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use nalgebra::Vector3;
use ndarray::{array, Array1, Array2};
use std::ops::{Add, Sub};
#[derive(Debug, Clone, PartialEq, Copy)]
pub struct FourMomentum {
pub e: f64,
pub px: f64,
pub py: f64,
pub pz: f64,
}
impl FourMomentum {
//! A four-momentum structure with helpful methods for boosts.
//!
//! This is the basic structure of a Lorentz four-vector
//! of the form $`(E, \overrightarrow{p})`$ where $`E`$ is the energy and $`\overrightarrow{p}`$ is the
//! momentum.
//!
//! # Examples
//! ```
//! use rustitude::prelude::*;
//!
//! let vec_a = FourMomentum::new(1.3, 0.2, 0.3, 0.1);
//! let vec_b = FourMomentum::new(4.2, 0.5, 0.4, 0.5);
//! ```
pub fn new(e: f64, px: f64, py: f64, pz: f64) -> Self {
//! Create a new [`FourMomentum`] from energy and momentum components.
//!
//! Components are listed in the order $` (E, p_x, p_y, p_z) `$
Self { e, px, py, pz }
}
pub fn to_array(&self) -> Array1<f64> {
//! Turns a [`FourMomentum`] into a [`ndarray::Array1<f64>`]
//!
//! # Examples
//! ```
//! use rustitude::prelude::*;
//! use ndarray::array;
//!
//! let vec_a = FourMomentum::new(20.0, 1.0, 0.2, -0.1);
//! assert_eq!(vec_a.to_array(), array![20.0, 1.0, 0.2, -0.1]);
//! ```
array![self.e, self.px, self.py, self.pz]
}
pub fn momentum(&self) -> Vector3<f64> {
//! Extract the 3-momentum as a [`nalgebra::Vector3<f64>`]
//!
//! # Examples
//! ```
//! use rustitude::prelude::*;
//! use nalgebra::Vector3;
//!
//! let vec_a = FourMomentum::new(20.0, 1.0, 0.2, -0.1);
//! assert_eq!(vec_a.momentum(), Vector3::new(1.0, 0.2, -0.1));
//! ```
Vector3::new(self.px, self.py, self.pz)
}
pub fn m2(&self) -> f64 {
//! Calculate the invariant $ m^2 $ for this [`FourMomentum`] instance.
//!
//! Calculates $` m^2 = E^2 - \overrightarrow{p}^2 `$
//!
//! # Examples
//! ```
//! use rustitude::prelude::*;
//!
//! let vec_a = FourMomentum::new(20.0, 1.0, 0.2, -0.1);
//! //assert_eq!(vec_a.m2(), 20.0 * 20.0 - (1.0 * 1.0 + 0.0 * 0.2 + (-0.1) * (-0.1)));
//!
//! ```
self.e.powi(2) - self.px.powi(2) - self.py.powi(2) - self.pz.powi(2)
}
pub fn m(&self) -> f64 {
//! Calculate the invariant $ m $ for this [`FourMomentum`] instance.
//!
//! Calculates $` m = \sqrt{E^2 - \overrightarrow{p}^2} `$
//!
//! # See Also:
//!
//! [`FourMomentum::m2`]
self.m2().sqrt()
}
pub fn beta3(&self) -> Vector3<f64> {
//! Construct the 3-vector $\overrightarrow{\beta}$ where
//!
//! $` \overrightarrow{\beta} = \frac{\overrightarrow{p}}{E} `$
self.momentum() / self.e
}
pub fn boost_matrix(&self) -> Array2<f64> {
//! Construct the Lorentz boost matrix $`\mathbf{\Lambda}`$ where
//!
//! ```math
//! \mathbf{\Lambda} = \begin{pmatrix}
//! \gamma & -\gamma \beta_x & -\gamma \beta_y & -\gamma \beta_z \\
//! -\gamma \beta_x & 1 + (\gamma - 1) \frac{\beta_x^2}{\overrightarrow{\beta}^2} & (\gamma - 1) \frac{\beta_x \beta_y}{\overrightarrow{\beta}^2} & (\gamma - 1) \frac{\beta_x \beta_z}{\overrightarrow{\beta}^2} \\
//! -\gamma \beta_y & (\gamma - 1) \frac{\beta_y \beta_x}{\overrightarrow{\beta}^2} & 1 + (\gamma - 1) \frac{\beta_y^2}{\overrightarrow{\beta}^2} & (\gamma - 1) \frac{\beta_y \beta_z}{\overrightarrow{\beta}^2} \\
//! -\gamma \beta_z & (\gamma - 1) \frac{\beta_z \beta_x}{\overrightarrow{\beta}^2} & (\gamma - 1) \frac{\beta_z \beta_y}{\overrightarrow{\beta}^2} & 1 + (\gamma - 1) \frac{\beta_z^2}{\overrightarrow{\beta}^2}
//! \end{pmatrix}
//! ```
//! where
//! $`\overrightarrow{\beta} = \frac{\overrightarrow{p}}{E}`$ and $`\gamma = \frac{1}{\sqrt{1 - \overrightarrow{\beta}^2}}`$.
