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su3spinor.h
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/* **********************************************************************
*
* Copyright (C) 2003 Ines Wetzorke
*
* This file is part of tmLQCD.
*
* tmLQCD is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* tmLQCD is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with tmLQCD. If not, see <http://www.gnu.org/licenses/>.
********************************************************************** */
#ifndef _SU3SPINOR_H
#define _SU3SPINOR_H
/* ******************************************************************************
*
* Macros for SU(3) spinors
*
* Arguments are variables of type spinor,
* gamma matrices in the chiral representation
*
* _spinor_null(r)
* _spinor_prod_re(r,s)
* _spinor_mul_complex(r,c,s)
* _gamma0(r,s)
* _gamma1(r,s)
* _gamma2(r,s)
* _gamma3(r,s)
* _gamma5(r,s)
* _gamma50(r,s)
* _gamma51(r,s)
* _gamma52(r,s)
* _gamma53(r,s)
*
*
****************************************************************************** */
#include "su3.h"
/*
* r.s0 = 0
* r.s1 = 0 for each color index
* r.s2 = 0
* r.s3 = 0
*/
#define _spinor_null(r) \
(r).s0.c0 = 0.0; \
(r).s0.c1 = 0.0; \
(r).s0.c2 = 0.0; \
(r).s1.c0 = 0.0; \
(r).s1.c1 = 0.0; \
(r).s1.c2 = 0.0; \
(r).s2.c0 = 0.0; \
(r).s2.c1 = 0.0; \
(r).s2.c2 = 0.0; \
(r).s3.c0 = 0.0; \
(r).s3.c1 = 0.0; \
(r).s3.c2 = 0.0;
/*
* Real part of the scalar product (r,s)
*/
#define _spinor_prod_re(r,s) \
creal((r).s0.c0) * creal((s).s0.c0) + cimag((r).s0.c0) * cimag((s).s0.c0) + \
creal((r).s0.c1) * creal((s).s0.c1) + cimag((r).s0.c1) * cimag((s).s0.c1) + \
creal((r).s0.c2) * creal((s).s0.c2) + cimag((r).s0.c2) * cimag((s).s0.c2) + \
creal((r).s1.c0) * creal((s).s1.c0) + cimag((r).s1.c0) * cimag((s).s1.c0) + \
creal((r).s1.c1) * creal((s).s1.c1) + cimag((r).s1.c1) * cimag((s).s1.c1) + \
creal((r).s1.c2) * creal((s).s1.c2) + cimag((r).s1.c2) * cimag((s).s1.c2) + \
creal((r).s2.c0) * creal((s).s2.c0) + cimag((r).s2.c0) * cimag((s).s2.c0) + \
creal((r).s2.c1) * creal((s).s2.c1) + cimag((r).s2.c1) * cimag((s).s2.c1) + \
creal((r).s2.c2) * creal((s).s2.c2) + cimag((r).s2.c2) * cimag((s).s2.c2) + \
creal((r).s3.c0) * creal((s).s3.c0) + cimag((r).s3.c0) * cimag((s).s3.c0) + \
creal((r).s3.c1) * creal((s).s3.c1) + cimag((r).s3.c1) * cimag((s).s3.c1) + \
