma~mu*gamma~alpha*gamma.mu = (2-dim)*gamma~alpha
@@ -170,7 +172,7 @@ 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(rl) + (dim - 4) * self[1] * self[2];
 			self[1] = _ex1();
 			self[2] = _ex1();
 			*other = _ex1();
@@ -200,6 +202,7 @@ ex clifford::simplify_ncmul(const exvector & v) const
 {
 	exvector s;
 	s.reserve(v.size());
+	unsigned rl = ex_to_clifford(v[0]).get_representation_label();
 
 	// Remove superfluous ONEs
 	exvector::const_iterator cit = v.begin(), citend = v.end();
@@ -251,7 +254,7 @@ ex clifford::simplify_ncmul(const exvector & v) const
 				const ex & ib = b.op(1);
 				if (ia.is_equal(ib)) {
 					a = lorentz_g(ia, ib);
-					b = dirac_ONE();
+					b = dirac_ONE(rl);
 					something_changed = true;
 				}
 			}
@@ -260,7 +263,7 @@ ex clifford::simplify_ncmul(const exvector & v) const
 	}
 
 	if (s.size() == 0)
-		return clifford(diracone()) * sign;
+		return clifford(diracone(), rl) * sign;
 	if (something_changed)
 		return nonsimplified_ncmul(s) * sign;
 	else
@@ -299,4 +302,126 @@ ex dirac_gamma5(unsigned char rl)
 	return clifford(diracgamma5(), rl);
 }
 
+ex dirac_slash(const ex & e, const ex & dim, unsigned char rl)
+{
+	varidx mu((new symbol)->setflag(status_flags::dynallocated), dim);
+	return indexed(e, mu.toggle_variance()) * dirac_gamma(mu, rl);
+}
+
+/** Check whether a given tinfo key (as returned by return_type_tinfo()
+ *  is that of a clifford object with the specified representation label. */
+static bool is_clifford_tinfo(unsigned ti, unsigned char rl)
+{
+	return ti == (TINFO_clifford + rl);
+}
+
+ex dirac_trace(const ex & e, unsigned char rl)
+{
+	if (is_ex_of_type(e, clifford)) {
+
+		if (ex_to_clifford(e).get_representation_label() == rl
+		 && is_ex_of_type(e.op(0), diracone))
+			return _ex4();
+		else
+			return _ex0();
+
+	} else if (is_ex_exactly_of_type(e, add)) {
+
+		// Trace of sum = sum of traces
+		ex sum = _ex0();
+		for (unsigned i=0; i<e.nops(); i++)
+			sum += dirac_trace(e.op(i), rl);
+		return sum;
+
+	} else if (is_ex_exactly_of_type(e, mul)) {
+
+		// Trace of product: pull out non-clifford factors
+		ex prod = _ex1();
+		for (unsigned i=0; i<e.nops(); i++) {
+			const ex &o = e.op(i);
+			unsigned ti = o.return_type_tinfo();
+			if (is_clifford_tinfo(o.return_type_tinfo(), rl))
+				prod *= dirac_trace(o, rl);
+			else
+				prod *= o;
+		}
+		return prod;
+
+	} else if (is_ex_exactly_of_type(e, ncmul)) {
+
+		if (!is_clifford_tinfo(e.return_type_tinfo(), rl))
+			return _ex0();
+
+		// Expand product, if necessary
+		ex e_expanded = e.expand();
+		if (!is_ex_of_type(e_expanded, ncmul))
+			return dirac_trace(e_expanded, rl);
+
+		// gamma5 gets moved to the front so this check is enough
+		bool has_gamma5 = is_ex_of_type(e.op(0).op(0), diracgamma5);
+		unsigned num = e.nops();
+
+		if (has_gamma5) {
+
+			// Trace of gamma5 * odd number of gammas and trace of
+			// gamma5 * gamma_mu * gamma_nu are zero
+			if ((num & 1) == 0 || num == 3)
+				return _ex0();
+
+			// Tr gamma5 S_2k =
+			//   epsilon0123_mu1_mu2_mu3_mu4 * Tr gamma_mu1 gamma_mu2 gamma_mu3 gamma_mu4 S_2k
+			ex dim = ex_to_idx(e.op(1).op(1)).get_dim();
+			varidx mu1((new symbol)->setflag(status_flags::dynallocated), dim),
+			       mu2((new symbol)->setflag(status_flags::dynallocated), dim),
+			       mu3((new symbol)->setflag(status_flags::dynallocated), dim),
+			       mu4((new symbol)->setflag(status_flags::dynallocated), dim);
+			exvector v;
+			v.reserve(num + 3);
+			v.push_back(dirac_gamma(mu1, rl));
+			v.push_back(dirac_gamma(mu2, rl));
+			v.push_back(dirac_gamma(mu3, rl));
+			v.push_back(dirac_gamma(mu4, rl));
+			for (int i=1; i<num; i++)
+				v.push_back(e.op(i));
+
+			return (eps0123(mu1.toggle_variance(), mu2.toggle_variance(), mu3.toggle_variance(), mu4.toggle_variance()) *
+			        dirac_trace(ncmul(v), rl)).simplify_indexed() / 24;
+
+		} else { // no gamma5
+
+			// Trace of odd number of gammas is zero
+			if ((num & 1) == 1)
+				return _ex0();
+
+			// Tr gamma_mu gamma_nu = 4 g_mu_nu
+			if (num == 2)
+				return 4 * lorentz_g(e.op(0).op(1), e.op(1).op(1));
+
+			// Traces of 4 or more gammas are computed recursively:
+			// Tr gamma_mu1 gamma_mu2 ... gamma_mun =
+			//   + eta_mu1_mu2 * Tr gamma_mu3 ... gamma_mun
+			//   - eta_mu1_mu3 * Tr gamma_mu2 gamma_mu4 ... gamma_mun
+			//   + eta_mu1_mu4 * Tr gamma_mu3 gamma_mu3 gamma_mu5 ... gamma_mun
+			//   - ...
+			//   + eta_mu1_mun * Tr gamma_mu2 ... gamma_mu(n-1)
+			exvector v(num - 2);
+			int sign = 1;
+			const ex &ix1 = e.op(0).op(1);
+			ex result;
+			for (int i=1; i<num; i++) {
+				for (int n=1, j=0; n<num; n++) {
+					if (n == i)
+						continue;
+					v[j++] = e.op(n);
+				}
+				result += sign * lorentz_g(ix1, e.op(i).op(1)) * dirac_trace(ncmul(v), rl);
+				sign = -sign;
+			}
+			return result;
+		}
+	}
+
+	return _ex0();
+}
+
 } // namespace GiNaC