Lorentz Vector

Interface registry

QEDbase.register_LorentzVectorLike — Function

register_LorentzVectorLike(T)

Function to register a custom type as a LorentzVectorLike.

Ensure the passed custom type has implemented at least the function getT, getX, getY, getZ and enables getter functions of the lorentz vector library for the given type. If additionally the functions setT!, setX!, setY!, setZ! are implemened for the passed custom type, also the setter functions of the Lorentz vector interface are enabled.

Built-in Lorentz vector types

QEDbase.AbstractLorentzVector — Type

abstract type AbstractLorentzVector{T} <: StaticArraysCore.FieldVector{4, T}

Abstract type to model generic Lorentz vectors, i.e. elements of a minkowski-like space, where the component space is arbitray.

QEDbase.AbstractFourMomentum — Type

AbstractFourMomentum{T_ELEM} where {T_ELEM<:Real}

Abstract base type for four-momentas, representing one energy and three spacial components.

Also see: QEDcore.SFourMomentum

Accessor functions

QEDbase.minkowski_dot — Function

minkowski_dot(v1,v2)

Return the Minkowski dot product of two LorentzVectorLike.

Example

If (t1,x1,y1,z1) and (t2,x2,y2,z2) are two LorentzVectorLike, this is equivalent to

t1*t2 - (x1*x2 + y1*y2 + z1*z2)

Note

We use the mostly minus metric.

QEDbase.mdot — Function

Function alias for minkowski_dot.

QEDbase.getT — Function

getT(lv)

Return the 0-component of a given LorentzVectorLike.

Example

If (t,x,y,z) is a LorentzVectorLike, this is equivalent to t.

QEDbase.getX — Function

getX(lv)

Return the 1-component of a given LorentzVectorLike.

Example

If (t,x,y,z) is a LorentzVectorLike, this is equivalent to x.

QEDbase.getY — Function

getY(lv)

Return the 2-component of a given LorentzVectorLike.

Example

If (t,x,y,z) is a LorentzVectorLike, this is equivalent to y.

QEDbase.getZ — Function

getZ(lv)

Return the 3-component of a given LorentzVectorLike.

Example

If (t,x,y,z) is a LorentzVectorLike, this is equivalent to z.

QEDbase.getMagnitude2 — Function

getMagnitude2(lv)

Return the square of the magnitude of a given LorentzVectorLike, i.e. the sum of the squared spatial components.

Example

If (t,x,y,z) is a LorentzVectorLike, this is equivalent to x^2+ y^2 + z^2.

Warning

This function differs from a similar function for the TLorentzVector used in the famous ROOT library.

QEDbase.getMag2 — Function

Functiom alias for getMagnitude2.

QEDbase.getMagnitude — Function

getMagnitude(lv)

Return the magnitude of a given LorentzVectorLike, i.e. the euklidian norm spatial components.

Example

If (t,x,y,z) is a LorentzVectorLike, this is equivalent to sqrt(x^2 + y^2 + z^2).

Warning

This function differs from a similar function for the TLorentzVector used in the famous ROOT library.

QEDbase.getMag — Function

Functiom alias for getMagnitude.

QEDbase.getInvariantMass2 — Function

getInvariantMass2(lv)

Return the squared invariant mass of a given LorentzVectorLike, i.e. the minkowski dot with itself.

Example

If (t,x,y,z) is a LorentzVectorLike, this is equivalent to t^2 - (x^2 + y^2 + z^2).

QEDbase.getMass2 — Function

Function alias for getInvariantMass2

QEDbase.getInvariantMass — Function

getInvariantMass(lv)

Return the the invariant mass of a given LorentzVectorLike, i.e. the square root of the minkowski dot with itself.

Example

If (t,x,y,z) is a LorentzVectorLike, this is equivalent to sqrt(t^2 - (x^2 + y^2 + z^2)).

Note

If the squared invariant mass m2 is negative, -sqrt(-m2) is returned.

QEDbase.getMass — Function

Function alias for getInvariantMass.

QEDbase.getE — Function

getE(lv)

Return the energy component of a given LorentzVectorLike, i.e. its 0-component.