creal((r).s3.c2) * creal((s).s3.c2) + cimag((r).s3.c2) * cimag((s).s3.c2)
/*
* Imaginary part of the scalar product (r,s)
*/
#define _spinor_prod_im(r,s) \
-creal((r).s0.c0) * cimag((s).s0.c0) + cimag((r).s0.c0) * creal((s).s0.c0) - \
creal((r).s0.c1) * cimag((s).s0.c1) + cimag((r).s0.c1) * creal((s).s0.c1) - \
creal((r).s0.c2) * cimag((s).s0.c2) + cimag((r).s0.c2) * creal((s).s0.c2) - \
creal((r).s1.c0) * cimag((s).s1.c0) + cimag((r).s1.c0) * creal((s).s1.c0) - \
creal((r).s1.c1) * cimag((s).s1.c1) + cimag((r).s1.c1) * creal((s).s1.c1) - \
creal((r).s1.c2) * cimag((s).s1.c2) + cimag((r).s1.c2) * creal((s).s1.c2) - \
creal((r).s2.c0) * cimag((s).s2.c0) + cimag((r).s2.c0) * creal((s).s2.c0) - \
creal((r).s2.c1) * cimag((s).s2.c1) + cimag((r).s2.c1) * creal((s).s2.c1) - \
creal((r).s2.c2) * cimag((s).s2.c2) + cimag((r).s2.c2) * creal((s).s2.c2) - \
creal((r).s3.c0) * cimag((s).s3.c0) + cimag((r).s3.c0) * creal((s).s3.c0) - \
creal((r).s3.c1) * cimag((s).s3.c1) + cimag((r).s3.c1) * creal((s).s3.c1) - \
creal((r).s3.c2) * cimag((s).s3.c2) + cimag((r).s3.c2) * creal((s).s3.c2)
/*
* r is the product of s with the complex number c
*
* Stefano Capitani <[email protected]>, June 2003
*/
#define _spinor_mul_complex(r,c,s) \
(r).s0.c0 = c * (s).s0.c0; \
(r).s0.c1 = c * (s).s0.c1; \
(r).s0.c2 = c * (s).s0.c2; \
(r).s1.c0 = c * (s).s1.c0; \
(r).s1.c1 = c * (s).s1.c1; \
(r).s1.c2 = c * (s).s1.c2; \
(r).s2.c0 = c * (s).s2.c0; \
(r).s2.c1 = c * (s).s2.c1; \
(r).s2.c2 = c * (s).s2.c2; \
(r).s3.c0 = c * (s).s3.c0; \
(r).s3.c1 = c * (s).s3.c1; \
(r).s3.c2 = c * (s).s3.c2;
/* square norm of spinor s */
#define _spinor_norm_sq(d,s) \
d = creal((s).s0.c0 * conj((s).s0.c0)) + creal((s).s0.c1 * conj((s).s0.c1)) + \
creal((s).s0.c2 * conj((s).s0.c2)) + creal((s).s1.c0 * conj((s).s1.c0)) + \
creal((s).s1.c1 * conj((s).s1.c1)) + creal((s).s1.c2 * conj((s).s1.c2)) + \
creal((s).s2.c0 * conj((s).s2.c0)) + creal((s).s2.c1 * conj((s).s2.c1)) + \
creal((s).s2.c2 * conj((s).s2.c2)) + creal((s).s3.c0 * conj((s).s3.c0)) + \
creal((s).s3.c1 * conj((s).s3.c1)) + creal((s).s3.c2 * conj((s).s3.c2))
/* gamma 0
* (r.s0) ( 0 0 + 1 0 ) (s.s0)
* (r.s1) = ( 0 0 0 + 1 ) * (s.s1)
* (r.s2) ( + 1 0 0 0 ) (s.s2)
* (r.s3) ( 0 + 1 0 0 ) (s.s3)
*/
#define _gamma0(r,s) \
(r).s0.c0 = (s).s2.c0; \
(r).s0.c1 = (s).s2.c1; \
(r).s0.c2 = (s).s2.c2; \
(r).s1.c0 = (s).s3.c0; \
