mirror of
https://github.com/paboyle/Grid.git
synced 2024-11-10 15:55:37 +00:00
589 lines
16 KiB
C++
589 lines
16 KiB
C++
#ifndef GRID_QCD_DIRAC_H
|
|
#define GRID_QCD_DIRAC_H
|
|
namespace Grid{
|
|
|
|
namespace QCD {
|
|
|
|
const int SpinorIndex = 2;
|
|
|
|
class Gamma {
|
|
|
|
public:
|
|
|
|
const int Ns=4;
|
|
|
|
enum GammaMatrix {
|
|
Identity,
|
|
GammaX,
|
|
GammaY,
|
|
GammaZ,
|
|
GammaT,
|
|
Gamma5,
|
|
MinusIdentity,
|
|
MinusGammaX,
|
|
MinusGammaY,
|
|
MinusGammaZ,
|
|
MinusGammaT,
|
|
MinusGamma5
|
|
// GammaXGamma5, // Rest are composite (willing to take hit for two calls sequentially)
|
|
// GammaYGamma5, // as they are less commonly used.
|
|
// GammaZGamma5,
|
|
// GammaTGamma5,
|
|
// SigmaXY,
|
|
// SigmaXZ,
|
|
// SigmaYZ,
|
|
// SigmaXT,
|
|
// SigmaYT,
|
|
// SigmaZT,
|
|
// MinusGammaXGamma5, easiest to form by composition
|
|
// MinusGammaYGamma5, as performance is not critical for these
|
|
// MinusGammaZGamma5,
|
|
// MinusGammaTGamma5,
|
|
// MinusSigmaXY,
|
|
// MinusSigmaXZ,
|
|
// MinusSigmaYZ,
|
|
// MinusSigmaXT,
|
|
// MinusSigmaYT,
|
|
// MinusSigmaZT
|
|
};
|
|
|
|
static GammaMatrix GammaMatrices[];
|
|
static const char *GammaMatrixNames[];
|
|
|
|
Gamma (GammaMatrix g) { _g=g; }
|
|
|
|
GammaMatrix _g;
|
|
|
|
};
|
|
|
|
/* Gx
|
|
* 0 0 0 i
|
|
* 0 0 i 0
|
|
* 0 -i 0 0
|
|
* -i 0 0 0
|
|
*/
|
|
// right multiplication makes sense for matrix args, not for vector since there is
|
|
// no concept of row versus columnar indices
|
|
template<class vtype> inline void rmultMinusGammaX(iMatrix<vtype,Ns> &ret,const iMatrix<vtype,Ns> &rhs){
|
|
for(int i=0;i<Ns;i++){
|
|
ret(i,0) = timesI(rhs(i,3));
|
|
ret(i,1) = timesI(rhs(i,2));
|
|
ret(i,2) = timesMinusI(rhs(i,1));
|
|
ret(i,3) = timesMinusI(rhs(i,0));
|
|
}
|
|
};
|
|
template<class vtype> inline void rmultGammaX(iMatrix<vtype,Ns> &ret, const iMatrix<vtype,Ns> &rhs){
|
|
for(int i=0;i<Ns;i++){
|
|
ret(i,0) = timesMinusI(rhs(i,3));
|
|
ret(i,1) = timesMinusI(rhs(i,2));
|
|
ret(i,2) = timesI(rhs(i,1));
|
|
ret(i,3) = timesI(rhs(i,0));
|
|
}
|
|
};
|
|
template<class vtype> inline void multGammaX(iMatrix<vtype,Ns> &ret, const iMatrix<vtype,Ns> &rhs){
|
|
for(int i=0;i<Ns;i++){
|
|
ret(0,i) = timesI(rhs(3,i));
|
|
ret(1,i) = timesI(rhs(2,i));
|
|
ret(2,i) = timesMinusI(rhs(1,i));
|
|
ret(3,i) = timesMinusI(rhs(0,i));
|
|
}
|
|
};
|
|
