HepLib
  • About HepLib
  • Installation
  • Usage in C++
  • Objects in C++
  • Examples in C++
  • Usage in Python
  • Objects in Python
  • Examples in Python
  • Utils in HepLib
  • Try & Run online
  • Release @GitHub
  • Document @Doxygen
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Objects in C++

Object

Example

Description

Symbol

Symbol("s")

a real variable s.

Index

Index("mu",Type::VD)

a Lorentz index mu with dimension D.

Index("mu",Type::CA)

a color index a with dimension NA.

Index("mu",Type::CF)

a color index i with dimension NF.

Vector

Vector("p")

a vector/momentum p.

Pair

Pair(mu,nu)

Pair(p,mu)

Pair(p,q)

SUNT

SUNT(a,i,j)

SUNT(lst{a,b,c},i,j)

SUNF

SUNF(a,b,c)

SUNF4

SUNF4(a,b,c,d)

Eps

Eps(mu1,mu2,mu3,mu4)

Eps(p1,p2,mu1,mu2)

Eps(p1,p2,p3,p4)

DGamma

DGamma(mu,l)

DGamma(p,l)

DGamma(1/5/6/7,l)

SP

SP(mu.nu)

SP(p+s*q,mu)

SP(2*p+q,p+s*q)

GAS

GAS(mu)

GAS(3*p+s*q)

GAS(1/5/6/7)

LC

LC(p,mu,p+s*q,k)

TR

TR(expr)

a wrapper for the Dirac trace of expression expr.

TTR

TTR(lst{a,b,c,d})

form

form(expr)

evaluate the expression expr using FORM program.

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Last updated 4 years ago

a Kronecker delta with Index mu and nu.

a Vector p with Lorentz Index mu, , p.mu.

a scalar product between Vector p and q.

a T-matrix element for SU(N) group.

a matrix element of a product of T, .

a structure constant of SU(N) group.

a contract of two SUNF, .

a Levi-Civita tensor .

a partially contracted Levi-Civita tensor .

a fully contracted Levi-Civita tensor .

a Dirac- matrix for a fermion line l.

a Dirac slash for a fermion line l.

a unit matrix, , , for a fermion line l.

evaluated to .

evaluated to .

evaluated to .

evaluated to .

evaluated to .

evaluated to a unit matrix, , , , respectively.

evaluated to .

a wraaper for the SU(N) trace of .

δμν\delta_{\mu\nu}δμν​
pμp^\mupμ
p⋅qp\cdot qp⋅q
TijaT^a_{ij}Tija​
(TaTbTc)ij(T^aT^bT^c)_{ij}(TaTbTc)ij​
fabcf^{abc}fabc
fabefecdf^{abe} f^{ecd}fabefecd
εμ1μ2μ3μ4\varepsilon_{\mu_1\mu_2\mu_3\mu_4}εμ1​μ2​μ3​μ4​​
εp1p2μ1μ2\varepsilon_{p_1p_2\mu_1\mu_2}εp1​p2​μ1​μ2​​
εp1p2p3p4\varepsilon_{p_1p_2p_3p_4}εp1​p2​p3​p4​​
γ\gammaγ
γμ\gamma_\muγμ​
p ⁣ ⁣ ⁣/=pμγνp\!\!\!/=p^\mu\gamma_\nup/=pμγν​
γ5\gamma_5γ5​
γ6\gamma_6γ6​
γ7\gamma_7γ7​
δμν\delta_{\mu\nu}δμν​
pμ+sqμp^\mu+sq^\mupμ+sqμ
2p2+(2s+1)p⋅q+sq22p^2+(2s+1)p\cdot q+sq^22p2+(2s+1)p⋅q+sq2
γμ\gamma_\muγμ​
3p ⁣ ⁣ ⁣/+sq ⁣ ⁣ ⁣/3p\!\!\!/+sq\!\!\!/3p/+sq/
γ5\gamma_5γ5​
γ6\gamma_6γ6​
γ7\gamma_7γ7​
sεkphμs\varepsilon_{kph\mu}sεkphμ​
TaTbTcTdT^aT^bT^cT^dTaTbTcTd