(r).s1.c1 = (s).s3.c1; \
(r).s1.c2 = (s).s3.c2; \
(r).s2.c0 = (s).s0.c0; \
(r).s2.c1 = (s).s0.c1; \
(r).s2.c2 = (s).s0.c2; \
(r).s3.c0 = (s).s1.c0; \
(r).s3.c1 = (s).s1.c1; \
(r).s3.c2 = (s).s1.c2;
/* gamma 1
* (r.s0) ( 0 0 0 + i ) (s.s0)
* (r.s1) = ( 0 0 + i 0 ) * (s.s1)
* (r.s2) ( 0 -i 0 0 ) (s.s2)
* (r.s3) ( -i 0 0 0 ) (s.s3)
*/
#define _gamma1(r,s) \
(r).s0.c0 = I * (s).s3.c0; \
(r).s0.c1 = I * (s).s3.c1; \
(r).s0.c2 = I * (s).s3.c2; \
(r).s1.c0 = I * (s).s2.c0; \
(r).s1.c1 = I * (s).s2.c1; \
(r).s1.c2 = I * (s).s2.c2; \
(r).s2.c0 = -I * (s).s1.c0; \
(r).s2.c1 = -I * (s).s1.c1; \
(r).s2.c2 = -I * (s).s1.c2; \
(r).s3.c0 = -I * (s).s0.c0; \
(r).s3.c1 = -I * (s).s0.c1; \
(r).s3.c2 = -I * (s).s0.c2;
/* gamma 2
* (r.s0) ( 0 0 0 + 1 ) (s.s0)
* (r.s1) = ( 0 0 -1 0 ) * (s.s1)
* (r.s2) ( 0 -1 0 0 ) (s.s2)
* (r.s3) ( + 1 0 0 0 ) (s.s3)
*/
#define _gamma2(r,s) \
(r).s0.c0 = (s).s3.c0; \
(r).s0.c1 = (s).s3.c1; \
(r).s0.c2 = (s).s3.c2; \
(r).s1.c0 = -(s).s2.c0; \
(r).s1.c1 = -(s).s2.c1; \
(r).s1.c2 = -(s).s2.c2; \
(r).s2.c0 = -(s).s1.c0; \
(r).s2.c1 = -(s).s1.c1; \
(r).s2.c2 = -(s).s1.c2; \
(r).s3.c0 = (s).s0.c0; \
(r).s3.c1 = (s).s0.c1; \
(r).s3.c2 = (s).s0.c2;
/* gamma 3
* (r.s0) ( 0 0 + i 0 ) (s.s0)
* (r.s1) = ( 0 0 0 -i ) * (s.s1)
* (r.s2) ( -i 0 0 0 ) (s.s2)
* (r.s3) ( 0 + i 0 0 ) (s.s3)
*/
#define _gamma3(r,s) \
(r).s0.c0 = I * (s).s2.c0; \
(r).s0.c1 = I * (s).s2.c1; \
(r).s0.c2 = I * (s).s2.c2; \
(r).s1.c0 = -I * (s).s3.c0; \
(r).s1.c1 = -I * (s).s3.c1; \
(r).s1.c2 = -I * (s).s3.c2; \
(r).s2.c0 = -I * (s).s0.c0; \
(r).s2.c1 = -I * (s).s0.c1; \
(r).s2.c2 = -I * (s).s0.c2; \
(r).s3.c0 = I * (s).s1.c0; \
(r).s3.c1 = I * (s).s1.c1; \
(r).s3.c2 = I * (s).s1.c2;
/* gamma 5
* (r.s0) ( + 1 0 0 0 ) (s.s0)
* (r.s1) = ( 0 + 1 0 0 ) * (s.s1)
* (r.s2) ( 0 0 -1 0 ) (s.s2)
* (r.s3) ( 0 0 0 -1 ) (s.s3)
*/
#define _gamma5(r,s) \
(r).s0.c0 = (s).s0.c0; \
(r).s0.c1 = (s).s0.c1; \
(r).s0.c2 = (s).s0.c2; \
(r).s1.c0 = (s).s1.c0; \
(r).s1.c1 = (s).s1.c1; \
(r).s1.c2 = (s).s1.c2; \
(r).s2.c0 = -(s).s2.c0; \
(r).s2.c1 = -(s).s2.c1; \
(r).s2.c2 = -(s).s2.c2; \
(r).s3.c0 = -(s).s3.c0; \
(r).s3.c1 = -(s).s3.c1; \
(r).s3.c2 = -(s).s3.c2;
/* P_plus
* (r.s0) ( + 1 0 0 0 ) (s.s0)
* (r.s1) = ( 0 + 1 0 0 ) * (s.s1)
* (r.s2) ( 0 0 0 0 ) (s.s2)
* (r.s3) ( 0 0 0 0 ) (s.s3)
*/
#define _P_plus(r,s) \
(r).s0.c0 = (s).s0.c0; \