template<class vtype> inline void multMinusGammaX(iMatrix<vtype,Ns> &ret, const iMatrix<vtype,Ns> &rhs){
|
|
for(int i=0;i<Ns;i++){
|
|
ret(0,i) = timesMinusI(rhs(3,i));
|
|
ret(1,i) = timesMinusI(rhs(2,i));
|
|
ret(2,i) = timesI(rhs(1,i));
|
|
ret(3,i) = timesI(rhs(0,i));
|
|
}
|
|
};
|
|
|
|
template<class vtype> inline void multGammaX(iVector<vtype,Ns> &ret, const iVector<vtype,Ns> &rhs){
|
|
ret._internal[0] = timesI(rhs._internal[3]);
|
|
ret._internal[1] = timesI(rhs._internal[2]);
|
|
ret._internal[2] = timesMinusI(rhs._internal[1]);
|
|
ret._internal[3] = timesMinusI(rhs._internal[0]);
|
|
};
|
|
template<class vtype> inline void multMinusGammaX(iVector<vtype,Ns> &ret, const iVector<vtype,Ns> &rhs){
|
|
ret(0) = timesMinusI(rhs(3));
|
|
ret(1) = timesMinusI(rhs(2));
|
|
ret(2) = timesI(rhs(1));
|
|
ret(3) = timesI(rhs(0));
|
|
};
|
|
|
|
|
|
/*Gy
|
|
* 0 0 0 -1 [0] -+ [3]
|
|
* 0 0 1 0 [1] +- [2]
|
|
* 0 1 0 0
|
|
* -1 0 0 0
|
|
*/
|
|
template<class vtype> inline void rmultGammaY(iMatrix<vtype,Ns> &ret, const iMatrix<vtype,Ns> &rhs){
|
|
for(int i=0;i<Ns;i++){
|
|
ret(i,0) = -rhs(i,3);
|
|
ret(i,1) = rhs(i,2);
|
|
ret(i,2) = rhs(i,1);
|
|
ret(i,3) = -rhs(i,0);
|
|
}
|
|
};
|
|
template<class vtype> inline void rmultMinusGammaY(iMatrix<vtype,Ns> &ret, const iMatrix<vtype,Ns> &rhs){
|
|
for(int i=0;i<Ns;i++){
|
|
ret(i,0) = rhs(i,3);
|
|
ret(i,1) = -rhs(i,2);
|
|
ret(i,2) = -rhs(i,1);
|
|
ret(i,3) = rhs(i,0);
|
|
}
|
|
};
|
|
template<class vtype> inline void multGammaY(iMatrix<vtype,Ns> &ret, const iMatrix<vtype,Ns> &rhs){
|
|
for(int i=0;i<Ns;i++){
|
|
ret(0,i) = -rhs(3,i);
|
|
ret(1,i) = rhs(2,i);
|
|
ret(2,i) = rhs(1,i);
|
|
ret(3,i) = -rhs(0,i);
|
|
}
|
|
};
|
|
template<class vtype> inline void multMinusGammaY(iMatrix<vtype,Ns> &ret, const iMatrix<vtype,Ns> &rhs){
|
|
for(int i=0;i<Ns;i++){
|
|
ret(0,i) = rhs(3,i);
|
|
ret(1,i) = -rhs(2,i);
|
|
ret(2,i) = -rhs(1,i);
|
|
ret(3,i) = rhs(0,i);
|
|
}
|
|
};
|
|
template<class vtype> inline void multGammaY(iVector<vtype,Ns> &ret, const iVector<vtype,Ns> &rhs){
|
|
ret(0) = -rhs(3);
|
|
ret(1) = rhs(2);
|
|
ret(2) = rhs(1);
|
|
ret(3) = -rhs(0);
|
|
};
|
|
template<class vtype> inline void multMinusGammaY(iVector<vtype,Ns> &ret, const iVector<vtype,Ns> &rhs){
|
|
ret(0) = rhs(3);
|
|
ret(1) = -rhs(2);
|
|
ret(2) = -rhs(1);
|
|
ret(3) = rhs(0);
|
|
};
|
|
/*Gz
|
|
* 0 0 i 0 [0]+-i[2]
|
|
* 0 0 0 -i [1]-+i[3]
|
|
* -i 0 0 0
|
|
* 0 i 0 0
|
|
*/
|
|
