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
DEFAULT_CTORS(diracone)
DEFAULT_CTORS(diracgamma)
DEFAULT_CTORS(diracgamma5)
+DEFAULT_CTORS(diracgammaL)
+DEFAULT_CTORS(diracgammaR)
//////////
// other constructors
DEFAULT_ARCHIVING(diracone)
DEFAULT_ARCHIVING(diracgamma)
DEFAULT_ARCHIVING(diracgamma5)
+DEFAULT_ARCHIVING(diracgammaL)
+DEFAULT_ARCHIVING(diracgammaR)
//////////
// functions overriding virtual functions from base classes
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))
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)
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
}
/** 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
+ex clifford::eval_ncmul(const exvector & v) const
{
exvector s;
s.reserve(v.size());
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;
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
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;
}
}
}
return clifford(diracgamma5(), rl);
}
-ex dirac_gamma6(unsigned char rl)
+ex dirac_gammaL(unsigned char rl)
{
- return clifford(diracone(), rl) + clifford(diracgamma5(), rl);
+ return clifford(diracgammaL(), rl);
}
-ex dirac_gamma7(unsigned char rl)
+ex dirac_gammaR(unsigned char rl)
{
- return clifford(diracone(), rl) - clifford(diracgamma5(), rl);
+ return clifford(diracgammaR(), rl);
}
ex dirac_slash(const ex & e, const ex & dim, unsigned char rl)
{
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;
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);
void print(const print_context & c, unsigned level = 0) const;
protected:
+ ex eval_ncmul(const exvector & v) const;
bool match_same_type(const basic & other) const;
- ex simplify_ncmul(const exvector & v) const;
ex thisexprseq(const exvector & v) const;
ex thisexprseq(exvector * vp) const;
unsigned return_type(void) const { return return_types::noncommutative; }
};
+/** 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. */
* @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);
-/** This returns (dirac_ONE(rl) - dirac_gamma5(rl)). */
-ex dirac_gamma7(unsigned char rl = 0);
+/** Create a Dirac gammaR object.
+ *
+ * @param rl Representation label
+ * @return newly constructed object */
+ex dirac_gammaR(unsigned char rl = 0);
/** Create a term of the form e_mu * gamma~mu with a unique index mu.
*
git://www.ginac.de / ginac.git / commitdiff