FourMomentum

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`FourMomentum`

class FourMomentum

A relativistic four-momentum in (energy, px, py, pz) order.

The class provides collider observables, invariant products, rotations, and boosts while keeping the component convention explicit.

Examples

from symbolica import S, E
from symbolica.community import hepkit as hep
momentum = hep.FourMomentum(5.0, 3.0, 4.0, 0.0)
p = momentum
first = hep.FourMomentum(5.0, 0.0, 5.0, 0.0)
second = hep.FourMomentum(5.0, 5.0, 0.0, 0.0)
assert momentum.mass_squared == 0.0

Parameters

energy (float) Energy component.
px (float) Momentum component along the x axis.
py (float) Momentum component along the y axis.
pz (float) Momentum component along the z axis.

Attributes

Name	Description
`energy`	Return the energy component.
`mass`	Return the invariant mass.
`mass_squared`	Return the invariant mass squared.
`phi`	Return the azimuthal angle in radians.
`pseudorapidity`	Return the pseudorapidity of the spatial momentum.
`pt`	Return the transverse-momentum magnitude.
`px`	Return the x component of spatial momentum.
`py`	Return the y component of spatial momentum.
`pz`	Return the z component of spatial momentum.
`rapidity`	Return the longitudinal rapidity.
`spatial`	Return the spatial three-momentum.

`energy`

FourMomentum.energy: builtins.float

Return the energy component.

Examples

Using the setup in the FourMomentum class example:

assert momentum.energy == 5.0

`mass`

FourMomentum.mass: builtins.float

Return the invariant mass.

Examples

Using the setup in the FourMomentum class example:

hep.FourMomentum(5.0, 0.0, 0.0, 0.0).mass
5.0

`mass_squared`

FourMomentum.mass_squared: builtins.float

Return the invariant mass squared.

Examples

Using the setup in the FourMomentum class example:

hep.FourMomentum(5.0, 3.0, 4.0, 0.0).mass_squared
0.0

`phi`

FourMomentum.phi: builtins.float

Return the azimuthal angle in radians.

Examples

Using the setup in the FourMomentum class example:

hep.FourMomentum(1.0, 1.0, 0.0, 0.0).phi
0.0

`pseudorapidity`

FourMomentum.pseudorapidity: builtins.float

Return the pseudorapidity of the spatial momentum.

Examples

Using the setup in the FourMomentum class example:

abs(hep.FourMomentum(1.0, 1.0, 0.0, 0.0).pseudorapidity) < 1e-12
True

`pt`

FourMomentum.pt: builtins.float

Return the transverse-momentum magnitude.

Examples

Using the setup in the FourMomentum class example:

hep.FourMomentum(13.0, 3.0, 4.0, 12.0).pt
5.0

`px`

FourMomentum.px: builtins.float

Return the x component of spatial momentum.

Examples

Using the setup in the FourMomentum class example:

assert momentum.px == 3.0

`py`

FourMomentum.py: builtins.float

Return the y component of spatial momentum.

Examples

Using the setup in the FourMomentum class example:

assert momentum.py == 4.0

`pz`

FourMomentum.pz: builtins.float

Return the z component of spatial momentum.

Examples

Using the setup in the FourMomentum class example:

assert momentum.pz == 0.0

`rapidity`

FourMomentum.rapidity: builtins.float

Return the longitudinal rapidity.

Examples

Using the setup in the FourMomentum class example:

hep.FourMomentum(1.0, 1.0, 0.0, 0.0).rapidity
0.0

`spatial`

FourMomentum.spatial: ThreeMomentum

Return the spatial three-momentum.

Examples

Using the setup in the FourMomentum class example:

hep.FourMomentum(5.0, 3.0, 4.0, 0.0).spatial.pt
5.0

Methods

Name	Description
`__add__`	Add two four-momenta component by component.
`__mul__`	Scale every four-momentum component.
`__neg__`	Reverse the four-momentum flow convention.
`__new__`	Construct a four-momentum from energy and Cartesian spatial components.
`__repr__`	Return a constructor-style representation of the components.
`__rmul__`	Scale every four-momentum component from the left.
`__sub__`	Subtract another four-momentum component by component.
`_repr_latex_`	Render the momentum as a contravariant four-vector.
`_repr_pretty_`	Write the constructor-style form to an IPython pretty printer.
`components`	Return `(energy, px, py, pz)`.
`delta_phi`	Return the wrapped azimuthal separation from another momentum.
`delta_r`	Return the distance in rapidity-azimuth space.
`dot`	Return the Minkowski dot product with another four-momentum.
`flux`	Return the decay denominator `2E` or the invariant two-particle flux

`add`

FourMomentum.__add__(other: FourMomentum) -> FourMomentum

Add two four-momenta component by component.