template<class vtype> inline void rmultGammaZ(iMatrix<vtype,Ns> &ret, const iMatrix<vtype,Ns> &rhs){
|
|
for(int i=0;i<Ns;i++){
|
|
ret(i,0) = timesMinusI(rhs(i,2));
|
|
ret(i,1) = timesI(rhs(i,3));
|
|
ret(i,2) = timesI(rhs(i,0));
|
|
ret(i,3) = timesMinusI(rhs(i,1));
|
|
}
|
|
};
|
|
template<class vtype> inline void rmultMinusGammaZ(iMatrix<vtype,Ns> &ret, const iMatrix<vtype,Ns> &rhs){
|
|
for(int i=0;i<Ns;i++){
|
|
ret(i,0) = timesI(rhs(i,2));
|
|
ret(i,1) = timesMinusI(rhs(i,3));
|
|
ret(i,2) = timesMinusI(rhs(i,0));
|
|
ret(i,3) = timesI(rhs(i,1));
|
|
}
|
|
};
|
|
template<class vtype> inline void multGammaZ(iMatrix<vtype,Ns> &ret, const iMatrix<vtype,Ns> &rhs){
|
|
for(int i=0;i<Ns;i++){
|
|
ret(0,i) = timesI(rhs(2,i));
|
|
ret(1,i) =timesMinusI(rhs(3,i));
|
|
ret(2,i) =timesMinusI(rhs(0,i));
|
|
ret(3,i) = timesI(rhs(1,i));
|
|
}
|
|
};
|
|
template<class vtype> inline void multMinusGammaZ(iMatrix<vtype,Ns> &ret, const iMatrix<vtype,Ns> &rhs){
|
|
for(int i=0;i<Ns;i++){
|
|
ret(0,i) = timesMinusI(rhs(2,i));
|
|
ret(1,i) = timesI(rhs(3,i));
|
|
ret(2,i) = timesI(rhs(0,i));
|
|
ret(3,i) = timesMinusI(rhs(1,i));
|
|
}
|
|
};
|
|
template<class vtype> inline void multGammaZ(iVector<vtype,Ns> &ret, const iVector<vtype,Ns> &rhs){
|
|
ret(0) = timesI(rhs(2));
|
|
ret(1) =timesMinusI(rhs(3));
|
|
ret(2) =timesMinusI(rhs(0));
|
|
ret(3) = timesI(rhs(1));
|
|
};
|
|
template<class vtype> inline void multMinusGammaZ(iVector<vtype,Ns> &ret, const iVector<vtype,Ns> &rhs){
|
|
ret(0) = timesMinusI(rhs(2));
|
|
ret(1) = timesI(rhs(3));
|
|
ret(2) = timesI(rhs(0));
|
|
ret(3) = timesMinusI(rhs(1));
|
|
};
|
|
/*Gt
|
|
* 0 0 1 0 [0]+-[2]
|
|
* 0 0 0 1 [1]+-[3]
|
|
* 1 0 0 0
|
|
* 0 1 0 0
|
|
*/
|
|
template<class vtype> inline void rmultGammaT(iMatrix<vtype,Ns> &ret, const iMatrix<vtype,Ns> &rhs){
|
|
for(int i=0;i<Ns;i++){
|
|
ret(i,0) = rhs(i,2);
|
|
ret(i,1) = rhs(i,3);
|
|
ret(i,2) = rhs(i,0);
|
|
ret(i,3) = rhs(i,1);
|
|
}
|
|
};
|
|
template<class vtype> inline void rmultMinusGammaT(iMatrix<vtype,Ns> &ret, const iMatrix<vtype,Ns> &rhs){
|
|
for(int i=0;i<Ns;i++){
|
|
ret(i,0) =- rhs(i,2);
|
|
ret(i,1) =- rhs(i,3);
|
|
ret(i,2) =- rhs(i,0);
|
|
ret(i,3) =- rhs(i,1);
|
|
}
|
|
};
|
|
template<class vtype> inline void multGammaT(iMatrix<vtype,Ns> &ret, const iMatrix<vtype,Ns> &rhs){
|
|
for(int i=0;i<Ns;i++){
|
|
ret(0,i) = rhs(2,i);
|
|
ret(1,i) = rhs(3,i);
|
|
ret(2,i) = rhs(0,i);
|