let b = self.beta3();
let b2 = b.dot(&b);
let g = 1.0 / (1.0 - b2).sqrt();
let out = array![
[g, -g * b[0], -g * b[1], -g * b[2]],
[
-g * b[0],
1.0 + (g - 1.0) * b[0] * b[0] / b2,
(g - 1.0) * b[0] * b[1] / b2,
(g - 1.0) * b[0] * b[2] / b2
],
[
-g * b[1],
(g - 1.0) * b[1] * b[0] / b2,
1.0 + (g - 1.0) * b[1] * b[1] / b2,
(g - 1.0) * b[1] * b[2] / b2
],
[
-g * b[2],
(g - 1.0) * b[2] * b[0] / b2,
(g - 1.0) * b[2] * b[1] / b2,
1.0 + (g - 1.0) * b[2] * b[2] / b2
]
];
out
}
pub fn boost_along(&self, other: &Self) -> Self {
//! Boosts an instance of [`FourMomentum`] along the $`\overrightarrow{\beta}`$
//! vector of another [`FourMomentum`].
//!
//! Calculates $`\mathbf{\Lambda} \cdot \mathbf{x}`$
//!
//! # Examples
//! ```
//! #[macro_use]
//! use approx::*;
//!
//! use rustitude::prelude::*;
//!
//! let vec_a = FourMomentum::new(20.0, 1.0, -3.2, 4.0);
//! let vec_a_COM = vec_a.boost_along(&vec_a);
//! assert_abs_diff_eq!(vec_a_COM.px, 0.0, epsilon = 1e-15);
//! assert_abs_diff_eq!(vec_a_COM.py, 0.0, epsilon = 1e-15);
//! assert_abs_diff_eq!(vec_a_COM.pz, 0.0, epsilon = 1e-15);
//! ```
let m_boost = other.boost_matrix();
m_boost.dot(&self.to_array()).into()
}
}
impl From<FourMomentum> for Array1<f64> {
fn from(val: FourMomentum) -> Self {
array![val.e, val.px, val.py, val.pz]
}
}
impl From<Array1<f64>> for FourMomentum {
fn from(value: Array1<f64>) -> Self {
Self {
e: value[0],
px: value[1],
py: value[2],
pz: value[3],
}
}
}
impl From<&Array1<f64>> for FourMomentum {
fn from(value: &Array1<f64>) -> Self {
Self {
e: value[0],
px: value[1],
py: value[2],
pz: value[3],
}
}
}
impl From<Vec<f64>> for FourMomentum {
fn from(value: Vec<f64>) -> Self {
Self {
e: value[0],
px: value[1],
py: value[2],
pz: value[3],
}
}
}
impl From<&Vec<f64>> for FourMomentum {
fn from(value: &Vec<f64>) -> Self {
Self {
e: value[0],
px: value[1],
py: value[2],
pz: value[3],
}
}
}
impl Add for FourMomentum {
type Output = FourMomentum;
fn add(self, rhs: Self) -> Self::Output {
Self {
e: self.e + rhs.e,
px: self.px + rhs.px,
py: self.py + rhs.py,
pz: self.pz + rhs.pz,
}
}
}
impl<'a, 'b> Add<&'b FourMomentum> for &'a FourMomentum {
type Output = FourMomentum;
fn add(self, rhs: &'b FourMomentum) -> Self::Output {
FourMomentum {
e: self.e + rhs.e,
px: self.px + rhs.px,
py: self.py + rhs.py,
pz: self.pz + rhs.pz,
}
}
}
impl Sub for FourMomentum {
type Output = FourMomentum;
fn sub(self, rhs: Self) -> Self::Output {
Self {
e: self.e - rhs.e,
px: self.px - rhs.px,
py: self.py - rhs.py,
pz: self.pz - rhs.pz,
}
}
}
impl<'a, 'b> Sub<&'b FourMomentum> for &'a FourMomentum {
type Output = FourMomentum;
fn sub(self, rhs: &'b FourMomentum) -> Self::Output {
FourMomentum {
e: self.e - rhs.e,
px: self.px - rhs.px,
py: self.py - rhs.py,
pz: self.pz - rhs.pz,
}
}
}
impl Default for FourMomentum {
fn default() -> Self {
Self {
e: 0.0,
px: 0.0,
py: 0.0,
pz: 0.0,
}
}
}
impl<'a> std::iter::Sum<&'a FourMomentum> for FourMomentum {
fn sum<I: Iterator<Item = &'a FourMomentum>>(iter: I) -> Self {
iter.fold(FourMomentum::default(), |a, b| a + b.clone())
}
}