equation_database.doi_10_1103_physrev_176_1700
Functions
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DOI, Simultaneous partial wave expansion in the Mandelstam variables: the group SU(3) |
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Mandelstam vectors. |
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Definition of Mandelstam variables in terms of \(S_mu\), \(T_mu\), and \(U_mu\). |
- equation_database.doi_10_1103_physrev_176_1700.equation_A3(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)[source]
Mandelstam vectors.
- Parameters:
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
- Returns:
\(S_{\mu} = p_{1 \mu} + p_{2 \mu}\), \(S_{\mu} = p_{3 \mu} + p_{4 \mu}\), \(U_{\mu} = p_{1 \mu} - p_{3 \mu}\), \(U_{\mu} = - p_{2 \mu} + p_{4 \mu}\), \(T_{\mu} = p_{1 \mu} - p_{4 \mu}\), \(T_{\mu} = - p_{2 \mu} + p_{3 \mu}\),
S_{\mu} = p_{1 \mu} + p_{2 \mu} S_{\mu} = p_{3 \mu} + p_{4 \mu} U_{\mu} = p_{1 \mu} - p_{3 \mu} U_{\mu} = - p_{2 \mu} + p_{4 \mu} T_{\mu} = p_{1 \mu} - p_{4 \mu} T_{\mu} = - p_{2 \mu} + p_{3 \mu}
<apply><eq/><ci><mml:msub><mml:mi>S</mml:mi><mml:mi>μ</mml:mi></mml:msub></ci><apply><plus/><ci><mml:msub><mml:mi>p</mml:mi><mml:mrow><mml:mi>1</mml:mi><mml:mo> </mml:mo><mml:mi>μ</mml:mi></mml:mrow></mml:msub></ci><ci><mml:msub><mml:mi>p</mml:mi><mml:mrow><mml:mi>2</mml:mi><mml:mo> </mml:mo><mml:mi>μ</mml:mi></mml:mrow></mml:msub></ci></apply></apply> <apply><eq/><ci><mml:msub><mml:mi>S</mml:mi><mml:mi>μ</mml:mi></mml:msub></ci><apply><plus/><ci><mml:msub><mml:mi>p</mml:mi><mml:mrow><mml:mi>3</mml:mi><mml:mo> </mml:mo><mml:mi>μ</mml:mi></mml:mrow></mml:msub></ci><ci><mml:msub><mml:mi>p</mml:mi><mml:mrow><mml:mi>4</mml:mi><mml:mo> </mml:mo><mml:mi>μ</mml:mi></mml:mrow></mml:msub></ci></apply></apply> <apply><eq/><ci><mml:msub><mml:mi>U</mml:mi><mml:mi>μ</mml:mi></mml:msub></ci><apply><minus/><ci><mml:msub><mml:mi>p</mml:mi><mml:mrow><mml:mi>1</mml:mi><mml:mo> </mml:mo><mml:mi>μ</mml:mi></mml:mrow></mml:msub></ci><ci><mml:msub><mml:mi>p</mml:mi><mml:mrow><mml:mi>3</mml:mi><mml:mo> </mml:mo><mml:mi>μ</mml:mi></mml:mrow></mml:msub></ci></apply></apply> <apply><eq/><ci><mml:msub><mml:mi>U</mml:mi><mml:mi>μ</mml:mi></mml:msub></ci><apply><plus/><apply><minus/><ci><mml:msub><mml:mi>p</mml:mi><mml:mrow><mml:mi>2</mml:mi><mml:mo> </mml:mo><mml:mi>μ</mml:mi></mml:mrow></mml:msub></ci></apply><ci><mml:msub><mml:mi>p</mml:mi><mml:mrow><mml:mi>4</mml:mi><mml:mo> </mml:mo><mml:mi>μ</mml:mi></mml:mrow></mml:msub></ci></apply></apply> <apply><eq/><ci><mml:msub><mml:mi>T</mml:mi><mml:mi>μ</mml:mi></mml:msub></ci><apply><minus/><ci><mml:msub><mml:mi>p</mml:mi><mml:mrow><mml:mi>1</mml:mi><mml:mo> </mml:mo><mml:mi>μ</mml:mi></mml:mrow></mml:msub></ci><ci><mml:msub><mml:mi>p</mml:mi><mml:mrow><mml:mi>4</mml:mi><mml:mo> </mml:mo><mml:mi>μ</mml:mi></mml:mrow></mml:msub></ci></apply></apply> <apply><eq/><ci><mml:msub><mml:mi>T</mml:mi><mml:mi>μ</mml:mi></mml:msub></ci><apply><plus/><apply><minus/><ci><mml:msub><mml:mi>p</mml:mi><mml:mrow><mml:mi>2</mml:mi><mml:mo> </mml:mo><mml:mi>μ</mml:mi></mml:mrow></mml:msub></ci></apply><ci><mml:msub><mml:mi>p</mml:mi><mml:mrow><mml:mi>3</mml:mi><mml:mo> </mml:mo><mml:mi>μ</mml:mi></mml:mrow></mml:msub></ci></apply></apply>