|
ret(3,i) = rhs(1,i);
|
|
}
|
|
};
|
|
template<class vtype> inline void multMinusGammaT(iMatrix<vtype,Ns> &ret, const iMatrix<vtype,Ns> &rhs){
|
|
for(int i=0;i<Ns;i++){
|
|
ret(0,i) =-rhs(2,i);
|
|
ret(1,i) =-rhs(3,i);
|
|
ret(2,i) =-rhs(0,i);
|
|
ret(3,i) =-rhs(1,i);
|
|
}
|
|
};
|
|
template<class vtype> inline void multGammaT(iVector<vtype,Ns> &ret, const iVector<vtype,Ns> &rhs){
|
|
ret(0) = rhs(2);
|
|
ret(1) = rhs(3);
|
|
ret(2) = rhs(0);
|
|
ret(3) = rhs(1);
|
|
};
|
|
template<class vtype> inline void multMinusGammaT(iVector<vtype,Ns> &ret, const iVector<vtype,Ns> &rhs){
|
|
ret(0) =-rhs(2);
|
|
ret(1) =-rhs(3);
|
|
ret(2) =-rhs(0);
|
|
ret(3) =-rhs(1);
|
|
};
|
|
/*G5
|
|
* 1 0 0 0 [0]+-[2]
|
|
* 0 1 0 0 [1]+-[3]
|
|
* 0 0 -1 0
|
|
* 0 0 0 -1
|
|
*/
|
|
template<class vtype> inline void rmultGamma5(iMatrix<vtype,Ns> &ret, const iMatrix<vtype,Ns> &rhs){
|
|
for(int i=0;i<Ns;i++){
|
|
ret(i,0) = rhs(i,0);
|
|
ret(i,1) = rhs(i,1);
|
|
ret(i,2) =-rhs(i,2);
|
|
ret(i,3) =-rhs(i,3);
|
|
}
|
|
};
|
|
template<class vtype> inline void rmultMinusGamma5(iMatrix<vtype,Ns> &ret, const iMatrix<vtype,Ns> &rhs){
|
|
for(int i=0;i<Ns;i++){
|
|
ret(i,0) =-rhs(i,0);
|
|
ret(i,1) =-rhs(i,1);
|
|
ret(i,2) = rhs(i,2);
|
|
ret(i,3) = rhs(i,3);
|
|
}
|
|
};
|
|
|
|
template<class vtype> inline void multGamma5(iMatrix<vtype,Ns> &ret, const iMatrix<vtype,Ns> &rhs){
|
|
for(int i=0;i<Ns;i++){
|
|
ret(0,i) = rhs(0,i);
|
|
ret(1,i) = rhs(1,i);
|
|
ret(2,i) =-rhs(2,i);
|
|
ret(3,i) =-rhs(3,i);
|
|
}
|
|
};
|
|
template<class vtype> inline void multMinusGamma5(iMatrix<vtype,Ns> &ret, const iMatrix<vtype,Ns> &rhs){
|
|
for(int i=0;i<Ns;i++){
|
|
ret(0,i) =-rhs(0,i);
|
|
ret(1,i) =-rhs(1,i);
|
|
ret(2,i) = rhs(2,i);
|
|
ret(3,i) = rhs(3,i);
|
|
}
|
|
};
|
|
|
|
template<class vtype> inline void multGamma5(iVector<vtype,Ns> &ret, const iVector<vtype,Ns> &rhs){
|
|
ret(0) = rhs(0);
|
|
ret(1) = rhs(1);
|
|
ret(2) =-rhs(2);
|
|
ret(3) =-rhs(3);
|
|
};
|
|
template<class vtype> inline void multMinusGamma5(iVector<vtype,Ns> &ret, const iVector<vtype,Ns> &rhs){
|
|
ret(0) =-rhs(0);
|
|
ret(1) =-rhs(1);
|
|
ret(2) = rhs(2);
|
|
ret(3) = rhs(3);
|
|
};
|
|
|
|
|
|
|
|
#ifdef GRID_WARN_SUBOPTIMAL
|
|
#warning "Optimisation alert switch over to multGammaX early "
|
|
#endif
|
|
|
|
///////////////////////////////////////////////////////////////////////////////////////////////////
|
|