Examples

Using the setup in the FourMomentum class example:

(first + second).energy == first.energy + second.energy
True

Parameters

other (FourMomentum) Momentum to add.

`mul`

FourMomentum.__mul__(scalar: builtins.float) -> FourMomentum

Scale every four-momentum component.

Examples

Using the setup in the FourMomentum class example:

half_momentum = momentum * 0.5

Parameters

scalar (float) Multiplicative scale factor.

`neg`

FourMomentum.__neg__() -> FourMomentum

Reverse the four-momentum flow convention.

Examples

Using the setup in the FourMomentum class example:

incoming_convention = hep.FourMomentum(5.0, 3.0, 4.0, 0.0)
outgoing_convention = -incoming_convention
assert outgoing_convention.energy == -5.0

`new`

FourMomentum.__new__(
    energy: builtins.float,
    px: builtins.float,
    py: builtins.float,
    pz: builtins.float,
) -> FourMomentum

Construct a four-momentum from energy and Cartesian spatial components.

Examples

Using the setup in the FourMomentum class example:

momentum = hep.FourMomentum(5.0, 3.0, 4.0, 0.0)

Parameters

energy (float) Temporal component.
px (float) Momentum along the x axis.
py (float) Momentum along the y axis.
pz (float) Momentum along the z axis.

`repr`

FourMomentum.__repr__() -> builtins.str

Return a constructor-style representation of the components.

Examples

Using the setup in the FourMomentum class example:

muon_momentum = hep.FourMomentum(5.0, 3.0, 4.0, 0.0)
print(f"muon four-momentum: {muon_momentum!r}")

`rmul`

FourMomentum.__rmul__(scalar: builtins.float) -> FourMomentum

Scale every four-momentum component from the left.

Examples

Using the setup in the FourMomentum class example:

half_momentum = 0.5 * momentum

Parameters

scalar (float) Multiplicative scale factor.

`sub`

FourMomentum.__sub__(other: FourMomentum) -> FourMomentum

Subtract another four-momentum component by component.

Examples

Using the setup in the FourMomentum class example:

(first - second).energy == first.energy - second.energy
True

Parameters

other (FourMomentum) Momentum to subtract.

`_repr_latex_`

FourMomentum._repr_latex_() -> builtins.str

Render the momentum as a contravariant four-vector.

Examples

Using the setup in the FourMomentum class example:

latex = momentum._repr_latex_()

`_repr_pretty_`

FourMomentum._repr_pretty_(pretty: typing.Any, cycle: builtins.bool) -> None

Write the constructor-style form to an IPython pretty printer.

Examples

Using the setup in the FourMomentum class example:

from IPython.lib.pretty import pretty
text = pretty(momentum)

Parameters

pretty (object) The IPython pretty-printer object.
cycle (bool) Whether this object is part of a recursive formatting cycle.

`components`

FourMomentum.components() -> tuple[builtins.float, builtins.float, builtins.float, builtins.float]

Return (energy, px, py, pz).

Examples

Using the setup in the FourMomentum class example:

hep.FourMomentum(5.0, 3.0, 4.0, 0.0).components()
(5.0, 3.0, 4.0, 0.0)

`delta_phi`

FourMomentum.delta_phi(other: FourMomentum) -> builtins.float

Return the wrapped azimuthal separation from another momentum.

Examples

Using the setup in the FourMomentum class example:

first.delta_phi(second)
1.5707963267948966

Parameters

other (FourMomentum) Momentum whose azimuth is compared.

`delta_r`

FourMomentum.delta_r(other: FourMomentum) -> builtins.float

Return the distance in rapidity-azimuth space.

Examples

Using the setup in the FourMomentum class example:

separation = first.delta_r(second)
same_jet = separation < 0.4

Parameters

other (FourMomentum) Momentum to compare with this one.

`dot`

FourMomentum.dot(other: FourMomentum) -> builtins.float

Return the Minkowski dot product with another four-momentum.

Examples

Using the setup in the FourMomentum class example:

momentum.dot(momentum)
0.0

Parameters

other (FourMomentum) Momentum to contract with this one.

`flux`

FourMomentum.flux(other: typing.Optional[FourMomentum] = None) -> builtins.float

Return the decay denominator 2E or the invariant two-particle flux.

Inputs must be physical, future-directed on-shell momenta. Decay rates refer to this momentum’s frame; the rest-frame result is 2M. No unit conversion, spin/color average or symmetry factor is included.

Examples

Using the setup in the FourMomentum class example:

p = hep.FourMomentum(5.0, 0.0, 0.0, 5.0)
q = hep.FourMomentum(5.0, 0.0, 0.0, -5.0)
p.flux(q)
200.0

Parameters

other (FourMomentum | None) Other incoming momentum; None selects a decay in this frame.