import sympy
from equation_database.util.doc import bib, equation
# s = sympy.symbols('s')
# """Mandelstam variable s"""
#
# t = sympy.symbols('t')
# """Mandelstam variable t"""
#
# u = sympy.symbols('u')
# """Mandelstam variable u"""
#
# p1_mu = sympy.symbols('p1_mu')
# p2_mu = sympy.symbols('p2_mu')
# p3_mu = sympy.symbols('p3_mu')
# p4_mu = sympy.symbols('p4_mu')
#
# S_mu = sympy.symbols('S_mu')
# T_mu = sympy.symbols('T_mu')
# U_mu = sympy.symbols('U_mu')
[docs]
@equation()
def equation_A3(
S_mu=sympy.Symbol("S_mu"),
U_mu=sympy.Symbol("U_mu"),
T_mu=sympy.Symbol("T_mu"),
p1_mu=sympy.Symbol("p1_mu"),
p2_mu=sympy.Symbol("p2_mu"),
p3_mu=sympy.Symbol("p3_mu"),
p4_mu=sympy.Symbol("p4_mu"),
):
"""
Mandelstam vectors.
Args:
S_mu: S_mu
U_mu: U_mu
T_mu: T_mu
p1_mu: p1_mu
p2_mu: p2_mu
p3_mu: p3_mu
p4_mu: p4_mu
"""
return (
sympy.Eq(S_mu, (p1_mu + p2_mu)),
sympy.Eq(S_mu, (p3_mu + p4_mu)),
sympy.Eq(U_mu, (p1_mu - p3_mu)),
sympy.Eq(U_mu, (p4_mu - p2_mu)),
sympy.Eq(T_mu, (p1_mu - p4_mu)),
sympy.Eq(T_mu, (p3_mu - p2_mu)),
)
[docs]
@equation()
def equation_A4(
s=sympy.Symbol("s"),
S_mu=sympy.Symbol("S_mu"),
t=sympy.Symbol("t"),
T_mu=sympy.Symbol("T_mu"),
u=sympy.Symbol("u"),
U_mu=sympy.Symbol("U_mu"),
):
"""
Definition of Mandelstam variables in terms of $S_mu$, $T_mu$, and $U_mu$.
Args:
s: Mandelstam variable s
S_mu: S_mu
t: Mandelstam variable t
T_mu: T_mu
u: Mandelstam variable u
U_mu: U_mu
"""
return sympy.Eq(s, S_mu**2), sympy.Eq(t, T_mu**2), sympy.Eq(u, U_mu**2)
[docs]
@bib()
def bibtex():
bibtex: str = r"""
@article{Balachandran:1968rj,
author = "Balachandran, A. P. and Nuyts, J. and Meggs, W. J. and Ramond, Pierre",
title = "{Simultaneous partial wave expansion in the Mandelstam variables: the group SU(3)}",
doi = "10.1103/PhysRev.176.1700",
journal = "Phys. Rev.",
volume = "176",
pages = "1700",
year = "1968"
}
"""
return bibtex