// Operator * : first case this is not a spin index, so recurse
|
|
///////////////////////////////////////////////////////////////////////////////////////////////////
|
|
|
|
// FIXME
|
|
//
|
|
// Optimisation; switch over to a "multGammaX(ret._internal,arg._internal)" style early and
|
|
// note that doing so from the lattice operator will avoid copy back and case switch overhead, as
|
|
// was done for the tensor math operator to remove operator * notation early
|
|
//
|
|
|
|
//left multiply
|
|
template<class vtype> inline auto operator * ( const Gamma &G,const iScalar<vtype> &arg) ->
|
|
typename std::enable_if<matchGridTensorIndex<iScalar<vtype>,SpinorIndex>::notvalue,iScalar<vtype> >::type
|
|
|
|
{
|
|
iScalar<vtype> ret;
|
|
ret._internal=G*arg._internal;
|
|
return ret;
|
|
}
|
|
template<class vtype,int N> inline auto operator * ( const Gamma &G,const iVector<vtype,N> &arg) ->
|
|
typename std::enable_if<matchGridTensorIndex<iVector<vtype,N>,SpinorIndex>::notvalue,iVector<vtype,N> >::type
|
|
{
|
|
iVector<vtype,N> ret;
|
|
ret._internal=G*arg._internal;
|
|
return ret;
|
|
}
|
|
template<class vtype,int N> inline auto operator * ( const Gamma &G,const iMatrix<vtype,N> &arg) ->
|
|
typename std::enable_if<matchGridTensorIndex<iMatrix<vtype,N>,SpinorIndex>::notvalue,iMatrix<vtype,N> >::type
|
|
{
|
|
iMatrix<vtype,N> ret;
|
|
ret._internal=G*arg._internal;
|
|
return ret;
|
|
}
|
|
|
|
|
|
//right multiply
|
|
template<class vtype> inline auto operator * (const iScalar<vtype> &arg, const Gamma &G) ->
|
|
typename std::enable_if<matchGridTensorIndex<iScalar<vtype>,SpinorIndex>::notvalue,iScalar<vtype> >::type
|
|
|
|
{
|
|
iScalar<vtype> ret;
|
|
ret._internal=arg._internal*G;
|
|
return ret;
|
|
}
|
|
template<class vtype,int N> inline auto operator * (const iVector<vtype,N> &arg, const Gamma &G) ->
|
|
typename std::enable_if<matchGridTensorIndex<iVector<vtype,N>,SpinorIndex>::notvalue,iVector<vtype,N> >::type
|
|
{
|
|
iVector<vtype,N> ret;
|
|
ret._internal=arg._internal*G;
|
|
return ret;
|
|
}
|
|
template<class vtype,int N> inline auto operator * (const iMatrix<vtype,N> &arg, const Gamma &G) ->
|
|
typename std::enable_if<matchGridTensorIndex<iMatrix<vtype,N>,SpinorIndex>::notvalue,iMatrix<vtype,N> >::type
|
|
{
|
|
iMatrix<vtype,N> ret;
|
|
ret._internal=arg._internal*G;
|
|
return ret;
|
|
}
|
|
|
|
////////////////////////////////////////////////////////
|
|