Eq(S_mu, p1_mu + p2_mu) Eq(S_mu, p3_mu + p4_mu) Eq(U_mu, p1_mu - p3_mu) Eq(U_mu, -p2_mu + p4_mu) Eq(T_mu, p1_mu - p4_mu) Eq(T_mu, -p2_mu + p3_mu)
S_mu == p1_mu + p2_mu S_mu == p3_mu + p4_mu U_mu == p1_mu - p3_mu U_mu == -p2_mu + p4_mu T_mu == p1_mu - p4_mu T_mu == -p2_mu + p3_mu
S_mu == p1_mu + p2_mu S_mu == p3_mu + p4_mu U_mu == p1_mu - p3_mu U_mu == -p2_mu + p4_mu T_mu == p1_mu - p4_mu T_mu == -p2_mu + p3_mu
(S_mu == p1_mu + p2_mu) (S_mu == p3_mu + p4_mu) (U_mu == p1_mu - p3_mu) (U_mu == -p2_mu + p4_mu) (T_mu == p1_mu - p4_mu) (T_mu == -p2_mu + p3_mu)
S_mu == p1_mu + p2_mu S_mu == p3_mu + p4_mu U_mu == p1_mu - p3_mu U_mu == -p2_mu + p4_mu T_mu == p1_mu - p4_mu T_mu == -p2_mu + p3_mu
S_mu == p1_mu + p2_mu S_mu == p3_mu + p4_mu U_mu == p1_mu - p3_mu U_mu == -p2_mu + p4_mu T_mu == p1_mu - p4_mu T_mu == -p2_mu + p3_mu
S_mu == p1_mu + p2_mu S_mu == p3_mu + p4_mu U_mu == p1_mu - p3_mu U_mu == -p2_mu + p4_mu T_mu == p1_mu - p4_mu T_mu == -p2_mu + p3_mu
S_mu == p1_mu + p2_mu S_mu == p3_mu + p4_mu U_mu == p1_mu - p3_mu U_mu == -p2_mu + p4_mu T_mu == p1_mu - p4_mu T_mu == -p2_mu + p3_mu
S_mu = p1_mu + p2_mu S_mu = p3_mu + p4_mu U_mu = p1_mu - p3_mu U_mu = -p2_mu + p4_mu T_mu = p1_mu - p4_mu T_mu = -p2_mu + p3_mu
Sₘᵤ = p₁ ₘᵤ + p₂ ₘᵤ Sₘᵤ = p₃ ₘᵤ + p₄ ₘᵤ Uₘᵤ = p₁ ₘᵤ - p₃ ₘᵤ Uₘᵤ = -p₂ ₘᵤ + p₄ ₘᵤ Tₘᵤ = p₁ ₘᵤ - p₄ ₘᵤ Tₘᵤ = -p₂ ₘᵤ + p₃ ₘᵤ
- equation_database.doi_10_1103_physrev_176_1700.equation_A4(s=s, S_mu=S_mu, t=t, T_mu=T_mu, u=u, U_mu=U_mu)[source]
Definition of Mandelstam variables in terms of \(S_mu\), \(T_mu\), and \(U_mu\).
- Parameters:
s – Mandelstam variable s
S_mu – S_mu
t – Mandelstam variable t
T_mu – T_mu
u – Mandelstam variable u
U_mu – U_mu
- Returns:
\(s = S_{\mu}^{2}\), \(t = T_{\mu}^{2}\), \(u = U_{\mu}^{2}\),
s = S_{\mu}^{2} t = T_{\mu}^{2} u = U_{\mu}^{2}
<apply><eq/><ci>s</ci><apply><power/><ci><mml:msub><mml:mi>S</mml:mi><mml:mi>μ</mml:mi></mml:msub></ci><cn>2</cn></apply></apply> <apply><eq/><ci>t</ci><apply><power/><ci><mml:msub><mml:mi>T</mml:mi><mml:mi>μ</mml:mi></mml:msub></ci><cn>2</cn></apply></apply> <apply><eq/><ci>u</ci><apply><power/><ci><mml:msub><mml:mi>U</mml:mi><mml:mi>μ</mml:mi></mml:msub></ci><cn>2</cn></apply></apply>
Eq(s, S_mu**2) Eq(t, T_mu**2) Eq(u, U_mu**2)
s == S_mu.^2 t == T_mu.^2 u == U_mu.^2
s == S_mu^2 t == T_mu^2 u == U_mu^2
(s == S_mu**2) (t == T_mu**2) (u == U_mu**2)
s == pow(S_mu, 2) t == pow(T_mu, 2) u == pow(U_mu, 2)
s == std::pow(S_mu, 2) t == std::pow(T_mu, 2) u == std::pow(U_mu, 2)
s == S_mu**2 t == T_mu**2 u == U_mu**2
s == S_mu.powi(2) t == T_mu.powi(2) u == U_mu.powi(2)
2 s = S_mu 2 t = T_mu 2 u = U_mu
2 s = Sₘᵤ 2 t = Tₘᵤ 2 u = Uₘᵤ
- equation_database.doi_10_1103_physrev_176_1700.bibtex()[source]
DOI, Simultaneous partial wave expansion in the Mandelstam variables: the group SU(3)
@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" }