(r).s0.c1 = (s).s0.c1; \
(r).s0.c2 = (s).s0.c2; \
(r).s1.c0 = (s).s1.c0; \
(r).s1.c1 = (s).s1.c1; \
(r).s1.c2 = (s).s1.c2; \
(r).s2.c0 = 0.; \
(r).s2.c1 = 0.; \
(r).s2.c2 = 0.; \
(r).s3.c0 = 0.; \
(r).s3.c1 = 0.; \
(r).s3.c2 = 0.;
/* gamma 5 + ID
* (r.s0) ( + 2 0 0 0 ) (s.s0)
* (r.s1) = ( 0 + 2 0 0 ) * (s.s1)
* (r.s2) ( 0 0 0 0 ) (s.s2)
* (r.s3) ( 0 0 0 0 ) (s.s3)
*/
#define _gamma5_plus_id(r,s) \
(r).s0.c0 = 2. * (s).s0.c0; \
(r).s0.c1 = 2. * (s).s0.c1; \
(r).s0.c2 = 2. * (s).s0.c2; \
(r).s1.c0 = 2. * (s).s1.c0; \
(r).s1.c1 = 2. * (s).s1.c1; \
(r).s1.c2 = 2. * (s).s1.c2; \
(r).s2.c0 = 0.; \
(r).s2.c1 = 0.; \
(r).s2.c2 = 0.; \
(r).s3.c0 = 0.; \
(r).s3.c1 = 0.; \
(r).s3.c2 = 0.;
/* P_minus
* (r.s0) ( 0 0 0 0 ) (s.s0)
* (r.s1) = ( 0 0 0 0 ) * (s.s1)
* (r.s2) ( 0 0 1 0 ) (s.s2)
* (r.s3) ( 0 0 0 1 ) (s.s3)
*/
#define _P_minus(r,s) \
(r).s0.c0 = 0.; \
(r).s0.c1 = 0.; \
(r).s0.c2 = 0.; \
(r).s1.c0 = 0.; \
(r).s1.c1 = 0.; \
(r).s1.c2 = 0.; \
(r).s2.c0 = (s).s2.c0; \
(r).s2.c1 = (s).s2.c1; \
(r).s2.c2 = (s).s2.c2; \
(r).s3.c0 = (s).s3.c0; \
(r).s3.c1 = (s).s3.c1; \
(r).s3.c2 = (s).s3.c2;
/* gamma 5 - ID
* (r.s0) ( 0 0 0 0 ) (s.s0)
* (r.s1) = ( 0 0 0 0 ) * (s.s1)
* (r.s2) ( 0 0 -2 0 ) (s.s2)
* (r.s3) ( 0 0 0 -2 ) (s.s3)
*/
#define _gamma5_minus_id(r,s) \
(r).s0.c0 = 0.; \
(r).s0.c1 = 0.; \
(r).s0.c2 = 0.; \
(r).s1.c0 = 0.; \
(r).s1.c1 = 0.; \
(r).s1.c2 = 0.; \
(r).s2.c0 = -2. * (s).s2.c0; \
(r).s2.c1 = -2. * (s).s2.c1; \
(r).s2.c2 = -2. * (s).s2.c2; \
(r).s3.c0 = -2. * (s).s3.c0; \
(r).s3.c1 = -2. * (s).s3.c1; \
(r).s3.c2 = -2. * (s).s3.c2;
/* gamma 50
* (r.s0) ( 0 0 -1 0 ) (s.s0)
* (r.s1) = ( 0 0 0 -1 ) * (s.s1)
* (r.s2) ( + 1 0 0 0 ) (s.s2)
* (r.s3) ( 0 + 1 0 0 ) (s.s3)
*/
#define _gamma50(r,s) \
(r).s0.c0 = -(s).s2.c0; \
(r).s0.c1 = -(s).s2.c1; \
(r).s0.c2 = -(s).s2.c2; \
(r).s1.c0 = -(s).s3.c0; \
(r).s1.c1 = -(s).s3.c1; \
(r).s1.c2 = -(s).s3.c2; \
(r).s2.c0 = (s).s0.c0; \
(r).s2.c1 = (s).s0.c1; \
(r).s2.c2 = (s).s0.c2; \
(r).s3.c0 = (s).s1.c0; \
(r).s3.c1 = (s).s1.c1; \
(r).s3.c2 = (s).s1.c2;
/* gamma 51
* (r.s0) ( 0 0 0 -i ) (s.s0)
* (r.s1) = ( 0 0 -i 0 ) * (s.s1)
* (r.s2) ( 0 -i 0 0 ) (s.s2)
* (r.s3) ( -i 0 0 0 ) (s.s3)
*/
#define _gamma51(r,s) \
(r).s0.c0 = -I * (s).s3.c0; \
(r).s0.c1 = -I * (s).s3.c1; \
(r).s0.c2 = -I * (s).s3.c2; \
(r).s1.c0 = -I * (s).s2.c0; \
(r).s1.c1 = -I * (s).s2.c1; \
(r).s1.c2 = -I * (s).s2.c2; \