// When we hit the spin index this matches and we stop
|
|
////////////////////////////////////////////////////////
|
|
template<class vtype> inline auto operator * ( const Gamma &G,const iMatrix<vtype,Ns> &arg) ->
|
|
typename std::enable_if<matchGridTensorIndex<iMatrix<vtype,Ns>,SpinorIndex>::value,iMatrix<vtype,Ns> >::type
|
|
{
|
|
iMatrix<vtype,Ns> ret;
|
|
switch (G._g) {
|
|
case Gamma::Identity:
|
|
ret = arg;
|
|
break;
|
|
case Gamma::MinusIdentity:
|
|
ret = -arg;
|
|
break;
|
|
case Gamma::GammaX:
|
|
multGammaX(ret,arg);
|
|
break;
|
|
case Gamma::MinusGammaX:
|
|
multMinusGammaX(ret,arg);
|
|
break;
|
|
case Gamma::GammaY:
|
|
multGammaY(ret,arg);
|
|
break;
|
|
case Gamma::MinusGammaY:
|
|
multMinusGammaY(ret,arg);
|
|
break;
|
|
case Gamma::GammaZ:
|
|
multGammaZ(ret,arg);
|
|
break;
|
|
case Gamma::MinusGammaZ:
|
|
multMinusGammaZ(ret,arg);
|
|
break;
|
|
case Gamma::GammaT:
|
|
multGammaT(ret,arg);
|
|
break;
|
|
case Gamma::MinusGammaT:
|
|
multMinusGammaT(ret,arg);
|
|
break;
|
|
case Gamma::Gamma5:
|
|
multGamma5(ret,arg);
|
|
break;
|
|
case Gamma::MinusGamma5:
|
|
multMinusGamma5(ret,arg);
|
|
break;
|
|
default:
|
|
assert(0);
|
|
break;
|
|
}
|
|
return ret;
|
|
}
|
|
// Could have used type trait for Matrix/vector and then an enable if to share code
|
|
template<class vtype> inline auto operator * ( const Gamma &G,const iVector<vtype,Ns> &arg) ->
|
|
typename std::enable_if<matchGridTensorIndex<iVector<vtype,Ns>,SpinorIndex>::value,iVector<vtype,Ns> >::type
|
|
{
|
|
iVector<vtype,Ns> ret;
|
|
switch (G._g) {
|
|
case Gamma::Identity:
|
|
ret = arg;
|
|
break;
|
|
case Gamma::MinusIdentity:
|
|
ret = -arg;
|
|
break;
|
|
case Gamma::GammaX:
|
|
multGammaX(ret,arg);
|
|
break;
|
|
case Gamma::MinusGammaX:
|
|
multMinusGammaX(ret,arg);
|
|
break;
|
|
case Gamma::GammaY:
|
|
multGammaY(ret,arg);
|
|
break;
|
|
case Gamma::MinusGammaY:
|
|
multMinusGammaY(ret,arg);
|
|
break;
|
|
case Gamma::GammaZ:
|
|
multGammaZ(ret,arg);
|
|
break;
|
|
case Gamma::MinusGammaZ:
|
|
multMinusGammaZ(ret,arg);
|
|
break;
|
|
case Gamma::GammaT:
|
|
multGammaT(ret,arg);
|
|
break;
|
|
case Gamma::MinusGammaT:
|
|
multMinusGammaT(ret,arg);
|
|
break;
|
|
case Gamma::Gamma5:
|
|
multGamma5(ret,arg);
|
|
break;
|
|
case Gamma::MinusGamma5:
|
|
multMinusGamma5(ret,arg);
|
|
break;
|
|
default:
|
|
assert(0);
|
|
break;
|
|
}
|
|
return ret;
|
|
}
|
|
|
|
