X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fclifford.cpp;h=8a8bfe09294e942e88023d0770784f09d5d9f289;hp=94f434a7710da07db1625332d7fae96b8968c095;hb=43e0a8f5ca5e1c48cef5daaf014acdbca4e44568;hpb=61b8ecb02c8212efbc15f59face8a9c620dc823c

diff --git a/ginac/clifford.cpp b/ginac/clifford.cpp
index 94f434a7..8a8bfe09 100644
--- a/ginac/clifford.cpp
+++ b/ginac/clifford.cpp
@@ -24,6 +24,8 @@
 #include "ex.h"
 #include "idx.h"
 #include "ncmul.h"
+#include "symbol.h"
+#include "print.h"
 #include "archive.h"
 #include "debugmsg.h"
 #include "utils.h"
@@ -35,54 +37,61 @@ 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)
-{
-	debugmsg("clifford constructor from ex", LOGLEVEL_CONSTRUCT);
-	tinfo_key = TINFO_clifford;
-}
-
-clifford::clifford(const exvector & v, bool discardable) : inherited(indexed::unknown, v, discardable)
+clifford::clifford(unsigned char rl, const exvector & v, bool discardable) : inherited(indexed::unknown, v, discardable), representation_label(rl)
 {
-	debugmsg("clifford constructor from exvector", LOGLEVEL_CONSTRUCT);
+	debugmsg("clifford constructor from unsigned char,exvector", LOGLEVEL_CONSTRUCT);
 	tinfo_key = TINFO_clifford;
 }
 
-clifford::clifford(exvector * vp) : inherited(indexed::unknown, vp)
+clifford::clifford(unsigned char rl, exvector * vp) : inherited(indexed::unknown, vp), representation_label(rl)
 {
-	debugmsg("clifford constructor from exvector *", LOGLEVEL_CONSTRUCT);
+	debugmsg("clifford constructor from unsigned char,exvector *", LOGLEVEL_CONSTRUCT);
 	tinfo_key = TINFO_clifford;
 }
 
@@ -90,9 +99,24 @@ 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
@@ -100,32 +124,69 @@ 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
 {
-	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)) {
 
+		ex dim = ex_to_idx(self->op(1)).get_dim();
+
 		// gamma~mu*gamma.mu = dim*ONE
 		if (other - self == 1) {
-			*self = ex_to_idx(self->op(1)).get_dim();
-			*other = dirac_one();
+			*self = dim;
+			*other = dirac_ONE(rl);
 			return true;
 
 		// gamma~mu*gamma~alpha*gamma.mu = (2-dim)*gamma~alpha
-		} else if (other - self == 2) {
-			*self = 2 - ex_to_idx(self->op(1)).get_dim();
+		} 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(rl) + (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;
 		}
@@ -135,52 +196,232 @@ 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());
+	unsigned rl = ex_to_clifford(v[0]).get_representation_label();
+
+	// 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;
+	}
 
-	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 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(rl);
+					something_changed = true;
+				}
+			}
+			it++;
+		}
 	}
 
 	if (s.size() == 0)
-		return clifford(diracone());
-	else if (s.size() == v.size())
-		return simplified_ncmul(v);
+		return clifford(diracone(), rl) * 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);
+}
+
+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