(r).s2.c0 = -I * (s).s1.c0; \
(r).s2.c1 = -I * (s).s1.c1; \
(r).s2.c2 = -I * (s).s1.c2; \
(r).s3.c0 = -I * (s).s0.c0; \
(r).s3.c1 = -I * (s).s0.c1; \
(r).s3.c2 = -I * (s).s0.c2
/* gamma 52
* (r.s0) ( 0 0 0 -1 ) (s.s0)
* (r.s1) = ( 0 0 + 1 0 ) * (s.s1)
* (r.s2) ( 0 -1 0 0 ) (s.s2)
* (r.s3) ( + 1 0 0 0 ) (s.s3)
*/
#define _gamma52(r,s) \
(r).s0.c0 = -(s).s3.c0; \
(r).s0.c1 = -(s).s3.c1; \
(r).s0.c2 = -(s).s3.c2; \
(r).s1.c0 = (s).s2.c0; \
(r).s1.c1 = (s).s2.c1; \
(r).s1.c2 = (s).s2.c2; \
(r).s2.c0 = -(s).s1.c0; \
(r).s2.c1 = -(s).s1.c1; \
(r).s2.c2 = -(s).s1.c2; \
(r).s3.c0 = (s).s0.c0; \
(r).s3.c1 = (s).s0.c1; \
(r).s3.c2 = (s).s0.c2
/* gamma 53
* (r.s0) ( 0 0 -i 0 ) (s.s0)
* (r.s1) = ( 0 0 0 + i ) * (s.s1)
* (r.s2) ( -i 0 0 0 ) (s.s2)
* (r.s3) ( 0 + i 0 0 ) (s.s3) (r).s3.c1 = (s).s1.c1; \
* (r).s3.c2 = (s).s1.c2;
*
*
/ * *gamma 51
* (r.c1) ( 0 0 0 -i ) (s.s0)
* (r.s1) = ( 0 0 -i 0 ) * (s.s1)
* (r.s2) ( 0 -i 0 0 ) (s.s2)
* (r.s3) ( -i 0 0 0 ) (s.s3)
*/
#define _gamma51(r,s) \
(r).s0.c0 = -I * (s).s3.c0; \
(r).s0.c1 = -I * (s).s3.c1; \
(r).s0.c2 = -I * (s).s3.c2; \
(r).s1.c0 = -I * (s).s2.c0; \
(r).s1.c1 = -I * (s).s2.c1; \
(r).s1.c2 = -I * (s).s2.c2; \
(r).s2.c0 = -I * (s).s1.c0; \
(r).s2.c1 = -I * (s).s1.c1; \
(r).s2.c2 = -I * (s).s1.c2; \
(r).s3.c0 = -I * (s).s0.c0; \
(r).s3.c1 = -I * (s).s0.c1; \
(r).s3.c2 = -I * (s).s0.c2
/* gamma 52
* (r.c1) ( 0 0 0 -1 ) (s.s0)
* (r.s1) = ( 0 0 + 1 0 ) * (s.s1)
* (r.s2) ( 0 -1 0 0 ) (s.s2)
* (r.s3) ( + 1 0 0 0 ) (s.s3)
*/
#define _gamma52(r,s) \
(r).s0.c0 = -(s).s3.c0; \
(r).s0.c1 = -(s).s3.c1; \
(r).s0.c2 = -(s).s3.c2; \
(r).s1.c0 = (s).s2.c0; \
(r).s1.c1 = (s).s2.c1; \
(r).s1.c2 = (s).s2.c2; \
(r).s2.c0 = -(s).s1.c0; \
(r).s2.c1 = -(s).s1.c1; \
(r).s2.c2 = -(s).s1.c2; \
(r).s3.c0 = (s).s0.c0; \
(r).s3.c1 = (s).s0.c1; \
(r).s3.c2 = (s).s0.c2
/* gamma 53
* (r.c1) ( 0 0 -i 0 ) (s.s0)
* (r.s1) = ( 0 0 0 + i ) * (s.s1)
* (r.s2) ( -i 0 0 0 ) (s.s2)
* (r.s3) ( 0 + i 0 0 ) (s.s3)
*/
#define _gamma53(r,s) \
(r).s0.c0 = -I * (s).s2.c0; \
(r).s0.c1 = -I * (s).s2.c1; \
(r).s0.c2 = -I * (s).s2.c2; \
(r).s1.c0 = I * (s).s3.c0; \
(r).s1.c1 = I * (s).s3.c1; \
(r).s1.c2 = I * (s).s3.c2; \
(r).s2.c0 = -I * (s).s0.c0; \
(r).s2.c1 = -I * (s).s0.c1; \
(r).s2.c2 = -I * (s).s0.c2; \
(r).s3.c0 = I * (s).s1.c0; \
(r).s3.c1 = I * (s).s1.c1; \
(r).s3.c2 = I * (s).s1.c2
#endif