Example

If (E,px,py,pz) is a LorentzVectorLike, this is equivalent to E.

QEDbase.getEnergy — Function

Function alias for getE.

QEDbase.getPx — Function

getPx(lv)

Return the $p_x$ component of a given LorentzVectorLike, i.e. its 1-component.

Example

If (E,px,py,pz) is a LorentzVectorLike, this is equivalent to px.

QEDbase.getPy — Function

getPy(lv)

Return the $p_y$ component of a given LorentzVectorLike, i.e. its 2-component.

Example

If (E,px,py,pz) is a LorentzVectorLike, this is equivalent to py.

QEDbase.getPz — Function

getPz(lv)

Return the $p_z$ component of a given LorentzVectorLike, i.e. its 3-component.

Example

If (E,px,py,pz) is a LorentzVectorLike, this is equivalent to pz.

QEDbase.getBeta — Function

getBeta(lv)

Return magnitude of the beta vector for a given LorentzVectorLike, i.e. the magnitude of the LorentzVectorLike divided by its 0-component.

Example

If (E,px,py,pz) is a LorentzVectorLike, this is equivalent to sqrt(px^2 + py^2 + pz^2)/E.

QEDbase.getGamma — Function

getGamma(lv)

Return the relativistic gamma factor for a given LorentzVectorLike, i.e. the inverse square root of one minus the beta vector squared.

Example

If (E,px,py,pz) is a LorentzVectorLike with beta vector β, this is equivalent to 1/sqrt(1- β^2).

QEDbase.getTransverseMomentum2 — Function

getTransverseMomentum2(lv)

Return the squared transverse momentum for a given LorentzVectorLike, i.e. the sum of its squared 1- and 2-component.

Example

If (E,px,py,pz) is a LorentzVectorLike, this is equivalent to px^2 + py^2.

Note

The transverse components are defined w.r.t. to the 3-axis.

QEDbase.getPt2 — Function

Function alias for getTransverseMomentum2.

QEDbase.getPerp2 — Function

Function alias for getTransverseMomentum2.

QEDbase.getTransverseMomentum — Function

getTransverseMomentum(lv)

Return the transverse momentum for a given LorentzVectorLike, i.e. the magnitude of its transverse components.

Example

If (E,px,py,pz) is a LorentzVectorLike, this is equivalent to sqrt(px^2 + py^2).

Note

The transverse components are defined w.r.t. to the 3-axis.

QEDbase.getPt — Function

Function alias for getTransverseMomentum.

QEDbase.getPerp — Function

Function alias for getTransverseMomentum.

QEDbase.getTransverseMass2 — Function

getTransverseMass2(lv)

Return the squared transverse mass for a given LorentzVectorLike, i.e. the difference of its squared 0- and 3-component.

Example

If (E,px,py,pz) is a LorentzVectorLike, this is equivalent to E^2 - pz^2.

Note

The transverse components are defined w.r.t. to the 3-axis.

QEDbase.getMt2 — Function

Function alias for getTransverseMass2

QEDbase.getTransverseMass — Function

getTransverseMass(lv)

Return the transverse momentum for a given LorentzVectorLike, i.e. the square root of its squared transverse mass.

Example

If (E,px,py,pz) is a LorentzVectorLike, this is equivalent to sqrt(E^2 - pz^2).

Note

The transverse components are defined w.r.t. to the 3-axis.

Note

If the squared transverse mass mT2 is negative, -sqrt(-mT2) is returned.

QEDbase.getMt — Function

Function alias for getTransverseMass

QEDbase.getRapidity — Function

getRapidity(lv)

Return the rapidity for a given LorentzVectorLike.

Example

If (E,px,py,pz) is a LorentzVectorLike, this is equivalent to 0.5*log((E+pz)/(E-pz)).

Note

The transverse components are defined w.r.t. to the 3-axis.

QEDbase.getRho2 — Function

Function alias for getMagnitude2

QEDbase.getRho — Function

Function alias for getMagnitude

QEDbase.getTheta — Function

getTheta(lv)

Return the theta angle for a given LorentzVectorLike, i.e. the polar angle of its spatial components in spherical coordinates.