template<class vtype> inline auto operator * (const iMatrix<vtype,Ns> &arg, const Gamma &G) ->
|
|
typename std::enable_if<matchGridTensorIndex<iMatrix<vtype,Ns>,SpinorIndex>::value,iMatrix<vtype,Ns> >::type
|
|
{
|
|
iMatrix<vtype,Ns> ret;
|
|
switch (G._g) {
|
|
case Gamma::Identity:
|
|
ret = arg;
|
|
break;
|
|
case Gamma::MinusIdentity:
|
|
ret = -arg;
|
|
break;
|
|
case Gamma::GammaX:
|
|
rmultGammaX(ret,arg);
|
|
break;
|
|
case Gamma::MinusGammaX:
|
|
rmultMinusGammaX(ret,arg);
|
|
break;
|
|
case Gamma::GammaY:
|
|
rmultGammaY(ret,arg);
|
|
break;
|
|
case Gamma::MinusGammaY:
|
|
rmultMinusGammaY(ret,arg);
|
|
break;
|
|
case Gamma::GammaZ:
|
|
rmultGammaZ(ret,arg);
|
|
break;
|
|
case Gamma::MinusGammaZ:
|
|
rmultMinusGammaZ(ret,arg);
|
|
break;
|
|
case Gamma::GammaT:
|
|
rmultGammaT(ret,arg);
|
|
break;
|
|
case Gamma::MinusGammaT:
|
|
rmultMinusGammaT(ret,arg);
|
|
break;
|
|
case Gamma::Gamma5:
|
|
rmultGamma5(ret,arg);
|
|
break;
|
|
case Gamma::MinusGamma5:
|
|
rmultMinusGamma5(ret,arg);
|
|
break;
|
|
default:
|
|
assert(0);
|
|
break;
|
|
}
|
|
return ret;
|
|
}
|
|
|
|
|
|
/* Output from test
|
|
./Grid_gamma
|
|
Identity((1,0),(0,0),(0,0),(0,0))
|
|
((0,0),(1,0),(0,0),(0,0))
|
|
((0,0),(0,0),(1,0),(0,0))
|
|
((0,0),(0,0),(0,0),(1,0)) OK
|
|
|
|
GammaX ((0,0),(0,0),(0,0),(0,1))
|
|
((0,0),(0,0),(0,1),(0,0))
|
|
((0,0),(0,-1),(0,0),(0,0))
|
|
((0,-1),(0,0),(0,0),(0,0)) OK
|
|
* Gx
|
|
* 0 0 0 i
|
|
* 0 0 i 0
|
|
* 0 -i 0 0
|
|
* -i 0 0 0
|
|
|
|
GammaY ((-0,-0),(-0,-0),(-0,-0),(-1,-0))
|
|
((0,0),(0,0),(1,0),(0,0))
|
|
((0,0),(1,0),(0,0),(0,0)) OK
|
|
((-1,-0),(-0,-0),(-0,-0),(-0,-0))
|
|
*Gy
|
|
* 0 0 0 -1 [0] -+ [3]
|
|
* 0 0 1 0 [1] +- [2]
|
|
* 0 1 0 0
|
|
* -1 0 0 0
|
|
|
|
GammaZ ((0,0),(0,0),(0,1),(0,0))
|
|
((0,0),(0,0),(0,0),(0,-1))
|
|
((0,-1),(0,0),(0,0),(0,0))
|
|
((0,0),(0,1),(0,0),(0,0)) OK
|
|
* 0 0 i 0 [0]+-i[2]
|
|
* 0 0 0 -i [1]-+i[3]
|
|
* -i 0 0 0
|
|
* 0 i 0 0
|
|
|
|
GammaT ((0,0),(0,0),(1,0),(0,0))
|
|
((0,0),(0,0),(0,0),(1,0)) OK
|
|
((1,0),(0,0),(0,0),(0,0))
|
|
((0,0),(1,0),(0,0),(0,0))
|
|
* 0 0 1 0 [0]+-[2]
|
|
* 0 0 0 1 [1]+-[3]
|
|
* 1 0 0 0
|
|
* 0 1 0 0
|
|
|
|
Gamma5 ((1,0),(0,0),(0,0),(0,0))
|
|
((0,0),(1,0),(0,0),(0,0))
|
|
((-0,-0),(-0,-0),(-1,-0),(-0,-0))
|
|
((-0,-0),(-0,-0),(-0,-0),(-1,-0))
|
|
* 1 0 0 0 [0]+-[2]
|
|
* 0 1 0 0 [1]+-[3] OK
|
|
* 0 0 -1 0
|
|
* 0 0 0 -1
|
|
*/
|
|
|
|
} //namespace QCD
|
|
} // Grid
|
|
#endif
|