Example

If (E,px,py,pz) is a LorentzVectorLike with magnitude rho, this is equivalent to arccos(pz/rho), which is also equivalent to arctan(sqrt(px^2+py^2)/pz).

Note

The spherical coordinates are defined w.r.t. to the 3-axis.

QEDbase.getCosTheta — Function

getCosTheta(lv)

Return the cosine of the theta angle for a given LorentzVectorLike.

Note

This is an equivalent but faster version of cos(getTheta(lv)); see getTheta.

QEDbase.getPhi — Function

getPhi(lv)

Return the phi angle for a given LorentzVectorLike, i.e. the azimuthal angle of its spatial components in spherical coordinates.

Example

If (E,px,py,pz) is a LorentzVectorLike, this is equivalent to atan(py,px).

Note

The spherical coordinates are defined w.r.t. to the 3-axis.

QEDbase.getCosPhi — Function

getCosPhi(lv)

Return the cosine of the phi angle for a given LorentzVectorLike.

Note

This is an equivalent but faster version of cos(getPhi(lv)); see getPhi.

QEDbase.getSinPhi — Function

getSinPhi(lv)

Return the sine of the phi angle for a given LorentzVectorLike.

Note

This is an equivalent but faster version of sin(getPhi(lv)); see getPhi.

QEDbase.getPlus — Function

getPlus(lv)

Return the plus component for a given LorentzVectorLike in light-cone coordinates.

Example

If (E,px,py,pz) is a LorentzVectorLike, this is equivalent to (E+pz)/2.

Note

The light-cone coordinates are defined w.r.t. to the 3-axis.

Warning

The definition p^+ := (E + p_z)/2 differs from the usual definition of light-cone coordinates in general relativity.

QEDbase.getMinus — Function

getMinus(lv)

Return the minus component for a given LorentzVectorLike in light-cone coordinates.

Example

If (E,px,py,pz) is a LorentzVectorLike, this is equivalent to (E-pz)/2.

Note

The light-cone coordinates are defined w.r.t. to the 3-axis.

Warning

The definition p^- := (E - p_z)/2 differs from the usual definition of light-cone coordinates in general relativity.

Setter functions

QEDbase.setE! — Function

setE!(lv,value)

Sets the energy component of a given LorentzVectorLike to a given value.

Note

The value set with setE! is then returned by getE.

QEDbase.setEnergy! — Function

Function alias for setE!.

QEDbase.setPx! — Function

setPx!(lv,value)

Sets the 1-component of a given LorentzVectorLike to a given value.

Note

The value set with setPx! is then returned by getPx.

QEDbase.setPy! — Function

setPy!(lv,value)

Sets the 2-component of a given LorentzVectorLike to a given value.

Note

The value set with setPy! is then returned by getPy.

QEDbase.setPz! — Function

setPz!(lv,value)

Sets the 3-component of a given LorentzVectorLike to a given value.

Note

The value set with setPz! is then returned by getPz.

QEDbase.setTheta! — Function

setTheta!(lv,value)

Sets the theta angle of a LorentzVectorLike to a given value.

Note

The value set with setTheta! is then returned by getTheta. Since the theta angle is computed on the call of getTheta, the setter setTheta! changes several components of the given LorentzVectorLike.

QEDbase.setCosTheta! — Function

setCosTheta!(lv,value)

Sets the cosine of the theta angle of a LorentzVectorLike to a given value.

Note

The value set with setCosTheta! is then returned by getCosTheta. Since the cosine of the theta angle is computed on the call of getCosTheta, the setter setCosTheta! changes several components of the given LorentzVectorLike.

QEDbase.setRho! — Function

setRho!(lv,value)

Sets the magnitude of a LorentzVectorLike to a given value.

Note

The value set with setRho! is then returned by getRho. Since the magnitude is computed on the call of getRho, the setter setRho! changes several components of the given LorentzVectorLike.

QEDbase.setPhi! — Function

setPhi!(lv,value)

Sets the phi angle of a LorentzVectorLike to a given value.

Note

The value set with setPhi! is then returned by getPhi. Since the phi angle is computed on the call of getPhi, the setter setPhi! changes several components of the given LorentzVectorLike.

QEDbase.setPlus! — Function

setPlus!(lv,value)

Sets the plus component of a LorentzVectorLike to a given value.

Note

The value set with setPlus! is then returned by getPlus. Since the plus component is computed on the call of getPlus, the setter setPlus! changes several components of the given LorentzVectorLike.

QEDbase.setMinus! — Function

setMinus!(lv,value)

Sets the minus component of a LorentzVectorLike to a given value.

Note

The value set with setMinus! is then returned by getMinus. Since the minus component is computed on the call of getMinus, the setter setMinus! changes several components of the given LorentzVectorLike.

QEDbase.setTransverseMomentum! — Function

setTransverseMomentum!(lv,value)

Sets the transverse momentum of a LorentzVectorLike to a given value.

Note

The value set with setTransverseMomentum! is then returned by getTransverseMomentum. Since the transverse momentum is computed on the call of getTransverseMomentum, the setter setTransverseMomentum! changes several components of the given LorentzVectorLike.

QEDbase.setPerp! — Function

Function alias for setTransverseMomentum!.

QEDbase.setPt! — Function

Function alias for setTransverseMomentum!.

QEDbase.setTransverseMass! — Function

setTransverseMass!(lv,value)

Sets the transverse mass of a LorentzVectorLike to a given value.

Note

The value set with setTransverseMass! is then returned by getTransverseMass. Since the transverse mass is computed on the call of getTransverseMass, the setter setTransverseMass! changes several components of the given LorentzVectorLike.

QEDbase.setMt! — Function

Function alias for setTransverseMass!.

QEDbase.setRapidity! — Function

setRapidity!(lv,value)

Sets the rapidity of a LorentzVectorLike to a given value.

Note

The value set with setRapidity! is then returned by getRapidity. Since the rapidity is computed on the call of setRapidity, the setter setRapidity! changes several components of the given LorentzVectorLike.

Utilities

QEDbase.isonshell — Function

isonshell(mom, mass)

On-shell check of a given four-momentum mom w.r.t. a given mass mass.

Precision

For AbstractFourMomentum, the element type defaults to Float64, limiting the precision of comparisons between elements. The current implementation has been tested within the boundaries for energy scales E with 1e-9 <= E <= 1e5. In those bounds, the mass error, which is correctly detected as off-shell, is 1e-4 times the mean value of the components, but has at most the value 0.01, e.g. at the high energy end. The energy scales correspond to 0.5 meV for the lower bound and 50 GeV for the upper bound.

QEDbase.assert_onshell — Function

assert_onshell(mom, mass)

Assertion if a FourMomentum mom is on-shell w.r.t a given mass mass.

See also

The precision of this functions is explained in isonshell.

QEDbase.AbstractCoordinateTransformation — Type

AbstractCoordinateTransformation

Abstract base type for coordinate transformations supposed to be acting on four-momenta. Every subtype of trafo::AbstractCoordinateTransformation should implement the following interface functions:

QEDbase._transform(trafo,p): transforms p
Base.inv(trafo): returns the inverted transform

Example

Implementing the interface by defining the interface functions:

julia> using QEDbase

julia> struct TestTrafo{T} <: AbstractCoordinateTransformation
           a::T
       end

julia> QEDbase._transform(trafo::TestTrafo,p) = trafo.a*p

julia> Base.inv(trafo::TestTrafo) = TestTrafo(inv(trafo.a))

The TestTrafo can then be used to transform four-momenta:

julia> trafo = TestTrafo(2.0)
TestTrafo{Float64}(2.0)

julia> p = SFourMomentum(4,3,2,1)
4-element SFourMomentum{Float64} with indices SOneTo(4):
 4.0
 3.0
 2.0
 1.0

julia> trafo(p) # multiply every component with 2.0
4-element SFourMomentum{Float64} with indices SOneTo(4):
 8.0
 6.0
 4.0
 2.0

julia> inv(trafo)(p) # divide every component by 2.0
4-element SFourMomentum{Float64} with indices SOneTo(4):
 2.0
 1.5
 1.0
 0.5